Investments & Portfolios

Initial Construction and Rebalancing of the Portfolio continued again

Rebalancing VUG position - You bought VUG in the prior period at $66.86 and will sell 13,973 shares at the current price of $73.55 - You will have a gain of ($73.55-$66.86)*13973 = $93479 - Record this profit Rebalancing AGG position - You need to buy 11,142 shares of AGG at $89.78/share - That means you will have 100,241 shares of AGG at $99.76/share - and 11,142 shares of AGG at $89.78/share - Keep both pieces of information at hand as it they probably be useful in the future

Determining Style

Style Grid: - Firm size - Value-growth characteristics Style Analysis: - Constrained least squares (wont go into this) - Fama French

Behavioral Finance

Suggests that various psychological traits influence investor pricing of securities Modern Portfolio Theory (MPT) assumes investors are rational, risk averse, and consider investment decisions in a portfolio context Behavioral Finance assumes investors are irrational, loss averse, and separate investment decisions The framing effect has significant impact on investment decisions The investment options are perceived differently by the investors based on whether is option presents more gains or more losses The ultimate outcome of two choices may be the same, but the decision will depend upon which option is framed to present more positive outcome

Swap Markets

Swaps are *not standardized* contracts *Swap dealers* (usually financial institutions) keep markets liquid by matching counterparties or by taking positions themselves The *International Swaps and Derivatives Association (ISDA)* is an association among 56 countries that sets codes of standards for swap documentation - these are not exchange traded items, they're all OTCs (one-offs)

Systematic vs. Unsystematic Risk

Systematic risk is not diversifiable - Systematic Risk: Risk of an overall movement in the market - Nondiversifiable = systematic = market Unsystematic risk is diversifiable - Unsystematic risk - risk of an event that is unique to the asset or a small group of assets - Diversifiable = unsystematic = unique You may want to diversify some of your risk away by going into another sector

Minimum Variance Portfolio

The minimum variance portfolio is the first portfolio on the frontier that satisfies Markowitz condition: - No other portfolio exists with a higher expected return but with the same standard deviation The formula to compute weights for the first minimum variance portfolio for 2 assets is:

(2) Active Management Strategies: Valuation Analysis

The portfolio manager attempts to select bonds based on their intrinsic value

Options Continued: Price

The price at which you agree to buy the underlying security via the option is called the "strike price," and the fee you pay for buying that option contract is called the "premium" (someone is on the other side saying they think you are wrong) When determining the strike price, you are betting that the asset (typically a stock) will go up or down in price The price you are paying for that bet is the premium, which is a percentage of the value of that asset

Forwards and Futures: Forward Contract

a non-standardized agreement to buy or sell an asset in the future, with the terms of the deal set when the contract is created

Swaps: Currency Swap

a periodic exchange of one currency for another between the parties - usually associated with borrowing money - The exchanges can be at a fixed or a variable rate of interest as negotiated in the contract, but the exchanges occur at a known currency exchange rate - Used to hedge exchange rate risk from mismatched currencies of assets and liabilities

Options: Put option

a put option is a contract that gives the investor the right to sell a certain amount of shares (again, typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time (allows you to hedge on a downward movement in prices) Just like call options, a put option allows the trader the right (but not obligation) to sell a security by the contract's expiration date Just like call options, the price at which you agree to sell the stock is called the strike price, and the premium is the fee you are paying for the put option - it's a bet the price is going to fall below the strike price by the end of the contract

A stock split is usually done by...

companies that have seen their share price increase to levels that are either too high or are beyond the price levels of similar companies in their sector

R Squared

how much of the variability in your dependent variable has been explained by the variation in your independent variables

Standardized Residuals

most points should be within 2 standard deviation of residuals Compute standard deviation and multiply by 2 - first clue to find out if you have skew or kurtosis... compute standard deviation and multiply by 2 .. Figure out if they're within 2 stdevs

Rebalancing of the Portfolio

need to do a rebalance even at the end You find out that at the end of the 2nd set of 3 month prices, the price of AGG climbed 20% while VUG stayed the same Once again, using the rule of thumb, AGG will need to be rebalanced Rebalancing AGG - 30%bond implies $10M/($89.78*1.2 or 107.74)= 92,816 shares of AGG -As you currently have 11,383 shares of AGG, so you need to sell 111,383-92,816 = 18,567 shares - of the 111,383 shares of AGG: 100,241 shares of AGG at $99.76/share and 11,142 shares of AGG at $89.78/share - To record the biggest gain, you will sell the 11,142 shares at $89.78/share and 7,425 shares (18,567 shares - 11,142 shares) at $99.76/share - so 11,142x(107.74-89.78)+7,425x(107.74-99.76)= $259,362

Futures Contracts: Long Position

the purchase of a futures contract

Futures Contracts: Short Position

the sale of a futures contract

Economically efficient markets

Assets are priced so that investors cannot exploit any discrepancies and earn unusual returns - Transaction costs matter

Final Tally

(dont need to account for transaction costs) - these are the calculations you do at the very end(the minimum)

SML & Under(Over)-Valued Assets

*Anything that's not on the SML means it's either overvalued or undervalued* - ABC is undervalued - LMN is under line means it has less return for same beta as portfolio that's on the line so you want to shy away from it - XYZ is above - Over line is undervalued - Under the line is overvalued

(3) Matched-Funding Techniques: Dedicated Portfolios

*Dedication refers to bond portfolio management techniques that are used to service a prescribed set of liabilities* (Cash flows are designed to match the anticipated liabilities) - Pure Cash: Matched Dedicated Portfolios (Most conservative strategy) - Dedication With Reinvestment: Cash flows do not have to exactly match the liability stream

Modified Duration

*Modified Duration* is an adjusted version of the Macaulay duration, which accounts for changing yield to maturities The formula for the modified duration is the value of the Macaulay duration divided by 1, plus the yield to maturity, divided by the number of coupon period per year The modified duration determines the changes in a bond's duration and price for each *percentage change* in the yield to maturity *interested in price changes with modified duration NOT MEASURED IN YEARS

Stock-Market Index Series

*Price Weighted Series* - Dow Jones Industrial Average (DJIA) - Nikkei-Dow Jones Average (225 stocks on the First Section of Tokyo Stock Exchange) *Market-Value Weighted Series* - NYSE Composite - S&P 500 Index *Unweighted Price Indicator Series* - Value Line Averages - Financial Times Ordinary Share Index

The Question Being Asked of VaR

- "What loss level is such that we are x% confident it will not be exceeded in N business days?" - VaR is the % loss level that will not be exceeded with a specified probability (typically 5%) - it captures an important aspect of risk in a single number - It is easy to understand - It asks the simple question: How bad can things get?

Preferred Habitat Theory

- *Market participants have preferred maturity segments* - *must be induced to move out of their preferred segment* - Market segmentation theory is a more extreme version - Interest rates are determined by supply and demand in each segment

Dividend Payments: Price Adjustment Example 2: If XYZ Corp announces a 2:1 stock dividend instead of a cash dividend, the adjusted closing price calculation will change

- A 2:1 stock dividend means that for every share an investor owns, he or she will receive two more shares. In this case, the adjusted closing price calculation will be $20*(1/(2+1)) - This will give you a price of $6.67, rounded to the nearest penny

Zero Coupon Bonds

- A Zero coupon bond pays just its par value at maturity - Example: Treasury bills are zero-coupon government bonds with maturity of up to one year

(1) Passive Portfolio Strategies: Buy and Hold

- A manager selects a portfolio of bonds based on the objectives and constraints of the client with the intent of holding these bonds to maturity - Two prominent strategies under this approach are the Laddered and Barbell strategies

Zero Coupon Bonds and the Par Yield Curve

- A par yield curve is a graphical representation of the yields of hypothetical Treasury securities with prices at par (this is hard cuz most bonds aren't trading at par) - On the par yield curve, the coupon rate will equal the yield-to-maturity of the security, which is why the Treasury bond will trade at par - The par yield curve is a plot of the yield to maturity against *term to maturity* for a group of bonds priced at par - The par yield curve gives a yield that is used to discount multiple cash flows for a coupon-paying bond - It uses the information in the spot yield curve, also known as the zero coupon curve, to discount each coupon by the appropriate spot rate

(3) Matched-Funding Techniques: Immunization Strategies

- A portfolio manager decides that the optimal strategy is to immunize the portfolio from interest rate changes - The immunization techniques attempt to derive a specified rate of return during a given investment horizon regardless of what happens to market interest rates - a risk-mitigation strategy that matches the duration of assets and liabilities, minimizing the impact of interest rates on net worth over time.

PP Plots

- A probability plot for assessing how closely two data sets agree, which plots the two cumulative distribution functions against each other - For the most part, the normal PP Plot is better at finding deviations from normality in the center of the distribution, and the normal QQ Plot is better at finding deviations in the tails

Again, Stock Splits Continued

- A stock's price is also affected by a stock split - After a split, the stock price will be reduced since the number of shares outstanding has increased. In the example of a 2-for-1 split, the share price will be halved - So, although the number of outstanding shares and the price change, the market capitalization remains constant

Stock Splits

- All publicly traded companies have a set number of shares that are outstanding - A stock split is a decision by a company's board of directors to increase the number of shares that are outstanding by issuing more shares to current shareholders

Full Replication

- All securities in the index are purchased in proportion to weights in the index - This helps ensure close tracking - Increases transaction costs, particularly with dividend reinvestment

Unweighted Price Index Series

- All stocks carry *equal weight* regardless of price or market value - May be used by individuals who *randomly* select stocks and invest the *same dollar amount* in each stock - Some use arithmetic average of the *percent price changes* for the stocks in the index

The Use of Futures in Asset Allocation

- Allows changing the portfolio allocation quickly to adjust to forecasts at lower transaction costs (as long as it's one that's already trading) - Futures can maintain an overall balance in a portfolio (cuz u can long or short a security without actually buying it) - Futures can gain exposure to international markets - Currency exposure can be managed using currency futures and options (big deal, tends to be how firms manage currency exposure)

Median and Interquartile Range

- An alternative to mean and standard deviation are median and interquartile range (IQR) - IQR is the difference between the third and first quartiles - Like mean and standard deviation, median and IQR measure the central tendency and spread, respectively, but are robust against outliers and non-normal data

When to use Arithmetic vs. Geometric Returns

- Arithmetic returns is a better measure for investors that rebalance their portfolio to begin each period with a fixed size investment - Geometric returns are a measure of the change in wealth over a period. It is used by investors to measure the compound rate of return

Insured Asset Allocation Continued

- As long as the portfolio achieves a return above its base, you exercise active management - relying on analytical research, forecasts and judgement and experience to decide what securities to buy, hold and sell, with the aim of increasing the portfolio value as much as possible - If, however, the portfolio should ever drop to the base value, you invest in risk-free assets, such as treasuries (especially T-bills, the SHY ETF in the project) - Insured asset allocation may be suitable for risk-averse investors who desire a certain level of active portfolio management but appreciate the security of establishing a guaranteed floor below which the portfolio is not allowed to decline - the strategy is referred to as the constant proportion strategy in the text (pg 565) -And it is often seen as a momentum based strategy

Initial Construction and Rebalancing of the Portfolio

- Assume the initial portfolio is 70% stocks and 30% bonds and you are using strategic asset allocation as your construction technique - The initial growth ETFs (VIG) price is $66.86/share and the initial bond's (AGG) price $99.76/share (both these prices are the last price in the initial data set) -Given $10M to invest, you buy $10M/$66.86 or 149,566 shares of VUG and $10M/$99.76 or 100,241 shares of AGG - You find out that at the end of the first three months, the price of VUG went up 10% while the price of AGG declined 10% *Knowing this, do you have to rebalance or not?* yes (i think cuz it's above hurdle rate)

Beta Characteristics

- Beta >1; security moves with the market only more, security is riskier than average - 0<Beta<1; security moves with the market only less - Beta < 0 security moves counter to the market - Market beta equals 1 - Portfolio beta is a weighted average of individual stock betas

Beta and the SML/CAPM

- Beta=1.0 equal risk to market (average) - Securities A and B are more risky than the market: Beta>1.0 - Security C is less risky than the market: Beta<1.0

VaR

- Better focus on tails and no assumptions about correct PDF - VaR computes maximum likely loss, e.g. what is the worst daily loss I can with 95% confidence - VaR depends on two parameters: Probability or confidence level (95%, 99%), and holding period (daily, weekly, monthly)

Sampling

- Buys a representative sample of stocks in the benchmark index according to their weights in the index - Fewer stocks mean lower commissions - Reinvestment of dividends is less difficult - Will not track the index as closely, so there will be some *tracking error*

Does Style Matter?

