Chapter 13
Basic statistical facts to remember:
-A distribution is just a picture of all possible outcomes -The mean return is the central point of the distribution -The standard deviation is the square root of the average squared deviation from the mean -Assuming normality of returns (two-parameter distribution), the mean is a proxy for expected return and the standard deviation is a proxy for total risk. -Variance of a portfolio is NOT the weighted average of the variances of returns of assets in the portfolio -The greater the number of assets in a portfolio, the more important the correlation (covariance) between assets to determining the portfolio variance
The Capital Asset Pricing Model (CAPM) states that expected return for any asset or portfolio depends on what three factors?
1. Pure Time Value of Money 2. Amount of Systematic Risk 3. Reward for Bearing Systematic Risk
Diversification tips:
1. We have seen that portfolio variability can be quite different from the variability of individual securities: -A typical single stock on the NYSE has a standard deviation of annual returns around 50%; -The typical large portfolio of NYSE stocks has a standard deviation of around 20% 2. Diversification is not just holding a lot of assets: -If you own 50 internet stocks, you are not diversified -However, if you own 50 stocks that span 20 different industries, then you are diversified
How many diverse securities are required to eliminate the majority of the diversifiable risk from a portfolio?
10
The slope of the Security Market Line (SML)
= market risk premium
The expected return on a portfolio: I. can never exceed the expected return of the best performing security in the portfolio. II. must be equal to or greater than the expected return of the worst performing security in the portfolio. III. is independent of the unsystematic risks of the individual securities held in the portfolio. IV. is independent of the allocation of the portfolio amongst individual securities.
I, II, and III only
Which one of the following is an example of systematic risk?
Investors panic causing security prices around the globe to fall precipitously
Which one of the following is represented by the slope of the security market line?
Market risk premium
A stock with an actual return that lies above the security market line has:
a higher return than expected for the level of risk assumed.
Variance of returns
a measure of the dispersion of the distribution of possible returns in the future
The standard deviation of a portfolio:
can be less than the standard deviation of the least risky security in the portfolio AND can be less than the weighted average of the standard deviations of the individual securities held in that portfolio.
Treynor Industries is investing in a new project. The minimum rate of return the firm requires on this project is referred to as the:
cost of capital
The absolute reduction in risk is lower, the _________ the number of stocks.
greater
A beta of 1
implies the asset has the same systematic risk as the overall market
market portfolio
includes all financial securities (or stocks) The proportion of each stock in it is equal to the stock's market cap divided by the total market cap
A beta < 0
is rare and only occurs in a few stocks such as gold.
The market risk premium is computed by:
market rate of return - risk free rate of return
systematic risk (m)
refers to the risk inherent to the entire market or market segment. Also known as nondiversifiable risk or market risk It includes changes in GDP, inflation, interest rates ...
The higher the risk, the higher the
risk premium
_________ investors require compensation for the risk they bear when holding financial assets
risk-averse
The expected risk premium on a stock is equal to the expected return on the stock minus the:
risk-free rate
Standard deviation of returns is a measure of ______ ________.
total risk
Historical data is used to estimate the
market risk premium -this tends to fluctuate over time -the realized market risk premium is approximately 8%
According to CAPM, the amount of reward an investor receives for bearing the risk of an individual security depends upon the:
market risk premium and the amount of systematic risk inherent in the security.
The expected rate of return on a stock portfolio is a weighted average where the weights are based on the:
market value of the investment in each stock.
If a stock portfolio is well diversified, then the portfolio variance:
may be less than the variance of the least risky stock in the portfolio.
It is the ________ component that affects P and R.
surprise **This is obvious when we watch how stock prices move when an unexpected announcement is made (e.g. earnings are different from the anticipated)
Which type of risk is priced?
systematic risk
The expected return on a risky asset depends only on that asset's _________ _____.
systematic risk Why? Because unsystematic risk can be diversified away at no cost -Mutual funds (often with minimal initial investment) are widely available to investors -No matter how much total risk an asset has, its expected return depends only on its systematic risk
You own a stock that you think will produce a return of 11 percent in a good economy and 3 percent in a poor economy. Given the probabilities of each state of the economy occurring, you anticipate that your stock will earn 6.5 percent next year. Which one of the following terms applies to this 6.5 percent?
