FIN 325 test 2
Equity risk premium excess return
(Risk-Risk free rate)
Sharpe Ratio
(Risk-Risk free rate)/SD
Factors
- APT assumes returns generated by a factor model - Factor Characteristics ◦ Each risk must have a pervasive influence on stock returns ◦ Risk factors must influence expected return and haven on-zero prices ◦ Risk factors must be unpredictable to the market
Covariance
- Absolute, not relative, measure of association - Not limited to values between -1 and +1 - Sign interpreted the same as correlation - Size depends on units of variables - Related to correlation coefficient
Characteristics of the 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 - All securities included in proportion to their market value
Selecting Optimal Asset Classes
- Another way to use Markowitz model is with asset classes ◦ Allocation of portfolio assets to asset types - Asset class rather than individual security decisions likely most important for investors ◦ Can be used when investing internationally ◦ Different asset classes offers various returns and levels of risk - Correlation coefficients may be quite low
Arithmetic Versus Geometric
- Arithmetic mean does not measure the compound growth rate over time - Does not capture the realized change in wealth over multiple periods - Does capture typical return in a single period - Geometric mean reflects compound, cumulative returns over more than one period. - Over multiple periods, the geometric mean shows the true average compound growth rate
Risk Reduction in Portfolios
- Assume all risk sources for a portfolio of securities are independent - This assumption is unrealistic when investing - Market risk affects all firms, cannot be diversified away - If risks independent, the larger the number of securities the smaller the exposure to any particular risk - "Insurance principle" - Only issue is how many securities to hold - Random (or naïve) diversification - Diversifying without looking at how security returns are related to each other - Marginal risk reduction gets smaller and smaller as more 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 for significant risk reduction
Capital Asset Pricing Model
- Assumes all investors: ◦ 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 personal income taxes, no inflation - No single investor can affect the price of a stock - Capital markets are in equilibrium
Tests of CAPM
- Assumptions are mostly unrealistic - Empirical evidence has not led to consensus - However, some points are widely agreed upon ◦ SML appears to be linear ◦ Intercept is generally higher than RF ◦ Slope of the CAPM is generally less than theory predicts ◦ It's likely that only systematic risk is rewarded
Arbitrage Pricing Theory
- Based on the Law of One Price ◦ Two otherwise identical assets 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 personal taxes, riskless borrowing or lending, mean-variance decisions
Beta
- Beta = 1.0 implies as risky as market - Securities A and B are more risky than the market ◦ Beta >1.0 - Security C is less risky than the market ◦ Beta <1.0 GRAPH IN CH.9 PPT
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 ◦ Approximates return on all common stocks - No one correct number of observations and time periods for calculating beta ◦ Therefore, estimates of beta vary - The regression calculations of the true a and B from the characteristic line are subject to estimation error - Portfolio betas more reliable than individual security betas
Security Market Line
- CML Equation only applies to markets in equilibrium and efficient portfolios - The Security Market Line depicts tradeoff between risk and expected return for individual securities - Under CAPM, all investors hold the market portfolio ◦ Relevant risk of any security is therefore its covariance with the market portfolio
Building a Portfolio
- Diversification is key to optimal risk management - Asset allocation is most important single decision - Using Markowitz Principles ◦ Step 1: Identify optimal risk-return combinations using the Markowitz efficient frontier analysis - Estimate expected returns, variances and covariances ◦ Step 2: Choose the final portfolio based on your preferences for return relative to risk
Selecting an Optimal Portfolio of Risky Assets
- Each indifference curve represents the combinations of risk and expected return that are equally desirable to a particular investor - In selecting one portfolio from the efficient frontier, we are matching investor preferences (as given by their indifference curves) with portfolio possibilities (as given by the efficient frontier).
Calculating Portfolio Risk
- Encompasses three factors - Variance (risk) of each security - Covariance between each pair of securities - Portfolio weights for each security - Goal: select weights to determine the minimum variance combination for a given level of expected return - Generalizations ◦ the smaller the positive correlation between securities, the better ◦ Covariance calculations grow quickly ◦ As the number of securities increases: - The importance of covariance relationships increases - The importance of each individual security's risk decreases
Calculating Expected Return
- Expected value - The weighted average of all possible return outcomes included in the probability distribution - Each outcome weighted by probability of occurrence - Referred to as expected return
Problems with APT
- Factors are not well specified ex ante ◦ To implement the APT model, need the factors that account for the differences among security returns - CAPM identifies market portfolio as single factor - Studies suggest certain factors are reflected in market ◦ Focus on cash flows and discount rate - Both CAPM and APT rely on unobservable expectations
Measuring Returns
- For comparing performance over time or across different securities. - Total Return is a percentage relating all cash flows received during a given time period, denoted CFt +(PE - PB), to the start of period price, PB.