- Choice to align with investment style communicates information to clients - Determining style is useful in measuring performance relative to a benchmark - Style identification allows an investor to diversify by portfolio - Style investing allows control of the total portfolio to be shared between the investment managers and a sponsor

Keys to test for Market Efficiency

- Consistency of returns in excess of risk - Length of time over which returns are earned

Style

- Construct a portfolio to capture one or more of the characteristics of equity securities - Small-capitalization stocks, low P/E stocks, etc... - Value stocks appear to be underpriced - Price/book or price/earnings - Growth stocks enjoy above-average earnings per share increases

Technical Strategies

- Contrarian investment strategy - Price momentum strategy - Earnings momentum strategy

Forwards and Futures: Forwards are... (RNC)

- Custom contracts; lack standard terms - not traded, so participants must perform - risky; have potential counterparty credit risk

Tests for Normality: Anderson-Darling

- Determines if the sample data has the mean and variance matching a normal distribution with the same mean and variance - Plots the CDF of the data vs the CDF of a normal with same mean and variance

Building a Portfolio: What is the key to risk management? What is the single most important decision?

- Diversification is key to risk management - Asset allocation most important single decision - Using Markowitz Principles Step 1: Identify optimal risk-return combinations using the Markowitz analysis - Inputs: Expected returns, variances, covariances Step 2: Choose the final portfolio based on your preferences for return relative to risk

Risk Reduction in Portfolios: Random (or naive) diversification

- Diversifying without looking at how security returns are related to each other - Marginal risk reduction gets smaller as securities are added Beneficial but not optimal - risk reduction kicks in as soon as additional securities added - Research suggests it takes a large number of securities to eliminate majority of risk

Classical Immunization: Duration Characteristics

- Duration declines more slowly than term to maturity, assuming no change in market interest rates - Duration changes with a change in market interest rates - There is not always a parallel shift of the yield curve (means that if rates go up, everything goes up the same, but that's not the case) - Bonds with a specific duration may not be available at an acceptable price (trying to keep duration and term to maturity lined up)

Simple model is the historical method in which we calculate VaR directly from past returns

- Ex. suppose we want to calculate the 1-day 95% VaR for a stock using 100 days of data - the 95th percentile corresponds to the least worst of the worst 5% of returns - In this case, because we are using 100 days of data, the VaR simply corresponds to the 5th worst day. If we have the following 100 returns, sorted from lowest to highest

Term Structure of Interest Rates: Term structure theories

- Explanations of the shape of the yield curve - Pure expectations, liquidity preference, and preferred habitat Know yield curve, spot curve, forward rates from this lecture

Stock Splits Continued

- For example, in a 2-for-1 stock split, an additional share is given for each share held by a shareholder - So, if a company had 10 million shares outstanding before the split, it will have 20 million shares outstanding after a 2-for-1 split

Dividend Payments: price adjustment example

- For example, let's assume that the closing price for one share of XYZ corp. is $20 on Thursday. - After close on Thursday, XYZ Corp announces a dividend distribution of $1.50 per share - The adjusted closing price for the stock would then be $18.50 ($20-$1.50)

Forward Rates

- Forward rates are theorized prices of financial transactions that might take place at some point in the future - The forward rate answers the question, "How much would it cost to execute a financial transaction at future date X?"

Modern Portfolio Theory - Framework for what? Used by who? What does it quantify? What is crucial?

- Framework for selection of portfolios based on risk and expected return - Used, to varying degrees, by financial managers - Quantifies benefits of diversification - Security correlations are crucial in determining portfolio risk - An asset with high volatility may have low risk

Index Portfolio Strategy Construction Techniques

- Full replication - Sampling - Quadratic optimization

An Overview of Active Equity Portfolio Management Strategies: Active Managers goal

- Goal is to earn a portfolio return that exceeds the return of a passive benchmark portfolio, net of transaction costs, on a risk-adjusted basis Practical difficulties of active manager - Transaction costs must be offset - Risk can exceed passive benchmark

Growth Continued: How do Growth Stocks differ from Value Stocks?

- Growth stocks differ from value stocks - investors expect growth stocks to earn substantial capital gains - These expectations can result in growth stocks being overvalued - Value stocks on the other hand, often are undervalued or ignored by the market - they may eventually gain value, but investors also attempt to profit from the dividends they typically pay

Style: Value versus Growth

- Growth stocks will outperform value stocks for a time and then the opposite occurs - Over time value stocks have offered somewhat higher returns than growth stocks Growth-oriented investor will: - focus on EPS and its economic determinants - Look for companies expected to have rapid EPS growth - assumes constant P/E ratio Value-oriented investor will: - focus on the price component - not care much about current earnings - assume the P/E ratio is below its natural level

Spread in Returns

- High minus low (HML) accounts for the spread in returns between value and growth stocks - Argues that companies with high book-to-market ratios, value stocks, outperform those with lower book-to-market values, growth stocks - Used to evaluate profit margins for a security over the short- and long-term - Provides an indication of the expected performance of the security in the future. The formula, high minus low, is used to calculate the associated range

CAPM/SML Implications

- Higher risk assets require higher returns - Investors are only compensated for bearing non-diversified risk, i.e. systematic risk - Asset prices are not impacted by diversifiable risk - Investors determine the risk they bear; market determines their compensation

Quadratic Optimization (Markowitz Analysis)

- Historical information on price changes are input into a Markowitz model that determines the composition of a portfolio that will minimize tracking error with the benchmark - This relies on historical covariances, which change over time, leading to failure to track the index - Goal is to make sure you have a tracking error of 0

Brief History of the lack of splits

- IBM hasn't split its stock since 1999 - Cheveron hasn't split its stock since 2004 - 3M has gone more than a decade without a stock split

Implications for Investors

- If anticipating a rate decrease, bond buyers should purchase low-coupon, long-maturity bonds - If interest rates are expected to increase, investors should consider bonds with large coupons or short maturities or both

Measuring Tail Risk: VaR

- If the 95% VaR of a portfolio is $100, then we expect the portfolio will lose $100 or less in 95% of the scenarios, and lose $100 or more in 5% of scenarios - We can define VaR for any confidence level, but 95% has become an extremely popular choice in finance. The time horizon also needs to be specified for VaR - On other settings, in which less liquid assets may be involved, time frames of up to one year are not uncommon

Classical Immunization

- Immunization is neither a simple nor a passive strategy - An immunized portfolio requires frequent rebalancing because the modified duration of the portfolio always should be equal to the remaining time horizon (except in the case of the zero-coupon bond)

Dynamic Asset Allocation

- In dynamic asset allocation, you constantly adjust the mix of assets as markets rise and fall -With this strategy you sell assets that are declining and purchase assets that are increasing - This makes dynamic asset allocation the polar opposite of a constant-weighting strategy. -For example, if the stock market is showing weakness, you sell stocks in anticipation of further decreases; and if the market is strong, you purchase stocks in anticipation of continued market gains

Beta (ß) - What does it tell us? Continued

- Indicated the risk an asset will add to a well-diversified portfolio (relative measure because you have portfolios beta and securities beta and can compare them) - Measures an asset's nondiversifiable risk - The slope of the line formed when an asset's returns are regressed against the market return - A measure of the sensitivity of an asset's returns to changed in the market return - Is the relevant risk measure for well-diversified investors

(2) Active Management Strategies: Bond Swaps

- Involve liquidating a current position and simultaneously buying a different issue in its place with similar attributes buy having a chance for improved return - Bonds are bought and sold simultaneously (to profit from changed in their market value) by swapping one type of bond with another

Market Capitalization (Market Cap)

- Is the market value of a company's outstanding shares - Market Capitalization is equal to the share price multiplied by the number of shares outstanding - Capitalization could be used as an indicator of public opinion of a company's net worth and is a determining factor in some forms of stock valuation MC=price*the shares outstanding

Criticism of the DJIA

- Limited to 30 non-randomly selected blue-chip stocks) - Does not represent a vast majority of stocks - Can be heavily skewed by the lack of stock splits

Estimating Beta: Characteristic Line

- Line fit to a security's return relative to the market index

Capital Market Line Equations

- Line from RF to L is capital market line (CML) - x = risk premium = E(RM)-RF - y=risk=standard deviation - Slope=x/y=[E(RM)-RF]/Standard Dev of the Market - Y-intercept = RF

Common Measures used to Identify Value Stocks

- Low PE ratio stocks (like 10 or 12) - Low price-to-cash-flow ratio stocks - Low price-to-book ratio stocks These are all good

Value-Weighted Series

- Market Value=Number of Shares Outstanding*Current Market Price - Assign a beginning index value (e.g. 100) and new market values are compared to the base index - Automatic adjustment for splits

Duration depends on three factors

- Maturity of the bond - Coupon payments - Yield to maturity

Kurtosis

- Measure of the "tailedness" of the distribution - 4th moment of the distribution - Any value other than 0 indicates some level of non-normality - greater than 0 means more values than the normal distribution are in the tail and there are more events in the tail than in the peak (heavy tailed) - If the value is <0, the data is light tailed with approx as many observations in the tails as in the peak

Cumulative Wealth Index: CWI

- Measures how wealth changes over time - Measures the cumulative effect of returns on an initial investment

Using Derivatives in Active Equity Portfolio Management

- Modifying Systematic Risk - Modifying unsystematic risk

Price momentum strategy

- Momentum investing involves a strategy to capitalize on the continuance of an existing market trend - it involved going long stocks, futures or market ETFs showing upward-trending prices and short the respective assets with downward-trending prices Momentum investing holds that trends can persist for some time, and it's possible to profit by staying with a trend until its conclusion, no matter how long that may be - For ex. momentum investors that entered the U.S. stock market in 2009 generally enjoyed an uptrend until December 2018

Options

- Options can enhance an individual's portfolio. They do this through added income, protection, and leverage (another leverage bet) - Depending on the situation, there is usually an option scenario appropriate for an investor's goal - A typical example is using options as an effective hedge against a declining stock market to limit downside losses - Options can also be used to generate recurring income - Additionally, they are often used for speculative purposes such as wagering on the direction of a stock

Selecting an allocation method depends on

- Perceptions of variability in the client's objectives and constraints - Perceived relationship between the past and future capital market conditions - for project 2, once you choose your strategy you cannot change it

Immunization Strategies: Components of Interest Rate Risk

- Price Risk - Coupon Reinvestment Risk - Immunization attempts to offset these

Dow Jones Industrial Average (DJIA)

- Price-weighted average of *thirty* large well-known industrial stocks, leaders in their industry, and listed on NYSE - Total the current price of the 30 stocks and divide by a divisor

Strong Form

- Prices reflect all information, public and private - No group of investors should expect to earn abnormal returns by using publicly or privately available information - Encompasses weak and semi-strong forms as subsets - Investor who believes in strong form should be passive

Semistrong Form

- Prices reflect all publicly available information - Investors cannot benefit from new public information after its announcement - Encompasses weak form as a subset

Another Efficient Frontier

- Random weights

Investment-Grade Bond Indexes

- Rated *BBB or higher* - Relationship among these bonds is strong (correlations average 0.95) - Returns for all these bonds are driven by *aggregate interest rates*- shifts in the government yield curve

Real and Nominal Risk Free Rates

- Real risk-free rate (real rate) unaffected by price changes or risk factors - Nominal (observed) risk-free rate (RF) includes a real component (rr) and expected inflation (ei)

Estimating Beta: Market Model

- Related a stock's return to the return on the market, assumes a linear relationship - Produces an estimate of return for any stock

(2) Active Management Strategies: Interest-rate anticipation

- Risky strategy relying on uncertain forecasts - Ladder strategy staggers maturities - Barbell strategy splits funds between short duration and long duration securities - Basic interest rate anticipation strategy involves moving between long-term government bonds and very short-term treasury bills, based on a forecast of interest rates over a certain time horizon, to provide the maximum increase in price for a portfolio. Given that long-term bonds change the most in value for a given change in interest rates, a manager would want to hold long-term bonds when rates are falling.

