Lecture 1 Investment Theory

The Investment Process

1. Define the investment objectives and constraints:• Maximize return • Maximize risk-adjusted return: sharp ratio 2. Evaluation and selection of securities: • Asset allocation vs. security selection (Top-down- 50% stocks/ 50% bonds, involves looking at big picture economic factors to make investment decisions, vs. Bottom-up- looks at company-specific fundamentals like financials, supply and demand, and the kinds of goods and services offered by a company.) asset allocation: Allocation of an investment portfolio across broad asset classes. "Top-down" portfolio construction starts with asset allocation. A top- down investor first makes this and other crucial asset allocation decisions before turning to the decision of the particular securities to be held in each asset class. security selection: Choice of specific securities within each asset class, In contrast to top-down portfolio management is the "bottom-up" strategy. In this process, the portfolio is constructed from securities that seem attractively priced without as much concern for the resultant asset allocation Such a technique can result in unintended bets on one or another sector of the economy. For example, it might turn out that the portfolio ends up with a very heavy representation of firms in one industry, from one part of the country, or with exposure to one source of uncertainty. However, a bottom-up strategy does focus the portfolio on the assets that seem to offer the most attractive investment opportunities. • Technical vs. fundamental vs. "quantitative" analysis Fundamental: review a company's financial statements, historical data, investor conference- long term, DCF models Technical: s historical returns, stock prices, and volume of trades to chart patterns in securities movement. Quantitative: algorithm, focuses on using simple financial ratio calculations to gain insight into the valuation of a specific company or broad market. While fundamental analysis attempts to show the intrinsic value of a security or specific market, technical data is meant to provide insight into the future activity of securities or the market as a whole • Other Issues: diversification, taxes, income vs. growth (dividend preference) , tax law harvesting 3. Monitor performance relative to initial objectives and constraints buy/sell to keep allocation

Security Returns: Example

12-10/10= 20 (12+0.5)-10/ 10 = 25% What if the dividend is paid at the beginning of the quarter? It depends if you cash out it looks like above but if you reinvest different: higher return

Inflation - Another example

2nd option

Mutual Funds and Alternatives: A First Look

Active mutual funds:• Charge relatively high fees• Perform poorly relative to benchmarks (broad-based indexes)- after fees Alternatives to traditional mutual funds:• Index funds/passive funds:• Charge very low fees and hence may outperform mutual funds after adjusting for costs ETFs:• Started with SPDR in 1993• Unlike mutual funds, they can be traded intra-day• Low fees (bid-ask spread can be important for less liquid ETFs)

What is an Investment

An investment is the current commitment of money or other resources in the expectation of reaping future benefits You sacrifice something of value now, expecting to benefit from that sacrifice later. Basic principles of investing: More money is better • Money now is better than money in the future(time value of money)• We dislike uncertainty/risk

Arithmetic vs. Geometric Average

Arithmetic Average Return (often used for forecasting futurereturns over the same horizon): R=(R1+R2...)/N R1= monthly return N= months Example: Assume annual returns are normally distributed with mean 8% and standard deviation 20% and we observe 100 years of data. The arithmetic average is a good estimate of expected return next year: what future return do we expect

Annual Risk and Return, 1991-2019

Arithmetic Average greater than Geometric Deviations between the two are larger when more volatile