The Risk-Return Record
- From 1926 - 2010, geometric average annual return was 9.6% for S&P 500 - Arithmetic mean was 11.4% - Standard deviation was 19.9% - Smaller common stocks show greater risks and returns than large common stocks in that period - T-bills showed lowest risk and return
Asset Valuation
- Function of both return and risk - At the center of security analysis - Historical risk-return relationships useful indicators - No guarantee future will be like the past - Also no reason to assume that relative relationships will be much different in the future than they are now - Especially useful in the long-run
Modern Portfolio Theory
- In the 1950s, Harry Markowitz, the father of Modern Portfolio Theory, developed the basic portfolio principles that underlie MPT. - The primary impact of MPT is that it provides a framework for the systematic selection of portfolios based on expected return and risk principles. - Markowitz was the first to develop the concept of portfolio diversification in a formal way—he quantified the concept of diversification. - He showed quantitatively why, and how, portfolio diversification works to reduce the risk of a portfolio to an investor. - He answered a basic question: Is the risk of a portfolio equal to the sum of the risks of the individual securities comprising it? The answer is no! - Markowitz was the first to show that we must account for the inter relationships among security returns in order to calculate portfolio risk and in order to reduce portfolio risk to its minimum level for any given level of return.
Asset Allocation
- Includes two dimensions ◦ Diversifying between asset classes ◦ Diversifying within asset classes - Asset classes include ◦ International equities ◦ Bonds ◦ Treasury Inflation-Indexed Securities (TIPS) ◦ Real estate ◦ Gold ◦ Commodities - Correlation among asset classes must be considered - Correlations change over time - For individual investors, allocation depends on ◦ Time horizon ◦ Risk tolerance - Diversified asset allocation doesn't necessarily provide benefits or guarantee against loss
Asset Allocation
- Index Mutual Funds and ETFs ◦ Investors can buy funds covering various asset classes - Domestic large-cap stocks, domestic small-cap stocks - International stocks - Bond funds - Life Cycle Analysis ◦ Varies asset allocation based on age of investor ◦ Life-cycle funds (target-date funds) hold various asset classes and the allocation changes as investor ages - No one "correct" approach to allocation
Risk Sources
- Interest Rate Risk - Affects income return - Market Risk - Recession, war, etc. - Inflation Risk - Purchasing power variability - Business Risk - Financial Risk - Tied to debt financing - Liquidity Risk - Marketability of security in secondary market - Currency Risk - Exchange Rate Risk - Country Risk - Political stability
Selecting an Optimal Portfolio of Risky Assets
- International diversification unlikely to offer as much risk reduction as it has in the past - 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 ◦ Cumbersome to apply
Measuring International Returns
- International investments subject to exchange rate risk - When you buy a foreign asset, you must use the foreign currency, so you must first exchange home currency - If foreign currency depreciates, returns lower in domestic currency terms - Total Return in domestic currency = =[RR x end variance for currency/begin value for currency]
The Separation Theorem
- Investors use their preferences (reflected in an indifference curve) to determine optimal portfolio - Separation Theorem ◦ The investment decision about which risky portfolio to hold is separate from the financing decision - Investment decision does not involve investor - Financing decision depends on investor's preferences
Investment Decisions
- Involve uncertainty - Focus on expected returns - Estimates of future returns needed 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
Estimating Beta
- Market model ◦ Relates the return on each stock to the return on the market, assuming a linear relationship ◦ Produces an estimate of return for any stock Ri =ai +Bi RM +ei - Characteristic line ◦ Line fit to total returns for a security relative to total returns for the market index
Simplifying Markowitz Calculations
- Markowitz full-covariance model ◦ Requires a covariance between the returns of all securities in order to calculate portfolio variance ◦ [n(n-1)]/2 set of covariances for n securities - Markowitz suggests using an index to which all securities are related to simplify
APT Model
- Most important are the deviations of the factors from their expected values ◦ Expected return is directly related to sensitivity ◦ CAPM assumes risk is only sensitivity to market - The expected return-risk relationship for the APT can be described as: E(Ri) =RF +bi1 (risk premium for factor 1) +bi2(risk premium for factor 2) +... +bin (risk premium for factor n)
Market Portfolio
- Most important implication of the CAPM ◦ The portfolio of all risky assets is the optimal risky portfolio (called the market portfolio) ◦ The expected price of risk is always positive ◦ The optimal portfolio is at the highest point of tangency between RF and the efficient frontier ◦ All investors hold the same optimal portfolio of risky assets
Measuring Portfolio Risk
- Needed to calculate risk of a portfolio: - Weighted individual security risks - Calculated by a weighted variance using the proportion of funds in each security For security i: (wi × oi) - Weighted co-movements between returns - Return covariances are weighted using the proportion of funds in each security - For securities i, j: 2wiwj × oij
Portfolio Theory