Measuring Tail Risk: Value at Risk (VaR)

- Skewness and Kurtosis do not give a return value (% loss) to the tail risk - VaR does

Capital Market Line

- Slope of CML is the market price of risk for efficient portfolios, or the equilibrium price of risk in the market - Relationship between risk and expected return for the portfolio P (Equation for CML): E(RM)=optimal portfolio expected return

Style Indexes: Styles (size and type)

- Small-Cap growth - Mid-Cap growth -Large-cap growth - Small-cap value - Mid-cap value - Large-cap value

Value Stocks

- Some value stocks are underpriced due to poor earnings reports or negative media attention - However, they often have strong dividend payout histories - A value stock with a strong dividend track record can provide reliable income to an investor - Many value stocks are older companies that can be counted on to stay in business, even if they aren't particularly innovative or poised to grow

Standard Deviation and Risk

- Standard deviation is often used as the sole risk measure - This is valid when returns are normal - This implies zero skew and kurtosis are 0 - But stdv is usually not a good risk measure when losses are seriously skewed and/or have kurtosis - In such cases, we need a measure that takes into account these variables - We can use Value at Risk (VaR) and Expectes Shortfall (ES)

Beta - What does it tell us? It's a standardized measure of what? What is the relative measure of risk? What does it relate?

- Standardized measure of systematic risk - Relative measure of risk: risk of an individual stock relative to the market portfolio of all stocks - Relates an asset's covariance with the market portfolio to the variance of the market portfolio *Homework problem that kind of looks like this*

Using Futures and Options in Equity Portfolio Management

- Systematic and unsystematic risk of equity portfolios can be modified by using futures and options derivatives - Selling futures on the portfolio's underlying assets reduces the portfolio's sensitivity to price changes of the asset (similar to shorting) - Options do not have symmetrical impact on returns (because they're only out there as pals or puts?) (you expect it to rise, you will capture that rise)

Tactical Asset Allocation

- Tactical asset allocation is an active management portfolio strategy that shifts the percentage of assets held in various categories to take advantage of market pricing anomalies or strong market sectors - This strategy allows portfolio managers to create extra value by taking advantage of certain situations in the marketplace - it is as a moderately active strategy since managers return to the portfolio's original strategic asset mix once reaching the desired short-term profits - Very flexible strategy - could end up doing really bad or really well with tactical

Tactical asset allocation continued again

- Tactical asset allocation is the process of taking an active stance on the strategic asset allocation itself and adjusting long-term target weights for a short period to capitalize on the market opportunities - Tactical shifts may also come within an asset class - Assume the 45% strategic allocation of stocks consists of 30% value and 15% growth holdings - If the outlook for growth does not look favorable, it may be a wise tactical decision to shift the allocation within stocks to 40% value and 5% growth for a short time until conditions change -momentum strategy

Bid/Ask Spread

- The "ask" (or "offer") is the market price at which an ETF can be bought, and the "bid" is the market price at which the same ETF can be sold - The difference between these two prices is commonly known as the bid/ask spread - You can think of it as a transaction cost similar to commissions except that the spread is built into the market price and is paid on each roundtrip purchase and sale - So, the larger the spread and the more frequently you trade, the more relevant this cost becomes (you would want to deal with a low expense ratio)

Fama French Multi-Factor Model

- The Fama and French Three Factor Model is an asset pricing model that expands on the capital asset pricing model (CAPM) by adding size and value factors to the market risk factor in CAPM - Three factore are (1) market risk (market return - risk free rate), (2) the outperformance of small versus big companies, and (3) the outperformance of high book/market versus small book/market companies - This model consdiers the "fact" that value and small-cap stocks outperform markets on a regular basis - By including these two additional factors, the model adjusts for the outperformance tendency, which is thought to make it a better tool for evaluating manager performance *It's the importance of HORIZON* how many years of data you're using - dont be too concerned if it fails because it's only cuz of the horizon

Forward Rates Continued

- The ability to lock in a future rate is something that can be done using forwards or futures - Bond futures (which are limited to Treasuries) are limited to 2-year, 5-year and 10-year bond contracts - Forwards can fill in the gap for rates less than 2 years and the interregnum between 2 and 5 and then 5 and 10

(1) Passive Portfolio Strategies: Indexing

- The objective is to construct a portfolio of bonds that will equal the performance of a specified bond index

Market Portfolio: Most important implications of CML

- The portfolio of all risky assets is the optimal risky portfolio (called the market portfolio) - the optimal portfolio is at the highest point of tangency between RF and efficient frontier - All investors hold the same optimal portfolio of risky assets - By borrowing funds at the risk-free rate, they can also invest more than 100% of their investable funds in the risky market portfolio, increasing both the expected return and the risk beyond that offered by the market portfolio

Measures of Shape: Skewness and Kurtosis

- The shape of the data is often described by its symmetry or non-symmetry (also called skewness) - Skew is the 3rd moment of the distribution - in a symmetric distribution, the mean and the median are the same value - if the values are not the same then the distribution maybe skewed, i.e. non-symmetric - If you see the mean and the median are not the same, you would typically compute the skew of the data at this point

Using Insured Asset Allocation

- The value of the multiplier is based on the investor's risk profile and is derived by asking what the maximum one-quarter loss could be on the risky investment - The multiplier will be the inverse of that percentage. So, if one decides that 20% is the maximum "crash" possibility, the multiplier value will be(1/0.2), or 5 - Multiplier values between 3 and 6 are very common

Zero Coupon Bonds: Price and YTM

- The yield to maturity is the effective rate of return per *period* for holding the bond from today until maturity *n periods in the future*

Small Minus Big (SMB)

- This factor is referred to as the "small firm effect," of the "size effect," where size is based on a company's market capitalization - If a portfolio has more small-cap companies in it, it should outperform the market over the long run

Core-Plus Bond Portfolio Management

- This involves having a significant (core) part of the portfolio managed passively in a widely recognized sector such as the U.S. Aggregate Sector of the U.S. Government/Corporate sector - The rest of the portfolio would be managed actively in one or several additional "plus" sectors, where it is felt that there is a higher probability of achieving positive abnormal rates of return because of potential inefficiencies

Strategic Asset Allocation

- This method establishes and adheres to a "base policy mix" - a proportional combination of assets based on expected rates of return for each asset class - For example, if stocks have historically returned 10% per year and bonds have returned 5% per year, a mix of 50% stocks and 50%bonds would be expected to return 7.5% per year - Strategic asset allocation implies a buy-and-hold strategy, even as the shift in values of assets causes a drift from the initially established policy mix - once you have allocation you can't change it besides rebalancing - Buy and hold still needs to rebalance

Fundamental Strategies

- Top-Down versus bottom-up approaches (using price/earnings) - Asset and sector rotation strategies (think of these as fama french)

Difficulties in Creating and Computing Bond-Market Indexes

- Universe of bonds is much broader than that of stocks - Range of bond quality varies from U.S. Treasury securities to bonds in default - Bond market changes constantly with new issues, maturities, and embedded options - Bond prices are affected by duration, which is dependent on maturity, coupon, and market yield - Correctly pricing individual bond issues without current and continuous transaction prices available poses significant problems

Capital Asset Pricing Model (CAPM) assumed that all investors: (RIT NPC)

- Use the same information to generate an efficient frontier - Have the same one-period time horizon - Can borrow or lend money at the risk-free rate of return - No transaction costs, no income taxes, no inflation - No single investor can affect the price of a stock - Capital markets are in equilibrium Efficient Market Hypothesis: all securities are trading at their fair value

Timing Between Styles

- Variations in returns among mutual funds are largely attributable to differences in styles - Different styles tend to move at different times in the business cycle

Strategic Asset Allocation Continued

- While strategic asset allocation is called a buy/hold strategy, there may be times when rebalancing may be needed - *A common rule of thumb is that the portfolio should be rebalanced to its original mix when any given asset class moves more than 5% from its original value*

Insured Asset Allocation

- With an insured asset allocation strategy, you establish a base portfolio value under which the portfolio should not be allowed to drop. - the two asset classes used are a risky asset (usually equities) and a conservative asset of either cash, equivalents or treasury bonds(for the Project, SHY) -The percentage allocated to each depends on the "cushion" value, defined as (current portfolio value minus floor value), and a multiplier coefficient, where a higher number denotes a more aggressive strategy

Integrated Asset Allocation (Not to be used in Project 2)

- With integrated asset allocation, you consider both your economic expectations and your risk in establishing an asset mix - while most strategies take into account expectations for future market returns, not all of the strategies account for the investor's risk tolerance - integrated asset allocation, on the other hand, includes aspects of all strategies, accounting not only for expectations but also actual changes in capital markets and your risk tolerance - Integrated asset allocation is a broader asset allocation strategy

Summary

- You are not "paid" for taking risk related to either skewness or kurtosis - You are "paid" for risk related to standard deviation - VaR and ES are tools that can be used to quantify the risks related to skewness and kurtosis - When comes to portfolio construction, the portfolio can contain securities that are Normal and those that are not - After determining the weights of each security, perform the Normality tests on the portfolio - After the tests, determine if the weights need to change

Forward Rate Calculation

- You may want to do this for lending purposes

"Smart Beta" or Low Volatility Index

- a low volatility index strategy might measure the performance of the 100 least-volatile stocks in the S&P500 - The index components are weighted relative to the inverse of their corresponding volatility, with the least volatile stocks receiving the highest weights

Expected Shortfall

- accounts for the things VaR doesnt - Does so be averaging the losses starting at the states percentile and going all the way to the end

Adjusting for Dividends: Total Returns

- again, example in slides

Compound Annual Average Rate of Return

- can help an investor compare alternatives for their investments - ex. an investor is comparing the performance of two investments that are uncorrelated - In any given year during the period, one investment may be rising while the other falls. This could be the case when comparing high-yield bonds to stocks, or a real estate investment to emerging markets - Using CAGR would smooth the annual return over the period so the two alternatives would be easier to compare

Portfolio Risk and Diversification

- constant number because we've already made decision about risk

Tests for Normality: Jarque-Bera

- determines if the sample data has the same skewness and kurtosis matching a normal distribution with the same skewness and kurtosis - Plots CDF of data vs CDF of normal with same skewness and kurtosis

Yield Spreads

- differences between 2 quotes rates of return Risk premiums Result from differences in - Default risk (bond rating), maturity, call features, coupon rates, marketability, taxes - Borrower actions - Interest rates Function of variables associated with issue or issuer Inversely related to business cycle

One more example

- each point is optimal combination for any measure of risk; black dots are all suboptimal

Information Ratio Continued

- identifies how much a portfolio has exceeded a benchmark on a risk-adjusted basis - Higher information ratios indicate a desired level of consistency, whereas low information ratios indicate the opposite Calculating IR: - another measure of performance Premium versus underlying benchmark

Correlation (pij)

- if its 0 they don't move together at all - if its 1 they move together in tandem (one goes up the other goes up, one goes down the other goes down) - -1 means one goes up and the other goes down and vice versa

CDF in XLSTAT Displays

- lower bound, upper bound for the intervals - The frequency (number of values of the sample within the interval) - The relative frequency (the number of values divided by the total number of values in the sample) - The density (the ration of the frequency to the size of the interval)

Selecting an allocation method depends on

- perceptions of variability in the client's objectives and constraints (will lead us to the construction technique) - perceived relationship between the past and future capital market conditions

Tactical Asset Allocaton continued once more

- the percentage of weighting that each asset class has over the long term is known as the strategic asset allocation - This allocation is the mix of assets and weights that help an investor reach their specific goals - A simple example of a typical portfolio allocation and the weight of each asset class is in the right panel pic is example of tactical allocation strategy - with strategic, you're stuck with those percentages and with Tactical you are not

Gather the price data, convert to returns and run Markowitz

- where it switches it the first portfolio to meet minimum variance requirement

Standardized Residuals should be inside...