Expected return
Which one of the following is an example of unsystematic risk?
National decrease in consumer spending on entertainment
Which one of the following is least apt to reduce the unsystematic risk of a portfolio?
Reducing the number of stocks held in a portfolio
Which one of the following will be constant for all securities if the market is efficient and securities are priced fairly?
Reward-to-risk ratio
Which one of the following is a positively sloped linear function that is created when expected returns are graphed against security betas?
Security market line
Common representations for a market portfolio:
Standard & Poor 500 (SP500): -value-weighted average of 500 large-cap stocks mostly in the NYSE Russell 3000 & Wilshire 5000: -value-weighted averages of 3,000 & 5000 largest stocks on NYSE, AMEX, & OTC Dow Jones Industrial Average (DJIA): -price-weighted average of 30 "blue chip" stocks in the NYSE
Which one of the following is a risk that applies to most securities?
Systematic
I and III only
Which of the following statements concerning risk are correct? I. Non-diversifiable risk is measured by beta. II. The risk premium increases as diversifiable risk increases. III. Systematic risk is another name for non-diversifiable risk. IV. Diversifiable risks are market risks you cannot avoid.
The expected return on a stock computed using economic probabilities is:
a mathematical expectation based on a weighted average and not an actual anticipated outcome.
idiosyncratic risk (or unsystematic risk)
a type of risk that comes when news affects a single asset or only a few of them. Also known as unique risk or asset-specific risk It includes labor strikes, part shortages ... Example: GM experiencing a strike by employees but if UAW stages a strike against all the auto industry: -In this case, labor strikes may become a systematic risk factor if they affects the entire economy
E[R] is a measure of _________ ________ in the future outcomes of X, while variance and standard deviation are measures of _________ of the outcomes of X
central tendency; dispersion **We compute it using probabilities for the entire range of possibilities **It is also an expected value: the weighted average of squared deviations
Required rate of return =
compensation for the time value of money + compensation for risk
________ allows to virtually eliminate idiosyncratic risk from a portfolio.
diversification
The reward-to-risk ratio for Stock A is less than the reward-to-risk ratio of Stock B. Stock A has a beta of .82 and Stock B has a beta of 1.29. This information implies that:
either Stock A is overpriced or Stock B is underpriced or both.
Announcement and news are the release of information not previously available and they contain both an ______ component and a _______ component.
expected; surprise **The expected component is already embedded in the price and expected return of the security
Stand-alone risk of a randomly selected stock is
high **standard deviation of roughly 50%
Because risk-averse, investors will try different strategies to minimize the stand-alone risk of the assets they _____.
hold
It is not the nature of the event, but its ______ to determine whether it's a systematic or idiosyncratic risk.
impact
Combining ___________ correlated assets can produce a portfolio with less variability than the typical individual asset.
imperfectly
A beta < 1
implies the asset has less systematic risk than the overall market Defensive asset
A beta > 1
implies the asset has more systematic risk than the overall market Aggressive asset
weighted average
is a calculation that takes into account the varying degrees of importance in the numbers in a data set.
portfolio
is a collection of assets An asset's risk and return is important in how it affects the risk and return of the portfolio The risk-return trade-off for a portfolio is measured by the portfolio expected return and standard deviation, just as with individual assets
Beta
is a statistical measure of the relation between the returns on an asset and the market portfolio it measures the amount of systematic risk present in an asset **it's simply an index measuring the statistical relationship between the returns on stock and the market portfolio.
Pure Time Value of Money
is the interest rate demanded by an investor for postponing his consumption and making available capital to a borrower, regardless of risk.
Expected Return E[R]
is the normal, expected return of the asset for the specified period -It is the relative price movement the holders of the asset expect over the period (ex. one year) -This expectation is based on the amount of information available to the investors today
reward-to-risk ratio
is the slope of the line derived from the expected risk premium per unit of systematic risk, or the ratio of risk premium to systematic risk. -the higher the (%) the more appealing the stock is to an investor.