- Optimal diversification considers all available information - Assumptions in portfolio theory ◦ A single investment period ◦ Liquid position (no transaction costs) ◦ Preferences based only on a portfolio's expected return and risk
Portfolio Risk
- Portfolio risk not simply the sum or the weighted average of individual security risks - Emphasis on the risk of the entire portfolio and not on risk of individual securities in the portfolio - Diversification almost always lowers risk - Measured by the variance or standard deviation of the portfolio's return
Selecting an Optimal Portfolio of Risky Assets
- Portfolio weights are only variable that can change in Markowitz analysis - Assume investors are risk averse - Indifference curves help select from efficient set ◦ Description of preferences for risk and return ◦ Portfolio combinations which are equally desirable ◦ Match investor preferences with portfolio possibilities
Capital Asset Pricing Model
- Positive rather than normative ◦ Describes how investors could behave not how they should be have - Focus on the equilibrium relationship between the risk and expected return on risky assets - Builds on Markowitz portfolio theory - Each investor is assumed to diversify his or her portfolio according to the Markowitz model
Risk Premiums
- Premium is additional return earned or expected for additional risk - Calculated for any two asset classes
Risk Premiums
- Premium is additional return earned or expected for additional risk - Calculated for any two asset classes - Equity risk premium is the difference between stock and risk-free returns - Stocks versus Treasury bills - Stocks versus Treasury bonds
Modern Portfolio Theory
- Provides framework for selection of portfolios based on expected return and risk - Used, to varying degrees, by financial managers - Shows benefits of diversification - The risk of a portfolio does not equal the sum of the risks of its individual securities - Must account for correlations among individual risks
CAPM's Expected Return-Beta Relationship
- Required rate of return on an asset (ki) is composed of ◦ risk-free rate (RF) ◦ risk premium (Bi [ E(RM) - RF ]) - Market risk premium adjusted for specific security ki = RF +Bi [ E(RM) - RF ] ◦ The greater the systematic risk, the greater the required return
Adjusting Returns for Inflation
- Return measures are nominal, i.e., are not adjusted for inflation - Purchasing power of investment may change over time - Nominal return = real return + expected inflation rate - Consumer Price Index (CPI) is possible measure of inflation TRia = (1+TR)/(1+CPI) - 1
Risk
- Risk and return are opposite sides of the same coin - Risk is the chance that the actual outcome from an investment will differ from the expected outcome - Investors willing to assume large risks may gain large returns, but they may also lose money
Risk-Free Assets, Borrowing, Lending
- Risk free assets ◦ No correlation with risky assets ◦ Usually proxied by a Treasury security - Adding a risk-free asset extends and changes the efficient frontier - "Lending" because investor lends money to issuer - With borrowing, investor no longer restricted to own wealth
Dealing With Uncertainty
- Risk that an expected return will not be realized - 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
The New Efficient Set
- Risk-free investing and borrowing creates a new set of expected return-risk possibilities - Addition of risk-free asset results in ◦ A change in the efficient set from an arc to a straight line tangent to the feasible set without the riskless asset ◦ Chosen portfolio depends on investor's risk-return preferences
Risk-Free Lending
- Riskless assets can be combined with any portfolio in the efficient set AB ◦ Z implies lending - Set of portfolios on line RF to T dominates all portfolios below it
Capital Market Line
- Slope of the 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 portfolio P (Equation for CML):
An Efficient Portfolio
- Smallest portfolio risk for a given level of expected return - Or largest expected return for a given level of portfolio risk - From the set of all possible portfolios ◦ Only locate and analyze the subset known as the efficient set - An efficient portfolio has the smallest portfolio risk for a given level of expected return or the largest expected return for a given level of risk. - All efficient portfolios for a specified group of securities are referred to as the efficient set of portfolios
Beta
- Standardized measure of systematic risk - Relative measure of risk: risk of an individual stock relative to the market portfolio of all stocks - Relates covariance of an asset with the market portfolio to the variance of the market portfolio
Correlation Coefficient
- Statistical measure of relative association - pij = correlation coefficient between securities i and j - pij = +1.0 = perfect positive correlation - pij = -1.0 = perfect negative (inverse) correlation - pij = 0.0 = zero correlation
Measures Describing a Return Series
- TR, RR, and CWI are useful for a given, single time period - What about summarizing returns over several time periods? - Arithmetic mean, or simply mean, X with line above = sum if X / n
overview
- There is no guarantee that the future will be exactly like the past. - A knowledge of historical risk-return relationships is a necessary first step for investors in making investment decisions for the future. - Furthermore, there is no reason to assume that relative relationships will differ significantly in the future. - If stocks have returned more than bonds, and Treasury bonds more than Treasury bills, over the entire financial history available, there is every reason to assume that such relationships will continue over the long run future. - Therefore, it is very important for investors to understand what has occurred in the past.