-2 and 2 - of a lot of data outside -2 and 2, data is not normally distributed

Tactical Asset Allocation continued

-To understand tactical asset allocation, first understand strategic asset allocation - A portfolio manager may create an investor policy statement (IPS) to set the strategic mix of assets for inclusion in the client's holdings - The manager will look at factors such as the required rate of return and acceptable risk levels

Using Insured Asset Allocation continued again

-risk tolerance needs to be pretty high cuz if you make 1 bad bet all risky assets need to be sold -The investor will make a beginning investment in the risky asset equal to the value of: (Multiplier) * (Cushion value in dollars) and will invest the remainder in the conservative asset - As the portfolio value changes over time,the investor will rebalance according to the same strategy -Consider a hypothetical portfolio of $100,000 of which the investor decides $90,000 is the absolute floor. If the portfolio falls to $90,000 in value, the investor would move all assets to cash (SHY) to preserve capital

Uses of Security-Market Indexes (BIM FS)

1. As *benchmarks* to evaluate the performance of professional money managers 2. To create and monitor an *index fund* 3. To measure *market rates of return* in economic studies 4. For predicting *future market movements* by technicians 5. As a substitute for the market portfolio of risky assets when calculating the *systematic risk* of an asset

On economic grounds, diversifying and holding a larger portfolio eliminates firm specific risk for two reasons

1. Each investment is a much smaller percentage of the portfolio, muting the effect (positive or negative) on the overall portfolio 2. Firm-specific actions can be either positive or negative. In a large portfolio, these effects will average out to zero

Remaining Questions Not Addressed by CML

1. How do you determine the expected return for individual securities or undiversified portfolios? 2. How do investors determine the risk a security will add to their portfolio? *Solution is achieved by assuming investors hold well-diversified portfolios

Three main types of bond swaps

1. Maturity Swap: Exchanging long-term bonds with short-term ones, and vice versa 2. Quality Swap: Exchanging highly-rated bonds with low-rated ones, and vice versa 3. Yield swap: exchanging deep-discounted bonds with high-interest bonds, and vice versa. See also swap.

Median and Interquartile Range Advantages (SO)

1. Outlier Identification: IQR makes it east to do an initial estimate of outliers by looking at values more than one-and-a-half times the IQR distance below the first quartile or above the third quartile 2. Skewness: comparing the median to the quartile values shows whether data is skewed. For example, if the median is closer to the third quartile than the first quartile, it has a higher proportion of larger values

Alternative Bond Portfolio Strategies

1. Passive portfolio strategies 2. Active management strategies 3. Matched-funding techniques

Differentiating Factors in Constructing Market Indexes: Weighting of sample members

1. Price-weighted series 2. market value-weighted series 3. unweighted (equally weighted) series

Problems with P-Tests

1st Hypothesis Tests - Rational: calculate a probability of what could of happened not what DID happen in fictional repeated trials - To do this you have to hypothesize a baseline that at infinity converges to, in our case, the mean and variance or skew and kurtosis of a normal - These steps violate common sense as most of us want to know what the evidence tells us about the truth or falsity of the data P-Values: - a small p-value does give us the probability the baseline is false - instead it is interpreting as asking us to believe in the absolute truth or falsity of a contingent hypothesis

Significance Tests: p-tests

2 Tail Test: - ex. the null for A-D is that the mean and variance are equal to x and y respectively - tests both if the mean is significantly greater than x and if the mean is significantly less than x - The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05

Durbin Watson

2 or greater implies negative AR(1) in residuals -AR(1) Process means that today's returns is not correlated to yesterdays returns, etc.

Interpreting Box Plots

2. The box plot is comparatively short -- suggesting that overall there is little variation in the data 1 and 3. are comparatively tall, suggesting that overall there is significant variation in the data 3 and 4. One box plot is much higher or lower than another -- this could suggest a difference between groups. For example, the box plot (3) has a higher median and a bigger IQR than box plot (4). This is an indication of more variability

What does the Yield Curve tell us?

> Upward: Investors expect interest rates to increase > Downward: investors expect interest rates to drop > Flat: investors expect interest rates to remain constant

Derivatives (make sure everything is in this lecture when you go over it...) *This lecture is not on final exam*

A *derivative* is a contract between two parties whose value is based on some underlying asset price or market condition In many derivatives, two parties agree to exchange a standard quantity of an asset at a predetermined price at a specific date in the future

Swap

A *swap* is an agreement between two parties to exchange assets or a series of cash flows for a specific period of time at a specified interval

Why Use a Barbell Strategy

A Barbell strategy is formed when a investor invests in long and short duration bonds, but does not invest in the intermediate duration bonds. This strategy is useful when interest rates are rising; as the short term maturities are rolled over they receive a higher interest rate, raising the value

Example of a Currency Swap

A US company, GE, is looking to acquire Japanese yen and a Japanese company, Hitachi, is looking to acquire U.S. dollars (USD), so these two companies could perform a swap. The Japanese company likely has better access to Japanese debt markets (then GE does) and could get more favorable terms on a yen loan than if the U.S. company went in directly to the Japanese debt market itself, and vice versa in the United States for the Japanese company. Assume General Electric needs ¥100 million. The Japanese company needs $11 million. If they agree to exchange this amount, that implies a USD/JPY exchange rate of 90.9. (you lock in interest payments and eliminate currency exposure)

Why use a Laddered Strategy Continued

A bond ladder - which attempts to match cash flows with the demand for cash - is a multi-maturity investment strategy that diversified bond holdings within a portfolio - It reduces the reinvestment risk associated with rolling over maturing bonds into similar fixed-income products all at once - It also helps manage the flow of money - helping to ensure a steady stream of cash flows throughout the year

Classic Passive Management Strategies: Credit Barbell

A bond portfolio containing a mix of high-grade and low-grade securities

McCauley Duration: Why is it important?

A bond with a longer maturity period is more sensitive to changes in interest rates than a bond with a short duration. Therefore, investors must stay with funds or bonds with longer maturity when interest rates are expected to go down and move to bonds or funds with short maturity when interest rates are either likely to stay stable or go up This makes it important for an investor to know the Macaulay Duration of a fund before buying it

Options: Call option and example

A call option is a contract that gives the investor the right to buy a certain amount of shares (typically 100 per contract) of a certain security or commodity at a specified price over a certain amount of time (making a bet that by the time the contract ends the price will have gone up above the strike) For example, a call option would allow a trader to buy a certain amount of shares of either stocks, bonds, or even other instruments like ETFs or indexes at a future time (by the expiration of the contract) If you're buying a call option, it means you want the stock (or other security) to go up in price so that you can make a profit off of your contract by exercising your right to buy those stocks (and usually immediately sell them to cash in on the profit) - futures are an obligation, but options are a right and not an obligation

Contrarian investment strategy

A contrarian believes that certain crowd behavior among investors can lead to exploitable mispricings in securities markets - For ex, widespread pessimism about a stock can drive a price so low that it overstates the company's risks, and understates its prospects for returning to profitability (Ex Boeing) - Identifying and purchasing such distressed stocks, and selling them after the company recovers, can lead to above-average gains - Conversely, widespread optimism can result in unjustifiably high valuations that will eventually lead to drops, when those high expectations don't pan out - Avoiding (or short-selling) investments in over-hyped investments reduces the risk of such drops These general principles can apply whether the investment in question is an individual stock, an industry sector, or an entire market or any other asset class

Growth, Value and Capitalization Defined: Growth Stock

A growth stock is a share in a company that is anticipated to grow at a rate significantly above the average for the market - it generates substantial positive cash flow and revenues/net income that are expected to increase at a faster rate than the average company within the same industry These stocks generally do not pay dividends, as the companies usually want to reinvest any earnings in order to accelerate growth in the short term Investors earn money through capital gains when they eventually sell their shares

Swaps: Plain vanilla *interest rate swap*

A plain vanilla *interest rate swap* is an exchange of fixed-interest payments for floating-interest payments by two counterparties (if you have a loan and it's paying a floating rate meaning it's floating with treasury rates, and you want it converted into a fixed rate cuz interest rates are going to rise but someone else thinks rates will drop and they have a fixed interest payment so you guys swap) - the *swap buyer* makes a periodic fixed interest rate payment on a stated notional principal amount - the *swap seller* makes a periodic floating-rate interest payments on the same stated notional principal amount - No principal is exchanged

Types of Distributions

A random variable/ observation is a variable/ observation whose value is determined by chance There are two types of random variables: - A discrete random variable can take on only specified, distinct values - A continuous random variable can take on any value within an interval Therefore there are also two types of probability distributions: - Discrete probability distributions - Continuous probability distributions

Sortino Ratio

A variation of the Sharpe Ratio - it differentiates harmful volatility from total overall volatility by using the asset's standard deviation of negative portfolio returns, downside deviation, instead of the total standard deviation of portfolio returns - The Sortino ratio takes an asset or portfolio's return and subtracts the risk-free rate then divided that amount by the asset's downside deviation - Denominator is standard deviation of downside deviation(standard deviation of negative returns) - also called half variance?