Security Market Line
is the straight line where expected returns and betas of all assets are plotted -is a representation of market equilibrium - can derive a relationship between the expected return of any security or portfolio and its exposure to systematic risk
correlation
is the tendency of two variables to move together in a linear fashion
Unexpected Return (U)
is the uncertain, risky part of the return It depends on unexpected information revealed during the year -News and announcements on the business of the firm -News and announcements on the business climate -Unexpected fluctuations in interest rates, etc.
Assume the market rate of return is 10.1 percent and the risk-free rate of return is 3.2 percent. Lexant stock has 2 percent less systematic risk than the market and has an actual return of 10.2 percent. This stock:
is underpriced.
__________ _________ is the best linear approximation to the relation between the return of stock (j) and the market return.
linear regression
Low beta implies
low systematic risk -Only systematic risk is priced by financial markets, because it is non-diversifiable -Securities with lower beta have lower systematic risk, hence lower expected returns
The ________ of a security divided by the beta of that security is equal to the slope of the security market line if the security is priced fairly.
risk premium
The excess return earned by an asset that has a beta of 1.34 over that earned by a risk-free asset is referred to as the:
risk premium
The principle of diversification tells us that:
spreading an investment across many diverse assets will eliminate some of the total risk.
Total risk is measured by ______ and systemic risk is measured by __________.
standard deviation; beta
two types of "surprises" (or sources of risk)
systematic risk idiosyncratic risk
Capital Asset Pricing Model (CAPM)
the equation of the SML showing the equilibrium relationship between expected return and beta of any security If we know an asset's systematic risk, we can use the CAPM to determine its expected return This is true whether we are talking about financial assets or physical assets
The intercept point of the security market line is the rate of return which corresponds to:
the risk-free rate.
Low beta does not imply low
total stand-alone risk **Stand-alone risk is the risk associated with a single operating unit of a company, a company division, or an area or asset, as opposed to a larger, well-diversified portfolio
What is a realistic representation for the theoretical market portfolio?
typically the S&P 500 because returns on the S&P 500 are calculated without dividends.
Diversification can substantially reduce the ____________ of returns without an equivalent reduction in expected returns.
variability **This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another **However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion Why? Because it affects all stocks!
_______ and _________ __________ of a random variable measure the volatility of its outcomes.
variance; standard deviation
The expected return of a portfolio is the _________ _________ of the expected returns for each asset in the portfolio
weighted average
The beta of a portfolio is simply the
weighted average of the betas of its securities See slide 22, Chapter 13.
The expected return on a stock given various states of the economy is equal to the:
weighted average of the returns for each economic state.
Which one of the following indicates a portfolio is being effectively diversified?
A decrease in the portfolio standard deviation
Which one of the following is the best example of a diversifiable risk?
A firm's sales decrease
Which one of the following statements is correct concerning a portfolio beta?
A portfolio beta is a weighted average of the betas of the individual securities contained in the portfolio.
II and IV only
At a minimum, which of the following would you need to know to estimate the amount of additional reward you will receive for purchasing a risky asset instead of a risk-free asset? I. Asset's standard deviation II. Asset's beta III. Risk-free rate of return IV. Market risk premium
Why does diversification work?
Because returns of stocks do not move exactly together. Bad days of one stock may be compensated by another having a good day instead. This reduces the dispersion (or standard deviation) of the portfolio.
Why is the risk of the portfolio NOT a simple weighted average of the standard deviation of the individual assets in the portfolio?
Because when an asset's return is positive, the other assets' return may be negative, less positive, or more positive -This would affect the dispersion of the returns of the portfolio ***Portfolio risk is generally smaller than the sum of individual standard deviations σ due to correlation among asset returns
Which one of the following measures the amount of systematic risk present in a particular risky asset relative to the systematic risk present in an average risky asset?
Beta
Which one of the following is the formula that explains the relationship between the expected return on a security and the level of that security's systematic risk?