Arithmetic vs. Geometric Average

Arithmetic average is easy to calculate, but not always a good measure of multi-period performance, especially if volatility is high. Example: This suggests that the Arithmetic Average is upward biased when measuring multi-period cumulative returns In finance, the time horizon refers to the length of time over which an investment is held or the period of time during which returns are calculated. When we say that arithmetic returns measure the same time horizon, it means that the calculation is based on a fixed time period, and the length of this period is the same for all the returns being measured. For example, if we are calculating the arithmetic returns of a stock over the last year, we would measure the return for each month or quarter, and then average those returns to get the total return for the year. In this case, the time horizon is one year, and all the returns being measured are for the same time period. It's important to note that when comparing returns, it is essential to ensure that they are calculated over the same time horizon. This is because different time periods can have different levels of volatility, and comparing returns over different time horizons could give a distorted picture of performance. For example, comparing the returns of a stock over a year with the returns of another stock over a month would not be a fair comparison because the two time periods are vastly different. Geometric Average Return equals the single-period return that, when compounded, results in the same cumulative performance as the actual sequence of returns (1+r)= (1+r1) * (1+r2) Thus, Geometric Average accurately measures changes in wealth and is a good measure of past long-term performance. The main difference between arithmetic and geometric averages is that geometric averages take into account the effect of compounding. Compounding is the process by which investment returns are reinvested back into the investment, so that returns are earned on both the initial investment and the accumulated returns. By contrast, arithmetic averages do not take compounding into account and measure the average return over a certain time period. Because geometric averages measure the compounded growth rate of an investment, they can be used to calculate the total return of an investment over a given time period, taking into account the effects of compounding. This makes them useful for measuring the long-term performance of an investment.

Investment Companies

Collect funds from individuals, pool those funds, and invest in a wide range of securities. They provide: • Record keeping : keep track of profits/losses for taxes • Diversification and divisibility benefits: more pooled assets, easier to diversify fractional shares of mutual fund, fractional shares of their holdings • Professional management (typically)- active manager • Reduced transaction costs, large trades, reduce cost on exchange Net Asset Value (NAV) is one share of an investment fund: Market Value- Liabilities / Shares Outstanding Example: A fund has a portfolio currently worth $370 million and liabilities of $13 million. If the fund has 10 million shares outstanding, what is the net asset value of the fund? 370-13/ 10 = 35.7 when you buy a mutufak fund, you buy shares at the NAV

Equity

Common Stock: - Shares of ownership in a firm • Voting rights • Dividends - Residual claim- bankruptcy equity holders gets claim on assets Residual claim means stockholders are the last in line of all those who have a claim on the assets and income of the corporation. In a liquidation of the firm's assets, the shareholders have claim to what is left after paying all other claimants, such as the tax authorities, employees, suppliers, bondholders, and other creditors. In a going concern, shareholders have claim to the part of operating income left after interest and income taxes have been paid. Management either can pay this residual as cash dividends to shareholders or reinvest it in the business to increase the value of the shares. - Limited liability- equity holder not liable to pay debt holder Limited liability means that the most shareholders can lose in event of the failure of the corporation is their original investment. Shareholders are not like owners of unincorporated businesses, whose creditors can lay claim to the personal assets of the owner— such as houses or cars. In the event of the firm's bankruptcy, corporate stockholders at worst have worthless stock. They are not personally liable for the firm's obligations: Their liability is limited. Common stocks, also known as equity securities, or equities, represent ownership shares in a corporation. Each share of common stock entitles its owners to one vote on any matter of corporate governance put to a vote at the corporation's annual meeting and to a share in the financial benefits of ownership. A corporation is controlled by a board of directors elected by the shareholders. The board, which meets only a few times each year, selects managers who run the firm on a day-to-day basis.We noted in Chapter 1 that such separation of ownership and control can give rise to "agency problems," in which managers pursue goals not in the best interests of shareholders. However, several mechanisms are designed to alleviate these agency problems. Among these are compensation schemes that link the success of the manager to that of the firm • Preferred stock (almost like a bond): - Shares of ownership in a firm • No voting rights • Fixed dividends that accumulate if not paid (bond-like feature)-actually commit to payments Preferred stock has features similar to both equity and debt. Like a bond, it promises to pay a fixed stream of income each year. In this sense, preferred stock is similar to an infinite-maturity bond, that is, a perpetuity. It also resembles a bond in that it does not give the holder voting power regarding the firm's management.Preferred stock is nevertheless an equity investment. The firm has no contractual obligation to make preferred dividend payments. Instead, preferred dividends are usually cumulative; that is, unpaid dividends cumulate and must be paid in full before any dividends may be paid to holders of common stock. Preferred stock also differs from bonds in terms of tax treatment. Because preferred stock payments are treated as dividends rather than as interest on debt, they are not tax-deductible expenses for the firm. Residual claim - Limited liability The performance of equity investments, therefore, is tied directly to the success of the firm and its real assets.