Zero Coupon Bonds: Price and YTM Example: Consider a risk-free zero coupon bond with a face value of $100 in two years. The current one year risk-free interest rate is 1%. It is also known with certainty that the one-year risk free interest rate will be at 3% the following year

A. Find the current price of the bond and its YTM B. At what price will the bond be trading in one year C. what is the return of buying the bond today and selling it at t=1 D. What is the return of buying the bond at time 1 and getting its FV at time 2

Factors

APT assumes returns generated by a factor model that allows for more than 1 factor Factor Characteristics: - Each risk must have a pervasive influence on stock returns - Risk factors must influence expected return and have non-zero prices - Risk factors must be unpredictable to the market ki=rf+BF1+BF2+BnFn Often used factors: - Short term interest rates - The difference in long term and short term interest rates - A diversified stock index such as the S&P 500 or NYSE Composite - Oil prices - Gold or other precious metal prices - Currency exchange rates

Market Anomalies: Value Line Ranking System

Advisory service that ranks 1700 stocks from best (1) to worst (5) - Probable price performance in next 12 months - Best investment letter performance overall Transaction costs may offset returns Data snooping/data mining could find patterns/techniques that have no basis

Risk Reduction in Portfolios

Assume security risk sources are independent - This assumption is unrealistic when investing - Market risk affects all firms, cannot be diversified away - Youre being paid to take market risk via the equity risk premium The larger the number of securities, the smaller the exposure to any particular risk - "Insurance principle" - Only issue is how many securities to hold

The New Efficient Set

All combinations of risk-free lending or borrowing with portfolio P lie on a straight line in expected return standard deviation space The intercept of line is Rf and the slops is (picture) Therefore, the existence of a risk-free lending and borrowing rate implies that there is a single portfolio of risky assets that is preferred to all other portfolios risk-free investing and borrowing creates a new set of risk-expected return possibilities Addition of risk-free asset results in: - A change in the efficient set from an arc to a straight line tangent to the original frontier - Chosen (optimal) portfolio depends on investor's risk-return preferences

Characteristics of Market Portfolio

All risky assets must be in portfolio, so it is completely diversified - includes only systematic risk Unobservable but approximated with portfolio of all common stocks - In turn, approximated with S&P 500 (called market capitalization index) (Market Cap=Shares Outstanding*Price) - we have a market cap index All securities included in proportion to their market value

Swaps: Credit Default Swaps (CDS)

Allow financial institutions to hedge credit risk A CDS buyer is buying insurance on a loan or bond - CDS seller receives periodic payments from the CDS buyer - If the insured loan or bond defaults, the CDS seller pays the par value of the loan or bond to the CDS buyer (has to pay back par for all defaulted mortgages) CDS played a major role in the financial crisis, AIG and others were major sellers of CDS that insured mortgage-backed securities, but lacked capital and could not pay when the mortgage securities failed

Why is Duration Important?

Allows comparison of effective lives of alternative bonds Used in bond management strategies, particularly immunization

M2

Allows returns between portfolios to be compared it measures the returns of the portfolio, adjusted for the risk of the portfolio, relative to that of a benchmark - Risk-adjusted excess return Measured in percentage terms, easy to understand all measures good at ranking portfolios - Ranking is what you're interested in in fama french and SML calculations - Do all security analysis (fama and SML) then sort them using any of these measures - Securities have various benchmarks (b) = measure manager risk??

Treynor Ratio

An Alternative to Sharpe - Based on SML - Equals excess return divided by beta - Higher the ratio --> better the performance - Provides a ranking measure for portfolios Excess return/Beta - Higher the ratio, the better the performance

Growth Stock Continued: What Ratios are used to Classify Growth Stocks?

Analysts compute return on equity (ROE) by dividing a company's net income by average common equity to be classified as a growth stock, analysts generally expect companies to achieve a 15% or higher return on equity P/E is also used to identify growth stocks - Computed by dividing a company's current share price by its earnings per share over the past 12 months. The higher the ratio, the more expensive the stock is considered - However, growth-stock investors typically have no problem buying a stock with a P-E ratio of even 50 or higher - You want high AND sustainable P/E

Selecting Optimal Asset Classes

Another way to use Markowitz model is with asset classes Allocation of portfolio to asset types - Asset class rather than individual security is most important for investors Can be used when investing internationally Different asset classes offer various returns and levels of risk - Correlation coefficients may be quite low

The (Two Fund) Separation Theorem

Any investor's optimal portfolio can be constructed by holding each of certain mutual funds in appropriate ratios, where the number of mutual funds is smaller than the number of individual assets in the portfolio(The theoretical result that all investors will hold a combination of the risk-free asset and the market portfolio) - reason being is that if they were the same, you'd want to go buy it off the market

Example of Initial and Maintenance Margins

Assume we have a speculator who has $10,000 in her trading account. She decides to buy August West Texas Intermediate Crude Oil (WRI) at $40 per barrel Each WTI futures contract represents 1000 barrels and requires an initial margin of $9,000 and has a maintenance margin level set at $6,500 Since her account is $10,000, which is more than the initial margin requirement, she can open up one august WTI futures position

(2) Active Management Strategies: Yield Spread Analysis

Assumes normal relationships exist between the yields for bonds in alternative sectors - An analysis that compares the liquidity, creditworthiness, and maturity of a fixed-income security to a benchmark, which is typically U.S. Treasury securities - how liquid is it

Fama French Multi-Factor Model: Are SMB and HML priced risk?

Assumption: SMB and HML are non-market factors proxy for predictors of fundamental risks that can affect future investment opportunities - What risk are they identifying? - Some have said financial risk, i.e. default risk ATP does not have this problem as the original model used economic factors It maybe that HML, for example, may proxy for growth oriented *index* portfolios, which some managers try to beat, and value-oriented *index* portfolios, which others try to beat

Tests of CAPM

Assumptions are mostly unrealistic Empirical evidence has not lef to consensus Points widely agreed upon - SML (CAPM) appears to be linear - Intercept is generally higher than RF - Slope of SML is generally less than theory predicts - It is likely that only systematic risk is rewarded

An overview of passive equity portfolio management strategies continued again

At first glance, it would appear that ETF B is less expensive because of its lower expense ratio

Arbitrage Pricing Theory

Based on Law of One Price - Two assets with identical future cash flow streams cannot sell at different prices - Equilibrium prices adjust to eliminate all arbitrage opportunities Unlike CAPM, APT does *not* assume - Single-period investment horizon, absence of taxes, riskless borrowing or lending, mean-variance decisions

Example of Initial and Maintenance Margins: Initial Margin

Before a futures position can be opened, there must be enough available balance in the futures trader's margin account to meet the initial margin requirement Upon opening the futures position, an amount equal to the initial margin requirement will be deducted from the trader's margin account and transferred to the exchange's clearing firm - You to pay to play This money is held by the exchange clearinghouse as long as the futures position remains open

Performance Measures

Besides the CML, SML, and Fama French, there are "single index" measures for ex post asset performance: - Sharpe ratio - Treynor ratio - Modigliani Risk-Adjusted performance (M2) - Information ratio - Sortino ratio

How Accurate Are Beta Estimates?

Betas change with a company's situation Estimating a *future* beta - May differ from the historical beta RM represents the total of all marketable assets in the economy - Approximated with a stock market index - Approximated return on all common stocks Methods for estimating beta vary by time period, market index, return interval, etc. - Therefore, estimates of beta vary Regression estimates of true alpha and beta from the characteristic line are subject to error Portfolio betas more reliable than individual security betas

Present Value of Cash Flows as Rates Change

Bond Value = PV of coupons + PV of Par Bond Value = PV annuity + PV of lump sum As interest rates increase the PV's decrease Therefore, as interest rates increase, bond prices decrease and vice versa The discount rate, when valuing bonds, is called *Yield to Maturity or YTM*

Estimating Price Changes with Duration

Bond price changes are directly related to duration Modified duration indicates change in bond's price for a given change in interest rates

Fama French as you will use it for the projects

Brought risk free rate from one side to the other Positive alpha means person running the whatever is adding value??? and if negative that person is not adding value

Security Market Line

CML only applies to efficient portfolios The security market line (SML) depicts tradeoff between risk and expected return for individual securities and portfolios Under CAPM, all investors hold the market portfolio - Relevant risk of any security is, therefore, its covariance with the market portfolio SML starts with the market portfolio and brings in covariance to get risk and return - CAPM works much better when it comes to portfolios

CAPM

Calculate the SML for stocks - We will see if the regression intercept is equal to Rf or not - This done by comparing the Intercept to it's t-value - We will see if the error (residual term) is Normal - Compare the SLM returns to the actual returns Calculate the Characteristic Line for Stocks - Check on the alphas - Compare the Characteristic Line returns to the actual return

Building a Portfolio: An example

Chosen at (semi) random: - Walt disney - Snap on - Apple - GM - Walmart

Portfolio Expected Return

Computed as the weighted average of the individual security expected returns - Each asset "i" has a weight, "w", which represents the asset's value as a percent of the portfolio value - weight assigned to each of the expected returns, multiply them, and sum them all up

Security Co-movement - What measures securities' tendencies to move in the same or opposite directions?

Correlation (Pij) and covariance (standard dev ij) measure the tendency for security returns to move in the same or opposite directions

Asset Allocation: Correlation

Correlation among assets classes must be considered Correlation change over time For investors, allocation depends on - Time horizon - Risk tolerance Diversified asset allocation does not guarantee against loss

Derivatives Uses

Derivatives are *leveraged instruments* where participants put up a small amount of money and obtain the gain or loss on a much larger position Derivatives are used for *speculation* and for *hedging*

XLSTAT for CDF

Describing Data --> Histogram

Normality Tests in XLSTAT

Describing Data --> Normality Tests --> click Anderson-Darling and Jarque-Bera --> click normal QQ plots in Charts tab

Fama French and SML Tests

Do any of the mutual funds have a significant alpha based on either FF or SML results - No (what does this imply about manager skills?) What are the results of the Fama French Test - For each one, the Fama French fits is a very good fit as measured by R^2 Significant betas by fund: - PMEGX: All 4 factors - VTMSX: Mkt-RF, HML, SMB - PIODX: All 4 factors What are the results of the SML test - For each one, the SML fit is a very good fit as measured by R^2 - Significant betas by fund: - PMEGX: Both factors - VTMSX: Both factors - PIODX: Both factors

Implications of EMH

EMH does not imply that prices will always be "correct" or that all market participants are always rational Suppose that stock prices are rationally determined as the discounted present value of all future cash flows Future cash flows can only be estimated and are never known with certainty. There will always be errors in the forecasts of future sales and earnings. Moreover, equity risk premiums are unlikely to be stable over time Prices are therefore likely to be "wrong" all the time! What EMH Implies is that we never can be sure whether prices are too high or too low at any given time Some portfolio managers may correctly determine when some prices are too high and others too low. But other times such judgements will be in error

Market Anomalies: Exceptions that appear to be contrary to market efficiency

Earnings announcements affect stock prices - Effect must be separated into market and unexpected (unexpected requires price adjustment) - In efficient market, prices should adjust quickly - Research shows substantial post-announcement adjustment for some stocks (this lag is contrary to efficient market theory)

Earnings Momentum

Earnings momentum occurs when corporate earnings per share (EPS) growth is accelerating or decelerating from the prior fiscal quarter or fiscal year Earnings momentum typically coincides with accelerating revenues and expanding margins caused by increased sales, cost improvements, or overall market expansion it is also an investment strategy that attempts to invest in companies experiencing an increase in share price due to positive earnings momentum or growth in EPS

The Efficient Frontier: The Markowitz Output

Efficient Frontier: represents the set of all mean/variance efficient (optimal) portfolio - Optimal portfolio has maximum return for a given level of risk or minimum risk for a given level or return - Portfolios on the efficient frontier dominate all other portfolios - No portfolio on the efficient frontier dominates another portfolio on the frontier

Market Efficiency Forms

Efficient market hypothesis (EMH) - To what extent do securities markets quickly and fully reflect *particular* information? Three levels of Market Efficiency - Weak Form: market-level data - Semistrong form: public information - Strong form: all (nonpublic) information It's not illegal to trade on insider information, but it's illegal to tell anyone else about the information. They then have to disclose all insider info trading so it becomes public info

Derivatives Uses: Hedging

Entering into a derivatives contract to reduce the risk associated with positions or commitments in their line of business

Semistrong-Form Tests (EC)

Event studies: Empirical analysis of stock price behavior surrounding a particular event Examine Company-unique returns - Residual error between security's actual return and index model prediction: abnormal return - Abnormal Return: equation (pic) - Cumulative abnormal return (CAR) is sum of Arit over time Rit is the expectation from CAPM, E(Rit) is the return already earned

Market Anomalies: Low Price Multiple Ratios (e.g.) P/E, P/S, P/B)

Evidence that low price multiple stocks tend to outperform high price multiple stocks - Low price multiples imply undervalued Rigid adherence could lead to poor diversification

Calculating Expected Return

Expected return for asset "i" E(Ri) - Weighted average of all possible returns (Ri,s) included in the probability distribution - Each outcome weighted by probability of occurrence (Ps) - Referred to as expected return

Caps, Floors, and Collars

Financial institutions use options on interest rates to hedge interest rate risk - a *cap* is a call option on interest rates, often with multiple exercise dates (this will cap your interest rate risk) - a *floor* is a put option on interest rates, often with multiple exercise dates - a *collar* is a position taken simultaneously in a cap and a floor (usually buying a cap and selling a floor) (one of each) (These tend to be embedded in another derivative)

An overview of passive equity portfolio management strategies continued (OER)

For example, a $5 commission on a $500 trade represents a somewhat large 1% fee, whereas the same commission paid on a $5,000 trade represents a 0.1% fee. ETF expenses are usually stated in terms of a fund's operating expense ratio (OER) - The expense ratio is an annual rate the fund charges on the total assets it holds to pay for portfolio management, administration and other costs - Since the OER is an ongoing expense, it's relevant for all investors, but particularly for *long-term, buy-and-hold investors*

Average Returns

For investments over a given horizon, it is often of interest to compute a measure of average return over the horizon.