Measuring returns
- To measure return in dollars and reflect compounding returns over a time period, given a specific initial investment, use Cumulative WealthIndex - Cumulative Wealth Index, CWIn, over n periods = = WIo(1 + TR1)(1+TR2)... (1+TRn)
Measuring Returns
- Total Return can be either positive or negative - When cumulating or compounding, negative returns are problem - A Return Relative solves the problem because it is always positive RR= (CFt + Pe)/Pb = 1 + TR
Impact of Diversification on Risk
- Total risk = systematic (nondiversifiable) risk + nonsystematic (diversifiable) risk ◦ Systematic risk is market risk and common to virtually all securities ◦ Nonsystematic risk is company-specific risk - Total risk can go no lower than systematic risk - Both risk components can vary over time - Affects number of securities needed to diversify
Estimating the SML
- Treasury Bill rate used to estimate RF - Expected market return unobservable ◦ Estimated using past market returns and taking an expected value - Estimating individual security betas difficult ◦ Only company-specific factor in CAPM ◦ Requires asset-specific forecast
Risk Types
- Two general types: - Systematic (general) risk - Pervasive, affecting all securities, cannot be avoided Interest rate or market or inflation risks - Nonsystematic (specific) risk - Unique characteristics specific to issuer - Total Risk = General Risk + Specific Risk
Calculating Risk
- Variance and standard deviation used to quantify and measure risk - Measure the spread or dispersion around the mean of the probability distribution - Variance of returns: σ² = (Ri - E(R))²pri - Standard deviation of returns:σ =(σ²)1/2 - σ is expected (ex ante) - Actual (ex post) σ useful but not perfect estimate of future
Portfolio Expected Return
- Weighted average of the individual security expected returns - Each portfolio asset has a weight, w, which represents the percent of the total portfolio value
Correlation Coefficient
- When does diversification pay? - With perfectly positive correlation, risk is a weighted average, therefore there is no risk reduction - With perfectly negative correlation, diversification assures the expected return - With zero correlation - If many securities, provides significant risk reduction - Cannot eliminate risk - Negative correlation or low positive correlation ideal but unlikely
The expected market return is 16 percent. The risk-free return is 7 percent, and BC Co. has a beta of 1.1. BC's required return is...
16.9 percent.
Karl invested his entire portfolio in a randomly-selected, single stock. Which of the following best approximates the standard deviation that Walter should expect for his portfolio?
35%
Geometric Mean
= Defined as the n^th root of the product of n return relatives minus one, or G= [(1+TR1)(1+TR2)...(1+TRn)]^1/n - 1
Which statement about arithmetic and geometric mean returns is correct? A) The arithmetic mean is a better measure of typical performance over a single period. B) The arithmetic mean does better at adjusting for inflation C) The arithmetic mean is a better measure of performance for a buy and hold investor. D) The arithmetic mean is a better measure of performance for a buy and hold investor.
A) The arithmetic mean is a better measure of typical performance over a single period.
All of the following are categories of a particular security's risk premium EXCEPT: A) The risk-free rate of return B) Equity risk premium between a stock and a Treasury security C) Time premium between long-term and short-term Treasury bonds D) Default premium between corporate bonds and Treasury bonds
A) The risk-free rate of return
Which of the following is not one of the assumptions of the CMT? A) There is no interest rate charged on borrowing. B) There are no personal income taxes. C) There are no transaction costs. D) All investors have the same one-period time horizon.
A) There is no interest rate charged on borrowing.
Which is the best way to calculate the inflation-adjusted return? A) [(1+ R) / (1+ rate of inflation)] - 1 B) R - rate of inflation C) [(1+ R)(1 - rate of inflation)] - 1 D) R + rate of inflation
A) [(1+ R) / (1+ rate of inflation)] - 1
What is the best answer for the missing definition below in the formula for return? CFt + (PE - PB) CFt + PC R = -------------- = --------- PB PB where CFt = ______________________________________________ PE = Price at end of period t (or sale price) PB = Price at beginning of the period (or purchase price) PC = Change in price during the period A) Cash flows over life of project B) Cash flows paid during measurement period t C) Future value of cash flows paid at time t D) Future value of interest payments paid at time t
B) Cash flows paid during measurement period t
Which of the following statements regarding indifference curves is NOT true? A) The indifference curves for all risk-averse investors will be upward sloping. B) Investors have a finite number of indifference curves. C) Indifference curves cannot intersect. D) The greater the indifference curve's slope, the greater the investor's risk aversion.