Security Returns

Dividend Yield+ Capital Gains = Holding Period Return

Classes of Securities

Fixed Income - Money Market Treasury Bills, CDs, Commercial Paper, Eurodollars, Repurchase Agreements• Fixed Income - Capital MarketTreasury Notes & Bonds, Corporate Bonds, Municipal Bonds, Federal Agency Debt, Securitized Assets, Eurobonds• both of these same category also called debt- fixed stream of income or a stream of income that is determined according to a specified formula the investment performance of debt securities typically is least closely tied to the financial condition of the issuer. Equity Common Stock, Preferred Stock• Derivatives Options, Forwards, Futures, Swaps, etc.

Taxes

If we let t denote the investor's combined federal plus local marginal tax rate and rtaxable denote the total before-tax rate of return available on taxable bonds, then rtaxable(1 − t) is the after-tax rate available on those securities. If this value exceeds the rate on municipal bonds, rmuni, the investor does better holding the taxable bonds.

Inflation (w/o Dividends)

Inflation = CPI = set basket of goods tracked with price red shows the growth of CPI

Impact of Fees: Example

John faces the following investment choices: • Choice A: Average actively managed fund:• 0.84% annually • Choice B: Average passively managed fund:• 0.14% annually For simplicity assume that both funds deliver 6% annually. What is the difference between the final investment value of the two choices if John were to invest 100,000 for 30 years? 100000 x (1.06-0.0084)^30 = 452.394 100000 x (1.06-0.0014)^30 = 552,022 difference almost 100k active- higher fees than passive

Most Common Types of Investment Companies

Managed: Closed-end funds- stocks/bonds • Fixed number of shares - never created or destroyed • Traded on a secondary market, individual traders can trade on NYSE, not the company (not only at the end of day) • Prices generally lower than the NAV (puzzle?)liquidity, harder to sell, arbitrage opportunity or investors weary of manager/past performance Managed: Open-end funds (mutual funds) • Shares issued and redeemed directly from the investment company at NAV- not traded in the open market, must be sold at NAV regulation • Number of shares can change daily • Do not trade on the market (bought/sold only at the end of the day)- sell it back to the investment company Sometimes managed: Exchange-Traded Funds (ETFs) (combo of the two) • Traded like stocks (secondary market) • Replicate the return on an index, industry, or specific investment strategy • Shares can be created and redeemed - price close to the NAV- arbitrage easier to impose cause shares can be created/destroyed- when demand is higher, price goes up, more shares created, closer to NAV Hedge Funds (technically not investment companies)• Lightly regulated, open only to wealthy individuals little regulations, only to accredited investors

Bond Market Indexes...

Most known:- Bloomberg Barclays • US Aggregate Bond Index• Global Aggregate Bond Index• US Treasury Index• High-Yield Index• ... (Bank of America) Merrill Lynch • Global Bond Index• High-Yield Master II Citi • World Government Bond Index• World Broad Investment-Grade Bond Index (WorldBIG) Problem: Bonds are often infrequently traded (illiquid)- Prices sometimes must be estimated from models index maintained by company heterogeneity vs few types of stocks options: different maturity/dates/interest rates for bonds

Mutual Fund Fees and Expenses

One-time fees: (once) - Front-end load (entry fee) - Back-end load (exit fee / redemption fee) fraction of total amount you invest Annual fees: (recurring costs) "Expense ratio" includes- Distribution costs paid by the fund (12 b-1 charges) - costs to market fund - Operating expenses (salaries, data, etc.) How do we account for fees? XT= X0 x (1-Entry Fee) x (1 + r -annual fees) ^t. x (1- exit fees) X0dollar amount invested r annual mutual fund return T holding period in years