Fundamentally Weighted index

Fundamentally weighted indexes provide a benchmark for passively managed funds offered to investors seeking exposure to stocks based on fundamental characteristics Fundamentally-weighted indexes may be based on metrics such as: - Revenue - Dividend rates - Earnings - Book value

Forward rates are the rates expected to prevail in the...

Future! - Are not observable, but are commonly estimated from longer-term bong rates - For example, the rate on a 2 year bond can be decomposed into the current 1-year rate and one-year forward rates

Using Derivatives in Passive Equity Portfolio Management

Futures and options can help control cash inflows and outflows from the portfolio - *inflows* - index contracts allow time to make investment - *Outflows* - large planned withdrawal is made by selling securities, which causes an increase in cash holdings; futures can counterbalance this until the withdrawal Options can be sold to reduce weightings in sectors or individual stocks during rebalancing

Futures Markets

Futures contract trading occurs in trading "pits" using an *open-outcry auction* (shouting and yelling info lol) among *exchange members* - *floor brokers*: place trades for the public - *professional traders* trade for their own accounts - *position traders* take a position in the futures market based on their expectations about the future direction of the prices of the underlying assets - *day traders* take a position within a day and liquidate it before day's end - *scalpers* take positions for very short period of time, sometimes only minutes, in an attempt to profit from active trading

Example of a Currency Swap continued

General Electric will pay 1% on the ¥100 million loan, and the rate will be floating. This means if interest rates rise or fall, so will their interest payments. Hitachi agrees to pay 3.5% on their $11 million loan. This rate will also be floating. The parties could also agree to keep the interest rates fixed if they so desire. Over the next 10 years, each party will pay the other interest. For example, General Electric will pay 1% on ¥100 million quarterly, assuming interest rates stay the same. That equates equate to ¥1 million per year or ¥250,000 per quarter. - gets you out of currency exposure and gets you into a market you want to be in

31% R2 interpretation

Given the R2, 31% of the variability of the dependent variable AMZN is explained by the explanatory variable

Initial Construction and Rebalancing of the Portfolio continued

Given the rule of thumb that the portfolio should be rebalanced to its original mix when any given asset class moves more than 5% from its original value, the answer here would be yes. Rebalancing: - 70% stock implies $10M/($66.86 x 1.10)= 135,583 shares of VUG - 30% bond implies $10M/(99.76 x 0.9)=111,383 shares of AGG - As you originally owned 149,566 shares of VUG, you now need to sell 149,566 shares minus 135,593 shares or 13,973 shares of VUG - and buy 111,383 shares minus 100,241 shares or 11,142 shares of AGG

Cumulative Distribution Function: CDF

Gives the proportion of the population that has values below a certain value, e.g. 10% of the observations are below 3, 20% are below 8 and 50% are below 16 The CDF can be used to determine if the data follows a particular distribution, such as a normal

Details of HML and SMB

HML accounts for the spread in returns between value and growth stocks and argues that companies with high book-to-market ratios, also known as value stocks - *Companies with high book-to-market ratios (value stocks) outperform those with low book-to-market values (growth stocks)* SMB accounts for the spread in returns between small-cap companies and large-cap companies - *SMB argues that in the long-term, small-cap securities outperform large-cap securities*

Non-Standard View

How to handle significant skewness and kurtosis at the individual security level: - VaR and ES

If intercept value is 0.001 and SPY is 1.126,

If market goes up 1%, AMZN goes up 1.126%

Skewness Interpretation

If the skew is zero then the distribution is symmetric - These are for skew values -0.5<x<0.5 If the skew is negative, then the distribution is skewed to the left - These are for skew values <=-0.5 If the skew is positive, then the distribution is skewed to the right - These are for skew values >=0.5

Standardized Residuals plot

If you can draw an ellipse, it's good. - you can go from -0.05 to 0.05 and get a lot of the info within there

Efficient Markets

In perfectly efficient markets, all securities are priced correctly Information is key: - prices quickly and fully reflect all available information - Prices offer expected return consistent with risk level - Prices reflect past, current, and reasonably inferred information - Price adjustments are not perfect, but are unbiased its saying that if you want to make more money than the average, you need to take more risk than the average!

Asset Allocation: What are the two dimensions and what do Asset Classes Include?

Include two dimensions: - Diversifying between asset classes - Diversifying within asset classes Asset classes include: - Equities: foreign and domestic - Bonds - Commodities

Methods of Index Portfolio Investing

Index Funds: - Attempt to replicate a benchmark index Exchange-Traded Funds - An ETF, or exchange traded fund, is a marketable security that tracks an index of stocks, commodity, bonds - maximum time between one price and another is 15 seconds

Asset Allocation Strategies

Integrated Asset Allocation - capital market conditions - investor's objectives and constraints Strategic asset allocation - constant mix Tactical asset allocation - mean reversion - inherently contrarian (argument in terms of computing SML) Insured asset allocation - constant proportion

Asset Allocation Strategies

Integrated asset allocation - Capital market conditions - investor's objectives and constraints Strategic asset allocation - Constant-mix Tactical asset allocation - mean reversion - inherently contrarian Insured asset allocation - constant proportion

Reinvestment Risk

Interest-on-interest Reinvestment rate risk - Risk that future reinvestment rates will be less than the YTM when bond is purchased Reinvestment increase in importance as coupon or time to maturity (or both) increase - For long-term bonds, interest-on-interest can be most important part of total return - Zero-coupon bonds eliminate reinvestment rate risk

Portfolio Returns

Invest $V in two assets, A and B for 1 period Assume Xa+Xb=1 - Portfolio is defined by investment shares Xa and Xb

Investment Decisions - What do they involve? What do they focus on? What is their goal?

Involved Uncertainty Focus on *expected* returns (Future returns) - Estimates of future returns need to consider and manage risk - Investors often overly optimistic about expected returns Goal is to reduce risk without affecting returns - Accomplished by building a portfolio - Diversification is key

(2) Active Management Strategies: Credit Analysis

Involves detailed analysis of the bond issuer to determine expected changes in its default risk

CAPM: SML & Characteristic Line

Is the SML intercept = Rf? - For ADBE, no - For AOS and AMD, yes (close enough) Are the error terms Normal? - No Do the SML returns match the actual returns? - For ADBE, yes - For AOS and AMD, no Are the Characteristic Line alphas significant? - For ADBE, yes - For AOS, and AMD, no Do the CAPM returns equal the actual returns - For ADBE, yes - For AOS and AMD, no - lesson is that individual securities and they're not diversified

Building a Portfolio: US Stock and Non-US ETES

Keeping Disney but adding: - VGK: European ETF - VPL: Asia Pacific ETF - VWO: Emerging Markets ETF

Conditions for an Efficient Market (LIIIU)

Large number of rational, profit-maximizing investors - Actively participate in the market - Individuals cannot affect market prices Information is costless, widely available, generated in a random/ independent fashion Investors react quickly and fully to new information U.S. security markets are likely efficient It is not possible to earn above average returns without taking on above average risk

Pure Expectations Theory (Forward rates derived from _____ will equal _________)

Long-term rates are na average of current and expected future short-term rates - No other considerations matter According to the theory, *forward rates derived from current longer-term rates EQUAL expected future rates* (focus on bold) - Theory is not that forward rates will be correct, but that there is a relationship between them and current rates

Conclusion About Market Efficiency

Many market observers convinced of efficiency Others are convinced they can outperform market - This belief increases market efficiency Historical returns suggest market is efficient - Some anomalies appear to exist, but could result from insufficient tests or data - Recent bubbles and crashes at odds with efficient market, may support behavioral finance

Testing for Market Efficiency: Market Efficiency Tests are Tests for 2 Hypotheses

Market efficiency tests are tests of 2 hypotheses: 1. The market is efficient 2. Abnormal returns are measured correctly Market-adjusted returns Risk-adjusted returns - CAPM and market model - Match to similar firm - 3 and 4 factor models

Selecting an Optimal Portfolio of Risky Assets

Markowitz portfolio selection model - Assumes investors use only risk and return to decide - Generates a set of equally "good" portfolios - Does not address the issues of borrowed money or risk-free assets

APT Model: Most Important?

Most important are the deviations of the factor from their expected values - Expected return is directly related to sensitivity - CAPM assumes only risk is sensitivity to market Expected return-risk relationship for the APT can be described as: (picture) - Risk premium getting multiplied by the beta (influence on factors on return you're looking for)

It is not uncommon for financial returns to have the central part of the distribution to be _______ and the tails________

Normal; Not be.

For most dividends, this price adjustment is usually ____ observed amid the up and down movements of a normal day's trading.

Not! - it becomes apparent however, on the ex-dividend dates for larger dividends, such as the $3 payment made by Microsoft in the fall of 2004, which causes shares to fall from $29.97 to $27.34

Behavioral Finance: For example, an investor is presented with two scenarios - He will gain $500 over the course of the year, but at the end of the year he will lose $100 of his profit due to market volatility - The second option is the one in which he will gain $500 over the course of the year and at the end of the year, he will be able to retain $400 of his profits.

Now, the final outcome in both scenarios is a profit of $400, but since the second option is framed to present gain instead of loss, it will be preferred over the first one. This is due to the framing effect. - People can accept or reject a proposal depending on the way it is framed - Even though the payoff is same, they will agree to the proposals portrayed as risky gains, and will reject the ones portrayed at risky losses. This makes the investment decisions inaccurate and clouded by bias.

The normal _____ plot is better at finding deviations from normality in the center of the distribution, and the normal _______ plot is better at finding deviations in the tails

P-P Plot; Q-Q Plot

Example of Initial and Maintenance Margins continued

One day later, the price of August WTI drops to $38 a barrel Out speculator has suffered an open position loss of $2000 ($2*1000 barrels) and thus her account balance drops to $8000 Although her balance is now lower than the initial margin requirement, she did not get the margin call as it is still above the maintenance level of $6500

Continued Conclusions about Market Efficiency

Operationally efficient markets imply that *some* investors with the skill to detect a divergence between price and semistrong value earn profits - Excludes the majority of investors - Anomalies offer opportunities Controversy about the degree of market efficiency still remains Following the tenets of the EMH - that is, buying and holding a portfolio of broad-based low-cost market index funds - is still the best game in town Although the market may not always be rational in the short run, it always is over the long haul

Bond Price Changes

Over time, bond prices move toward face - on bond's maturity date, it must be worth its face value Bonds prices move inversely to market yields - Long term bond prices fluctuate more than short term *The change in bond prices due to a yield change is directly related to time to maturity and inversely related to coupon rate*

Passive versus Active Management

Passive Equity Portfolio Management: - Long term buy and hold strategy - Usually tracks an index over time - Designed to match market performance - Manager is judged on how well they track the target index Active equity portfolio management: - Attempts to outperform a passive benchmark portfolio on a risk-adjusted basis

Liquidity Preference Theory

Rates reflect current and expected short rates, plus liquidity risk premiums - Uncertainty increases with time - *Investors prefer to lend for short run, borrowers to borrow for long-run* *Liquidity premium is required to induce long-term lending* Derived forward rates do not equal expected future rates

Portfolio Risk - What is it measured by? What characteristics is portfolio variance impacted by?