Capital asset pricing model
Realized returns are generally ________ from expected returns.
Different R = E[R] + U U = Unexpected component of return -At any point in time, the unexpected return U can be either positive or negative -Over time, the average of U is zero: E[U] = 0
Which one of the following statements is correct concerning unsystematic risk?
Eliminating unsystematic risk is the responsibility of the individual investor.
Which one of the following is most directly affected by the level of systematic risk in a security?
Expected rate of return
Which one of the following statements is correct concerning a portfolio of 20 securities with multiple states of the economy when both the securities and the economic states have unequal weights?
Given both the unequal weights of the securities and the economic states, an investor might be able to create a portfolio that has an expected standard deviation of zero.
The expected return on a portfolio considers which of the following factors? I. Percentage of the portfolio invested in each individual security II. Projected states of the economy III. The performance of each security given various economic states IV. Probability of occurrence for each state of the economy
I, II, III, and IV
stand-alone risk
It is the set of risks surrounding the cash flows of an asset
Which one of the following statements is correct?
Over time, the average unexpected return will be zero.
Suzie owns five different bonds and twelve different stocks. Which one of the following terms most applies to her investments?
Portfolio
Steve has invested in twelve different stocks that have a combined value today of $121,300. Fifteen percent of that total is invested in Wise Man Foods. The 15 percent is a measure of which one of the following?
Portfolio weight
Two measures of risk of financial assets:
Stand-alone risk Portfolio risk
I, III, and IV only
The capital asset pricing model (CAPM) assumes which of the following? I. A risk-free asset has no systematic risk. II. Beta is a reliable estimate of total risk. III. The reward-to-risk ratio is constant. IV. The market rate of return can be approximated.
Portfolio risk
The risk of two (or more) assets put together is different from the risk of each of the assets considered separately
Which one of the following statements related to risk is correct?
The systematic risk of a portfolio can be effectively lowered by adding T-bills to the portfolio.
Which one of the following events would be included in the expected return on Sussex stock?
This morning, Sussex confirmed that its CEO is retiring at the end of the year as was anticipated.
Standard deviation measures which type of risk?
Total risk
Which one of the following statements related to unexpected returns is correct?
Unexpected returns can be either positive or negative in the short term but tend to be zero over the long-term.
A news flash just appeared that caused about a dozen stocks to suddenly increase in value by 12 percent. What type of risk does this news flash best represent?
Unsystematic (or idiosyncratic) because unsystematic risk is a specific risk that affects a very small number of assets.
Which one of the following risks is irrelevant to a well-diversified investor?
Unsystematic risk
The primary purpose of portfolio diversification is to:
eliminate asset-specific risk.
I and IV only
Which of the following are examples of diversifiable risk? I. An earthquake damages an entire town II. The federal government imposes a $100 fee on all business entities III. Employment taxes increase nationally IV. All toymakers are required to improve their safety standards
I, II and III only
Which of the following statements are correct concerning diversifiable risks? I. Diversifiable risks can be essentially eliminated by investing in 30 unrelated securities. II. There is no reward for accepting diversifiable risks. III. Diversifiable risks are generally associated with an individual firm or industry. IV. Beta measures diversifiable risk.
A) Diversified portfolio with returns similar to the overall market B) Stock with a beta of 1.38 C) Stock with a beta of .74 D) U.S. Treasury bill E) Portfolio with a beta of 1.01 ***B***
Which one of the following should earn the highest risk premium based on CAPM?
Beta = 0 mean
an asset has no risk
Systematic risk is measured by:
beta
The systematic risk of the market is measured by a:
beta of 1
How do we measure systematic risk?
by estimating the sensitivity of a security's return to the market return Why? No idiosyncratic risk in market portfolio
Unsystematic risk (or idiosyncratic risk):
can be effectively eliminated by portfolio diversification. -it includes losses caused by labor problems, nationalization of assets, or weather conditions. This type of risk can be reduced by assembling a portfolio with significant diversification so that a single event affects only a limited number of the assets.
Adding randomly selected stocks to a portfolio _________ risk.
reduces