Fixed Income- Capital Markets

Over one year to maturity, various degrees of default risk• Types of securities: • Treasury Notes & Bonds: pays coupon payments • Issued by US Treasury with maturities of up to 10 years for notes and between 10 and 30 years for bonds (low risk of default) • Make semiannual interest payments • Corporate Bonds • Different maturities, default risk and payment structure• Municipal Bonds- infastructure prokects • Issued by state and local governments • Tax -exempt status They are similar to Treasury and corporate bonds, except their interest income is exempt from federal income taxation. Capital gains taxes, however, must be paid on munis if the bonds mature or are sold for more than the investor's purchase price. • Federal Agency Debt • Issued by government agencies (e.g. Freddie Mac, Fannie Mae)• Some government agencies issue their own securities to finance their activities. Although the debt of federal agencies was never explicitly insured by the federal government, it had long been assumed that the government would assist an agency nearing default. Securitized Assets • E.g., claims on a pool of mortgages (mortgage-backed securities) a mortgage-backed security is either an ownership claim in a pool of mortgages or an obligation that is secured by such a pool. group a bunch of mortgages and sell it as one

price-weighted average.

Portfolio: Initial value = $25 + $100 = $125 Final value = $30 + $90 = $120 Percentage change in portfolio value = −5/125 = −.04 = −4% Initial index value = (25 + 100)/2 = 62.5 Final index value = (30 + 90)/2 = 60 Percentage change in index = −2.5/62.5 = −.04 = −4% Notice that price-weighted averages give higher-priced shares more weight in determining the performance of the index. For example, although ABC increased by 20% while XYZ fell by only 10%, the index dropped in value. This is because the 20% increase in ABC represented a smaller dollar price gain ($5 per share) than the 10% decrease in XYZ ($10 per share). The "Dow portfolio" has four times as much invested in XYZ as in ABC because XYZ's price is four times that of ABC. We conclude that a high-price stock can dominate a price-weighted average.

Inflation

Real Returns (r) depend on what money can buy over time.• Part of your Nominal Return (R) is offset by a reduction in the purchasing power of dollars (i): • Note: Tax codes do not account for inflation, so you are taxed on your nominal return (including the portion that is compensation for inflation) Calculate Return, then calculate after tax return, then subtract inflation to get real return

Background

Real assets (the land, buildings, equipment, and knowledge)• Tangible and liquid, actually produce things, units of economy, Financial assets (stocks, bonds, derivatives) - represent claims on the cashflow of real assets, While real assets generate net income to the economy, financial assets simply define the allocation of income or wealth among investors. • Financial markets and the economy: • The informational role of financial markets: price/cost info, tells us performance of a company, and future prospects : they're output is more valuable, play a major role in the allocation of capital in market economies, directing capital to the firms and applications with the greatest perceived potential. • Consumption timing: helps investors put money today for future consumption , In high-earnings periods, you can invest your savings in financial assets such as stocks and bonds. In low-earnings periods, you can sell these assets to provide funds for your consumption needs.By so doing, you can "shift" your consumption over the course of your lifetime, thereby allocating your consumption to periods that provide the greatest satisfaction. • Allocation of risk• financial markets allow you to invest to your risk factors Separation of Ownership and Management: if some stockholders decide they no longer wish to hold shares in the firm, they can sell their shares to other investors, with no impact on the management of the firm. Thus, financial assets and the ability to buy and sell those assets in the financial markets allow for easy separation of ownership and management. Players in the financial markets: • Firms are net demanders of capital. They raise capital now to pay for investments in plant and equipment. The income generated by those real assets provides the returns to investors who purchase the securities issued by the firm. Households (individuals): Households typically are suppliers of capital. They purchase the securities issued by firms that need to raise funds. • Government taxes and provides social services : Governments can be borrowers or lenders, depending on the relationship between tax revenue and government expenditures.

21

Rebalancing: As the prices of individual stocks in the index change, the fund would need to constantly rebalance the portfolio to ensure that each stock has an equal weight in the portfolio. This requires significant trading activity and could result in higher transaction costs.