Portfolio risk is measured by the variance or standard deviation of portfolio returns Portfolio variance is impacted by two characteristics: 1. The variance in returns for the individual assets included in the portfolio 2. The co-movement (covariance) of returns for the individual assets included in the portfolio - your concern should be issue of covariance; if they're all moving together at one time, it's not really a bad thing just depends on how much risk you want in the portfolio Portfolio risk is "not" the weighted average of individual security risks (only true when the correlation is 1) - The risk of individual securities is "not" the crucial consideration - Diversification almost always lowers risk - An asset with high standard deviation may add little to portfolio risk

Sector Rotation

Position a portfolio to take advantage of the market's next move, e.g. fundamental tilts (changing up the sectors you are invested in) Screening can be based on various stock characteristics: - Value - Growth - P/E - Capitalization - Sensitivity to economic variables

Capital Asset Pricing Model

Positive Rather than Normative - Describes how investors could behave, not how they should behave Builds on Markowitz portfolio theory Each investor is assumed to diversify his or her portfolio according to the Markowitz model

Riskiest? Premium, discount, or par

Premium because a higher coupon payment means higher investment risk - a bond is selling at a premium if it has a higher coupon than the YTM

Interest Rate Risk

Price Risk - Change in price due to changes in interest rates - Long-term bonds have more price risk than short-term bonds Reinvestment Rate Risk - Uncertainty concerning rates at which cash flows can be reinvested - Long-term bonds have more reinvestment rate risk than short-term bonds

Futures Markets Continued

Price volatility and trading interest determines which contracts are offered Profit pressures for derivatives exchanges to merge - CME Group Contains, CME, CBOT, NYMEX, and COMEX *Electronic Trading* is increasingly dominating 'pit' trading - Intercontinental Exchange only has electronic trading

Weak Form

Prices reflect all past price and volume data - History of price information is of no value in predicting price changes - Technical analysis, which relies on past price history, is of no value in assessing future changes in price Market adjusts or incorporates this information quickly and fully Believer in weak form could trade actively

Equity Portfolio Management Strategies

Questions to be answered: - What are the two generic equity portfolio management styles? - What are three techniques for constructing a passive index portfolio? - How does the goal of a passive equity portfolio manager differ from the goal of an active manager? - What is a portfolio's tracking error and how is it useful int he construction of a passive equity investment? - What is the difference between an index mutual fund and an exchange-traded fund? - What are the three themes that active equity portfolio managers can use? - What stock characteristics differentiate value-oriented and growth-oriented investment styles? - What is style analysis and what does it indicate about a manager's investment performance? - What techniques are used by active managers in an attempt to outperform their benchmark? - What are differences between the integrated, strategic, tactical, and insured approaches to asset allocation? - How can future and options be useful in managing an equity portfolio?

What is Financial Risk

Prospect of unexpected loss (or gain) or uncertainty of loss (gain) Financial risk taken is quantifiable - uncertainty is represented by a correctly fit PDF - Typically a normal distribution The correct PDF gives a complete representation of possible outcomes and their probabilities

Information Ratio (IR)

Relates performance to a designated benchmark Where, - mean active return often references as "alpha" (this is not Jensen's alpha) - Standard deviation of active return often referenced as "tracking error"

Term Structure of Interest Rates

Relationship between time to maturity and yield to maturity (yield curve) Yield curves - Graphical depiction of the relationship between yields and time to maturity - Observations involve tendencies rather than exact relationships - Blue expecting rates to rise into future - Light blue is rise a little then after 3 years theyll stay the same - red is slightly inverted, meaning 2 year money is highest rate until you get out to 30 years - tells you there might be a recession on the horizon

Interest Rate (and basis point and riskless rate)

Rental Rate for loanable funds basis point - 100 basis points equal one percentage point Riskless rate is foundation for other rates - Approximated by rate on Treasury securities - Other rates differ because of - Maturity differentials - Security risk premiums

An overview of passive equity portfolio management strategies

Replicates the performance of an index May slightly underperform the target index due to fees and commissions Commissions: - The more frequently you trade, the more you'll pay in total commissions - Because commissions are typically a flat fee no matter how large or small the trade, the percentage cost per trade will be larger for smaller trades and smaller for larger trades

CAPM's Expected Return-Beta Relationship

Required Rate of return on asset (ki) is composed of: - Risk-free Rate (RF) - Risk Premium (ßi [ E(RM) - RF ] ) - Risk Premium adjusted for specific security: Ki=RF+ßi[E(RM)-RF] The greater the systematic risk, the greater the required return

Risk-Free Asset, Borrowing, Lending

Risk Free Asset: - No correlation with risky assets - Usually proxied by a Treasury security Adding a risk-free asset extends and changed the efficient frontier Risk-free investing is "Lending" because investor lends money to issuer - Investors can lend at the risk-free rate by buying government bonds With borrowing, investor no longer restricted to personal wealth

Problems with APT

Risk factors are not specified ex ante - To implement APT model, need factors that account for differences in security returns - CAPM identifies market portfolio as single factor Studies suggest certain factors are reflected in security returns - With Fama French, it is market capitalization and book value vs. market value - Book value vs. market value Bot CAPM and APT rely on unobservable expectations (Farma French does not)

Dealing with uncertainty

Risk that an expected return will not be realized - think of returns as being part of a PDF, CDF, some return distribution Investors must think about return *distributions* Probabilities weight outcomes - Assigned to each possible outcome to create a distribution - History provides guide but must be modified for expected future changes - Distributions can be discrete or continuous

Risk-Free Lending/Borrowing

Risk-free asset can be combined with any portfolio in the efficient set AB - RF to T are lending portfolios - T to L are borrowing portfolios Portfolios on line RF to L dominate all portfolios below (even efficient return) - Line drawn so it's tangent to the efficient frontier; everything along efficient frontier is superior T=optimal portfolio

Comparing Performance Measures

Sharpe ratio evaluates performance on basis of both return and diversification, i.e. total risk If portfolio is completely diversified, Sharpe, Treynor, M2, and Jensen agree on ranking - If not diversified, Jensen and Treynor can rank portfolio(s) higher than Sharpe - hes not a good fan of jensen's alpha - Sortino is good measure (volatility on the negative side) M2 produces percentage return Sortino useful measure when return distributions are not symmetric - Looking for sustainable ratios, low PE and low priced book, etc? - good way of picking up stocks in terms of value - see if any portfolios are generating alpha or have a negative alpha - Is it small cap or large cap or mid cap - premium should look good

Regression of AMZN by SPY

Should be within the Confidence Interval lines - we'd expect most of the data within SP and MSFT to be within 95% confidence interval (the lines)

Market Anomalies: January effect

Small-firms tend to produce abnormal returns in January

If the Return data is normal, and using current financial theory, the _____ is a sufficient statistic to trade off return and risk

Standard Deviation. - If the returns are not normal, additional statistics may need to be used - Skewness and Kurtosis are the stats to start with

Weak-Form Tests (ST)

Statistical tests for independence (randomness) of stock price changes - if independent, trends in price changes cannot be profitably exploited Test specific trading rules that attempt to use past price data - Account for costs, compare to buy-and-hold Statistical dependence no the same as economic dependence

Minimum variance Portfolio Example using MV Formula to arrive at 1st MV portfolio

Stock A is N (4%, 6%) Stock B is N (8%, 15%) Correlation between A & B is -0.70 Plugging in the values, we get x=74.42%. This means, to achieve a minimum variance portfolio that is invested in Stocks A and B, you should invest 74.42% in Stock A and 25.58% in Stock B

Standard Stock Return Model

Stock Return = Risk Free Return + Sensitivity of Stock Return to Market Return * Market Return + Idiosyncratic Return - Risk Free Return: Return on short term treasuries - Sensitivity of stock return to market return: riskiness of the stocks return vs market return - Idiosyncratic return Sensitivity of Stock Return to Market Return is a measure of volatility and is the only risk you are directly compensated for - Equity Risk Premium - The greater the sensitivity, the greater the expected return and vice versa This measure of volatility assumed normality, so you get paid for any standard deviation risk you take on Any other risks, such as skewness or kurtosis are in Idiosyncratic Returns And this risk you are not compensated for

Strong Form Evidence

Test performance of groups which have access to "true" nonpublic information - Corporate insiders have valuable private information - Evidence that many have consistently earned abnormal returns on their stock transactions Insider transactions must be publicly reported - Information can mislead investors

Problems with VaR

The "deeper in the tail" losses at the 95th or 99th percentile are not accounted for - Expected Shortfall does account for these

Option Markets

The *Chicago Board of Options Exchange (CBOE)* opened in 1973 as the first exchange devoted solely to the trading of stock options Options on futures contracts began trading in 1982 An *American option* can be exercised at any time before (and on) the expiration date A *European option* can be exercised only on the expiration date The trading process for options is similar to that for futures contracts

Rebalancing of the Portfolio Continued

The 3rd set of monthly prices show that neither price moved from the end of the prior quarter There are no further gains or losses as prices did not move from quarter-end to quarter-end - if prices had moved from quarter to quarter, any gains and/or losses would need to be taken and recorded if a rebalance was required - If following a buy-and-hold strategy, you would record any gains and/or losses as the difference in the purchase price minus the ending price of the ETF -If you followed another strategy so that by 3rd quarter end you had unrecorded gains and/or losses, now will be the time to record them

Average Returns: Arithmetic Average

The average wealth over the period

Average Returns: Geometric Average

The change in wealth over the period can also be calculated with =geomean in excel

Sharpe Ratio

The classic return-risk trade off measure - Based on the CML - Equals excess return divided by standard deviation - Higher the ratio --> better the performance - Provides a ranking measure for portfolios

The contribution of a security to the risk of a diversified portfolio should be rewarded by _______, not the _______

The market; total risk of the security (this contribution is measured by the beta of the security)

Jensen's Alpha

The estimated alpha coefficient in pic is a means to identify superior or inferior portfolio performance - CAPM implies alpha is zero - Measures contribution of portfolio manager If alpha>0 (<0,=0), risk-adjusted performance is superior (inferior, equal) to market

Options: fees

The fee you are paying to buy the call option is called the premium (it's essentially the cost of buying the contract which will allow you to eventually buy the stock or security) In this sense, the premium of the call option is sort of like a down-payment like you would place on a house or car. When purchasing a call option, you agree with the seller on a strike price and are given the option to buy the security at a predetermined price (which doesn't change until the contract expires)

Modeling in Finance/ The goal of all models is...

The goal os all models is *decision*, not probability it is an error to conflate in any finance model Statistical announcements must be in a form so they can be *verified* (by comparison to reality) Models which fail are to be expunged - No explicit parameters, only observables and assumptions - The model is now ready to be tested against new observables, i.e. tested against reality

Calculating Portfolio Risk: Generalizations

The lower the correlation between securities, the better As the number of securities increases: - Number of covariances grows quickly - The importance of covariance relationships increases - The importance of each individual security's risk decreases

Example of Initial and Maintenance Margins: Maintenance Margin

The maintenance margin is the minimum amount a futures trader is required to maintain in her margin account in order to hold a futures position - The maintenance margin level is usually slightly below the initial margin If the balance in the futures trader's margin account falls below the maintenance margin level, she will receive a margin call to top up her margin account so as to meet the initial margin requirement

Quantile-Quantile (QQ) Plots

The quantiles of the first data set (such as returns) against the quantiles of the second data set (normal distribution) - Quantile = fraction or percent of points below a given value Helps us assess if a data set came from some theoretical distribution such as Normal or Exponential If data has same distribution as the assumed distribution, points will fall on the reference line

Notice That...