B) Investors have a finite number of indifference curves.
Which of the following statements is most accurate? The: A) SML plots individual securities and efficient portfolios, only. B) SML plots individual securities, inefficient portfolios, and efficient portfolios. C) CML plots both efficient and inefficient portfolios. D) CML plots individual stocks and efficient portfolios.
B) SML plots individual securities, inefficient portfolios, and efficient portfolios.
Which of the following is not a source of risk involved with investing in financial assets? A) Liquidity risk B) Interest rate risk C) Investment risk D) Inflation risk
C) Investment risk
How does one calculate the "Cumulative Wealth Index"? A) Add the total returns for each year and add to the starting amount. B) Adding the return relatives for each year, and add to the starting amount. C) Multiply the return relatives for each year, and multiply by the starting amount. D) Multiply the total returns for each year, and multiply by the starting amount.
C) Multiply the return relatives for each year, and multiply by the starting amount.
The standard deviation of returns can be calculated for all but which of the following? A) The series of returns for a mutual fund over a specified period in the past B) The series of returns for a specific stock over a specified period in the past C) The series of returns for a specific stock over a specified period in the future D) The series of returns for a portfolio of securities over a specified period in the past
C) The series of returns for a specific stock over a specified period in the future
Return = (CFt + PE -PB) / PB Which part of the formula represents the yield? A) CFt B) PE -PB C) (PE -PB) / PB D) CFt / PB
D) CFt / PB
Investments in non-U.S. firms and funds expose investors to all of the following EXCEPT: A) country (political) risk. B) market risk. C) exchange rate risk. D) diversification risk.
D) diversification risk.
Return on any investment is measured by: A) dividends plus capital appreciation or depreciation. B) price change plus capital appreciation or depreciation. C) interest payments plus capital appreciation or depreciation. D) yield plus capital appreciation or depreciation.
D) yield plus capital appreciation or depreciation.
What are the three factors in the three-factor model?
Market risk premium, SMB and HML
Return Components
Returns consist of two elements: - Yield - Periodic cash flows such as interest or dividends - Measures return relative to purchase or current price - Capital gain (loss) - The change in price of the asset - Total Return =Yield + Price Change - Investors sometimes focus only on yield
Which of the following funds would provide the most diversification benefit if added to a portfolio of 50 stocks that was spread across industries? A fund that tracks the: Correct!
S&P GSCI.
Which of the following statements about the difference between the SML and the CML is true?
The CML applies to efficient portfolios, whereas the SML applies to all portfolios or securities.
Which of the following statements is true regarding TIPS?
The correlation between TIPS and the S&P 500 Index has often been negative.
Which of the following is generally used as a proxy for the risk-free return?
Treasury security
Portfolios lying on the upper right portion of the efficient frontier are likely to be chosen by...
aggressive investors.
An indifference curve shows...
all combinations of portfolios that are equally desirable to an investor
If markets are efficient and in equilibrium:
all securities would lie on the SML.
Capital Market Line
ch.9 slides
For an investor in a life-cycle fund, the bond allocation generally:
increases over time.
Under the CMT, the relevant risk to consider with any security is...
it's covariance with the market portfolio.
Because of increasing correlation between U.S. markets and foreign markets, most professional investors now recommend...
maintaining some reasonable exposure to foreign markets.
The optimal portfolio for a risk-averse investor...
occurs at the point of tangency between the highest indifference curve and the efficient set of portfolios
The Capital Asset Pricing Model (CAPM)
shows the relationship between risk and expected return
If a stock has a beta greater than 1.0, it means...
the stock's return has greater than average sensitivity to the market return.
Different investors estimate the inputs to the Markowitz model differently because...
there is an inherent uncertainty in security analysis
Equity risk premium
‐ difference between stock return and risk‐free return - Stocks versus Treasury bills - Stocks versus Treasury bonds
Fundamental Analysis
• Discounted Cash Flow Techniques • Intrinsic value based on the discounted value of the expected stream of cash flows • Dividend discount model can be challenging to apply in many cases • Multiplier Approaches • Relative Valuation Metrics • Emphasize stock comparisons rather than valuation