14

Sure, here are the calculations for the after-tax yield for both types of bonds for each combined tax bracket: For a combined tax bracket of zero, the after-tax yield for both municipal and taxable bonds is 4%. For a combined tax bracket of 10%, the after-tax yield for both municipal and taxable bonds is 4% (5% x 0.9 = 4.5%). For a combined tax bracket of 20%, the after-tax yield for municipal bonds is 4% and for taxable bonds is 4% (5% x 0.8 = 4%). For a combined tax bracket of 30%, the after-tax yield for municipal bonds is 4% and for taxable bonds is 3.5% (5% x 0.7 = 3.5%).

Splits and Price-Weighted Averages

The DJIA no longer equals the average price because the averaging procedure is adjusted whenever a stock splits or pays a stock dividend of more than 10% or when one company in the group of 30 industrial firms is replaced by another. When these events occur, the divisor used to compute the "average price" is adjusted so as to leave the index unaffected by the event.

Taxes Continued

The equivalent taxable interest rate increases with the investor's tax bracket; the higher the bracket, the more valuable the tax-exempt feature of municipals. Thus, high-bracket individuals tend to hold municipals.

Stock Market Indexes

The level of the overall stock market and particular segments of the market can be followed using stock indexes: • Price-weighted Index (DJIA, Nikkei 225) • Places more weight on the highest priced stocks (complication: stock splits) • Replicates the buy-and-hold return on a portfolio that invests in an equal number of shares of each stock Because the Dow measures the return (excluding dividends) on a portfolio that holds one share of each stock, the investment in each company in that portfolio is proportional to the company's share price. For this reason, the Dow is called a price-weighted average. • Value-weighted Index (S&P 500, FTSE) • Places more weight on the largest market capitalization stocks • Replicates the buy-and-hold return on a portfolio that invests in each stock according to its market cap The S&P 500 is computed by calculating the total market value of the 500 firms in the index and the total market value of those firms on the previous day of trading. The percentage increase in the total market value from one day to the next represents the increase in the index. The rate of return of the index equals the rate of return that would be earned by an investor holding a portfolio of all 500 firms in the index in proportion to their market value, except that the index does not reflect cash dividends paid by those firms. A nice feature of both market value-weighted and price-weighted indexes is that they reflect the returns to straightforward portfolio strategies. If you buy each share in the index in proportion to its outstanding market value, your return will match that of the value- weighted index. Similarly, a price-weighted index tracks the returns on a portfolio composed of equal shares of each firm. • Equally-weighted Index • Places equal weight on all stocks • Cannot be replicated with a buy-and hold investment strategy (i.e., need to rebalance every time prices change!) Equally Weighted Indexes Market performance is sometimes measured by an equally weighted average of the returns of each stock in an index. Such an averaging technique, by placing equal weight on each return, corresponds to a portfolio strategy that places equal dollar values in each stock. This is in contrast to both price weighting, which requires equal numbers of shares of each stock, and market value weighting, which requires investments in proportion to outstanding value.

Value-Weighted Index

The value of a value-weighted Index is determined as follows: MV (market value) is just the price of a stock in the index times the number of shares held in the index The return on a value-weighted Index can be determined from the index value or as a weighted-average of the individual security returns. market value rates= t-1 sum of w = 1

Equally-Weighted Index

The value of an equally-weighted Index is simply the sum of the dollar investments in each individual security. The return on an equally-weighted Index can be determined from the index value or as a weighted-average of the individual security returns. $600 for 50 stocks is $2 per stock for index equal weights sum to 1

Price-Weighted Index

This is just the average price of stocks in the index The return on a price-weighted Index can be determined from the index value or as a weighted-average of the individual security returns. where weight is equal to the individual stock's price divided by the sum of all prices the weights sum to 1 t-1 for PN/Pi