The return of holding the bond during the first year is 1% The return of holding the bond during the second year is 3%

Zero Coupon Rates and Forward Rates : Suppose a hypothetical two-year bond is yielding 10%, while a one year bond is yielding 8%

The return produced from the two-year bond is the same as if an investor receives 8% for the one-year bond and then rolls it over into another one year bond at 12.04%

Benefits of Diversification

The risk (variance) on any individual investment can be broken down into two sources: - Firm specific risk (only faced by that firm) - Market wide risk (affects all investments) Firm-specific risk can be reduced, if not eliminated, by increasing the number of investments in your portfolio (i.e. by being diversified). - Market wide risk cannot Free lunch from diversification (less risk without giving up return)

Differentiating Factors in Constructing Market Indexes: The sample

The sample: - Size - Breadth (be representative) - source

More on Options

The underlying asset on a *stock option* is the stock of a publicly traded company The underlying asset on a *stock index option* is the value of a major stock market index (e.g. DJIA or S&P500) The underlying asset on a *futures option* is a futures contract *Credit spread call options* - the value of a *credit spread call option*(transfers credit risk from one party to another) increases as the default (risk) premium or yield spread on a specified benchmark bond of the borrower increases above some exercise spread (spread and price move in opposite directions) A *digital default option* pays a stated amount in the event of a loan default

Systematic and Unsystematic Risk Calculation (Total Risk = ? and Total Variance = ?)

The variance (risk) of a portfolio, or a single security, consists of both systematic risk and unsystematic risk - Systematic Risk = Market Risk -Unsystematic Risk = firm risk, idiosyncratic risk

At the end of the period, the investments in A and B grow to/ Simple portfolio return

The weighted average of the simple returns on the individual assets - Examples in slides again

McCauley Duration

The weighted average term to maturity of the cash flows from a bond The weight of each cash flow is determined by dividing the present value of the cash flow by the price

Factor Focused Indexes

These methodologies can offer higher potential return based on aggregate fundamental measures of the market versus market capitalization The excess return of such strategies can be at least partially explained by time-varying exposures to various risk factors such as size and style

Market Anomalies: Data snooping/data mining

This is a misuse of data analysis to find patterns in data that can be presented as statistically significant when in fact there is no real underlying effect Done by performing many statistical tests on the data and *only paying attention to those that come back with significant results,* instead of stating a single hypothesis about an underlying effect before the analysis and then conducting a single test for it

Calculating Portfolio Risk: 3 Inputs and the Goal (CVP)

Three inputs to calculate portfolio risk: 1. Variance (risk) of each security (computed first) 2. Covariance between each pair of securities (computed second) 3. Portfolio weights for each security (come up with these) Goal: select weights to determine the *minimum variance* combination for a given level of expected return

Constant Weighting Continued

To determine the percentage allocated to each asset class, some level of risk tolerance is used - a 70/30 stock/bond split would indicate more tolerance for risk than a 50/50 split There are no hard-and-fast rules for timing portfolio rebalancing under constant-weighting asset allocation However, a common rule of thumb is that the portfolio should be rebalanced to its original mix when any given asset class moves more than 5% from its original value Constant weighting is often seen as a contrarian strategy

Estimating the SML

Treasury bond rate used to estimate RF Expected market return unobservable - Often estimated using past market returns and taking a mean value - of course not everyone behaves this way Estimating security betas is difficult - Beta is only company-specific factor in CAPM - Beta estimation requires asset-specific forecast

Variance of Portfolio with two assets

Two asset portfolio equation

Two Period Returns Formula

Two month relative return = the product of two one-month relative returns - Examples of all of these in slides

Term Structure of Interest Rates: Upward-sloping yield curve

Typical, interest rates rise with maturity

Example of Initial and Maintenance Margins continued again

Unfortunately, on the very next day, the price of August WTI crashed further to $35, leading to an additional $3000 loss on her open WTI position With only $5000 left in her trading account, which is below the maintenance level of $6500, she received a call from her broker asking her to top up her trading account back to the initial level of $9000 in order to maintain his open WTI position this means that if the speculator wishes to stay in the position, she will need to deposit an additional $4000 into his trading account Otherwise, if she decides to quit the position, the remaining $5000 in his account will be available to use for trading once again

Managing Risk in a Portfolio

Unlike with a security, it is possible to manage portfolio risk without resorting to VaR and ES When assembling a portfolio, compute the skewness and kurtosis of each security A portfolio can include securities that have significant skewness and kurtosis as long as there are some securities normally distributed

Term Structure of Interest Rates: Downward-sloping yield curves

Unusual, predictor of recession?

Mallows Coefficient

Used in Multiple Regression

Calculating Risk

Variance and standard deviation used to quantify and measure risk - Measure dispersion about the mean - Variance of returns is in percent squared - Standard deviation of returns is the square root of variance and is measured in percent

Mean Squared Error (MSE)

Variance of Residuals - This is where skew and kurtosis sit

Assembling an Approx. Normal Portfolio

Weight each security as you wish Do the normality tests on the proposed portfolio if there is a split decision with the tests, you can go forward with the current weights or consider changing them

Expected Tracking Error Between the S&P 500 Index and Portfolio Samples of Less Than 500 Stocks

What you see if you have over 100 stocks; with 100 or less stocks tracking error is up to 4%

Dividend Payments: Price Adjustment

When a dividend is paid, several things can happen The first is changes to the price of the security - On the ex-dividend date, the stock price is adjusted downward by the amount of the dividend by the exchange The adjusted closing price is often used when examining historical returns or performing a detailed analysis on historical returns when distributions are made, the adjusted closing price calculations are quite simple. For cash dividends, the value of the dividend is deducted from the last closing sale price of the stock

When does diversification pay?

With perfect positive correlation, risk is a weighted average, therefore, no diversification benefit With perfect negative correlation, expected return can be assured With zero correlation, significant risk reduction can be achieved - Cannot eliminate risk Negative correlation or low positive correlation is ideal, but unlikely

Why Use a Laddered Strategy

a bond ladder is a strategy that attempts to minimize risks associated with fixed-income securities while managing cash flows for the individual investor

Futures Contracts: Initial Margin

a deposit required on futures trades to ensure that the terms of the contracts will be met

Forwards and Futures: Futures Contract.

a standardized, exchange-traded version of a forward contract Futures contracts *differ* from forwards in that futures are: - Marketable - Have no default risk - Employ margin requirements and daily marking the market - Margin requirement is a performance bond posted by a buyer and a seller of a futures contract

Forwards and Futures: Spot Contract

an agreement to transact involving the immediate exchange of assets and funds

Derivatives Uses: Speculation

buying or selling a derivative contract in order to earn a *leveraged* rate of return (profiting from market changes)

Adjusted R squared takes into account...

degrees of freedom (as the number of variables goes up, the more the R squared gets dinged)

Classic Passive Management Strategies: Barbell Strategy

differs from the laddered strategy in that less investment is made in the middle maturities

Classic Passive Management Strategies: Laddered Strategy

distributes fixed income dollars throughout the yield curve

Fama French model can be used to

evaluate a portfolio manager's returns. (can attribute the factors to tilt towards small cap, towards growth, etc) - If the portfolio's performance can be attributed to the three factors, then the portfolio manager has not added any value or demonstrated any skill - This is because of the three factors can completely explain the portfolio's performance then none of the performance can be attributed to the manager's ability - a good portfolio manager should add to performance by picking good stocks. This outperformance is known as "generating alpha"

Adjusting for Inflation

example in slides

Bond Prices: Relationship Between Coupon and Yield

if YTM = coupon rate, then par value = bond price If YTM > Coupon rate, then par value> bond price - Selling at a discount, called a discount bond If YTM < coupon rate, then par value < bond price - Selling at a premium, called a premium bond

Constant Weighting

if declining in value purchase more and if asset is increasing you sell it. Need to keep weights the exact same - Strategic asset allocation generally implies a buy-and-hold strategy, even as the shift in values of assets causes a drift from the initially established policy mix - For this reason, you may prefer to adopt a constant-weighting approach to asset allocation. With this approach, you continually rebalance your portfolio - For example, if one asset is declining in value, you would purchase more of that asset. And if that asset value is increasing, you would sell it

Shapiro-Wilk Test... p value

if less than 0.05, it's significant - if significant, the residuals do not follow a normal distribution

Sortino Ratio: Alternative Version

in either form, it's a useful measure when return distributions are not symmetric MAR=Minimal Acceptable Return - look at portfolio and subtract mar away then divide that by downside deviation - Rmar is your statement/minimum amount of money you want to make -from lognormal you can calculate the mar

Stock Splits and the DJIA

in the past, the DJIA high-priced stocks did stock splits to keep their share prices down, reducing their relative influence in the average

If your residuals are +/-3...

it means that something extremely unusual is happening

Stock Split's primary motive is to

make shares seem more affordable to small investors even though the underlying value of the company has not changed - This has the practical effect of increasing liquidity in the stock

All interest rates are describes according to the following formula

rp contains all the risk premiums associated with features such as time to maturity, liquidity, credit quality, etc.

Residuals are where...

skew and kurtosis lies

Market Anomalies: Size Effect

small firms tend to have higher risk-adjusted returns than large firms

The reason for the adjustment is that

the amount paid out in dividends no longer belongs to the company and this is reflected by a reduction in the company's market cap

Mean Absolute Percent Error (MAPE)

the average of the absolute differences between the forecast and actual values, expressed as a percent of actual values =Average(|Actuals-Fcsts|/Actuals|)*100

If residual is less than -2...

the cell's observed frequency is less than the expected frequency

Tracking Error

the difference between a portfolio's returns and the benchmark or index it was meant to mimic or beat - Calculated same way as STDEV (I think?)

The dividend belongs to...

the individual shareholders. - for those purchasing shares after the ex-dividend date, they no longer have a claim to the dividend, so the exchange adjusts the price downward to reflect this fact.

Futures Contracts: Maintenance Margin

the margin a futures trader must maintain once a futures position is taken - If losses occur such that margin account funds fall below the maintenance margin, the customer is required to deposit additional funds in the margin account to keep the position open

If residual is greater than 2

the observed frequency is greater than the expected frequency

Futures Contracts: Open Interest

the total number of the futures, put options, or call options outstanding at the beginning of the day

Futures Contracts: Clearinghouse

the unit that oversees trading on the exchange and guarantees all trades made by the exchange

Sharpe Adjusted for significant skewness and kurtosis

what happens if you have skewness and kurtosis? There are adjustments! Lambda is the value for the sharpe Tau is the skewness value Kappa is the kurtosis value If Tau is negative, it reduces sharpe ratio and kappa also reduces sharpe ratio - Kappa ALWAYS reduces sharpe ratio, Tau only reduces if negative

After closer examination of the bid/ask spreads..

you learn that ETF B has a much larger spread than ETF A. - This tells you that in a roundtrip trade, you're estimated to lose 1.29% more of your investment in ETF B and ETF A because of the difference in spreads Assuming you hold each ETF for one year, pat zero commissions and all other costs remain constant, ETF A looks to have a lower cost despite its higher expense ratio Furthermore, the 0.03% spread of ETF A also indicates that it likely has a higher trade volume than ETF B, which might make ETF A preferable for liquidity reasons as well - most liquid measure in the world is US Treasuries