Fixed Income - Money Market

Up to one year to maturity, highly liquid, low default risk • Types of securities: • Treasury Bills (no coupon payments), less than 1 year • Issued by US Treasury (government borrowing) • Considered "largely" risk-free Investors buy the bills at a discount from the stated maturity (equivalently, face) value. At maturity, the government pays the investor the face value of the bill. The difference between the purchase price and the ultimate maturity value constitutes the interest paid on the bills. While the income earned on T-bills is taxable at the federal level, it is exempt from state and local taxes, another characteristic distinguishing bills from other money market instruments. • CDs • Issued by depository institutions (i.e. commercial, savings banks and credit unions) no deposit account cause you could withdraw, set time/interest terms with the bank A certificate of deposit (CD) is a time deposit with a bank. Time deposits (in contrast to "demand deposits" or checking accounts) may not be withdrawn on demand. The bank pays interest and principal to the depositor only at maturity. • Commercial Paper• short term loans, debt less than 3 months Issued by corporations The typical corporation is a net borrower of both long-term funds (for capital investments) and short-term funds (for working capital). Large, well-known companies often issue their own short-term unsecured debt notes directly to the public, rather than borrowing from banks. These notes are called commercial paper (CP). Sometimes, CP is backed by a bank line of credit, which gives the borrower access to cash that can be used if needed to pay off the paper at maturity. CP trades in secondary marketsand so is quite liquid. • Eurodollars (in foreign banks) • Dollar denominated deposits outside of the U.S. By locating outside the United States, these banks escape regulation by the Federal Reserve Board. Despite the tag "Euro," these accounts need not be in European banks Most Eurodollar deposits are for large sums, and most are time deposits of less than six months' maturity. A Eurodollar certificate of deposit resembles a domestic bank CD except that it is the liability of a non-U.S. branch of a bank, typically a London branch. • Repurchase Agreements (i.e. repos and reverse repos)• Typically overnight borrowing/lending between the banks• uses assets as collateral Dealers in government securities use repurchase agreements, also called repos (RPs), as a form of short-term, usually overnight, borrowing. The dealer sells securities to an investor on an overnight basis, with an agreement to buy back those securities the next day at a slightly higher price. The increase in the price is the overnight interest. The dealer thus takes out a one-day loan from the investor. The securities serve as collateral for the loan. Example: See composition of a Vanguard money market fund

Derivatives

Value of a derivative is related to the performance of the underlying asset• Used to speculate and/or hedge • Examples: • Options one party has a right, other has an obligation, pre-specified price/date • Call option: buyer has a right to purchase asset- strike price not an obligation • Put option: buyer has a right to sell asset • Forwards both parties have an obligation to trade in the future • Party that agrees to buy is called "long" • Party that agrees to sell is called "short"• Futures both parties have an obligation to trade in the future• Similar to forward but traded on an exchange and with standardized contracts Derivative securities are so named because their values derive from the prices of other assets. For example, the value of the call option will depend on the price of Intel stock. . One use of derivatives, perhaps the primary use, is to hedge risks or transfer them to other parties.

Equal versus Value-weighting

Why is equal greater as opposed to value wieghted equal weight has more small cap stocks whereas larger cap stocks: lower returns value weight puts more in large caps if questions asked which one next period? we don't know but expected average over long term = equal

Example: Mutual Fund Fees

You are considering a $1,000 investment in a mutual fund that offers two kinds of shares: Class A: 6% front-end load Class B: 0.5% annual 12b-1 fees plus 5% redemption fee that decreases by 1% per year What would your investment be worth after four years in each of the two share classes, assuming a 10% annual rate of return? Which share class should you choose? 1000 * (1-0.06) * (1+0.1)^4 = 1376 1000* (1+0.1-0.005)^4 * (1-0.01) = 1423 prefer B How does your answer change if you hold the investment for 15 years? 1000 * (1-0.06) * (1+0.1)^15 = 3926 1000* (1+0.1-0.005)^15 = 3901 A because there's no annual fees outweighs the front end load

Most Common Types of Investment Compani

open mutual fund the majority next are ETFS