Chapter 8 DSM
Which of the following correlation coefficients would generate the most benefit in terms of risk reduction for a 2-asset portfolio that consists of 40% in Asset A and 60% in Asset B?
-.65 If Assets A and B had a correlation coefficient of -.65 it would generate the most benefit in terms of risk reduction for a 2-asset portfolio that consists of 40% invested in Asset A and 60% invested in Asset B. Any negative correlation provides more benefit than a positive correlation in terms of risk reduction. Assets that are negatively correlated should move in opposite directions and therefore reduce return volatility of any portfolio. Positive correlations can provide benefits but the greater the positive correlation the less benefit it provides. The +.98 will provide little benefit since it is nearly perfectly positively correlated indicating the assets move almost in unison. A correlation coefficient ranges from -1 to +1 and tells you how closely two assets move together. Assets that do not move together provide the most benefit when combined into a portfolio.
According to the security market line, a security with a beta of 1.5 should provide a risk premium that is _________ times the risk premium existing for the market as a whole.
1.5 According to the security market line, a security with a beta of 1.5 should provide a risk premium that is 1.5 times the risk premium existing for the market as a whole. The security market line (SML) shows us the linear relationship between a stock's beta and its expected return, or in other words it is the graphical representation of the CAPM. In an efficient market all stocks will plot on the SML. Looking at the CAPM equation we see that the beta coefficient is multiplied by the market risk premium (the difference between the market rate of return and the risk-free rate of return) in order to determine the risk premium for an individual stock. rj = RF + [Betaj * (rm - RF)] where; rj = Required return RF = Risk-free rate of return rm = Market return; Return on the market portfolio of assets Betaj = Beta coefficient for the asset
Under the capital asset pricing model, the relevant risk is:
systematic risk Under the capital asset pricing model, the relevant risk is systematic risk. The capital asset pricing model (CAPM) is premised on efficient markets. In an efficient market rational investors will be able to eliminate the diversifiable risk through combining assets in an efficient manner. Since investors have this ability to eliminate this risk the only remaining risk that matters is the risk associated with the overall system or the systematic risk. Standard deviation measures an asset's total risk and has both systematic risk and diversifiable risk when looking at a single asset.
Diversification is the process of:
combining assets to reduce risk and/or increase returns. Diversification is the process of combining assets to reduce risk and/or increase returns. Efficient diversification can either 1) increase portfolio returns while holding risk constant, 2) reduce portfolio risk while holding returns constant, or 3) simultaneously reduce portfolio risk and increase portfolio returns. Increasing risk to increase returns is an investor decision that will be made after diversification eliminates all asset-specific risk. And, combining assets from the same industry does little to reduce risk. The best combinations are assets that are not highly correlated. The benefits of diversification were first mathematically proven by Harry Markowitz who is considered to be the father of Modern Portfolio Theory which is based on his work.
Assume you have the following assets, expected returns, and betas: Asset A Expected Return - 16% Beta - 1.2 Asset B Expected Return - 14% Beta - 1.0 Asset C Expected Return - 21% Beta - 1.6 What is the beta of a portfolio consisting of 25% invested in Asset A, 45% in Asset B, and 30% in Asset C?
1.23 Assume you have the following assets, expected returns, and betas: Asset A Expected Return - 16% Beta - 1.2 Asset B Expected Return - 14% Beta - 1.0 Asset C Expected Return - 21% Beta - 1.6 The beta of a portfolio consisting of 25% invested in Asset A, 45% in Asset B, and 30% in Asset C is 1.23. The portfolio beta is simply the weighted average beta weighted according to the percentage of your investment in each asset so is; Bp = .25(1.2) + .45(1.0) + .30(1.6) = .30 + .45 + .48 = 1.23.
An asset with a beta of 1.6 will have an expected return of __________ when the risk-free rate is 4% and the expected return on the market is 12%.
16.8% An asset with a beta of 1.6 will have an expected return of 16.8% when the risk-free rate is 4% and the expected return on the market is 12%. Use the following CAPM formula to compute the expected return. rj = RF + [Betaj * (rm - RF)] where; rj = Required return RF = Risk-free rate of return rm = Market return; Return on the market portfolio of assets Betaj = Beta coefficient for the asset So, substituting the numbers into the formula yields; rj = 4% + [1.6 x(12% - 4%)] = 16.8%
What is the percentage return of a stock that was purchased for $45 and sold one year later for $55 if the stock also paid $3 in dividends over that time period?
28.9% The percentage return of a stock that was purchased for $45 and sold one year later for $55 if the stock also paid $3 in dividends over that time period is 28.9%. The following formula computes percentage returns: rt = (Ct + Pt - P(t-1)) / P(t-1) So, for this stock: rt = ($3 + $55 - $45) / $45 = .289 or 28.9% In order to compare holding period returns you need to make sure the holding period is identical. It is not a valid comparison to compare a percentage return for a stock held two years to a percentage return for a stock held six months.
If the required return for a security is 15% and the risk-free rate is 6%, the risk premium is:
9% If the required return for a security is 15% and the risk-free rate is 6%, the risk premium is 9%. The risk premium is the difference between the market rate and the risk-free rate.
You are considering two securities. Security A has a historical average annual return of 7% and a standard deviation of 3%. Security B has a historical average annual return of 7% and a standard deviation of 9%. From this information you can conclude that:
Security B is more risky than Security A. You are considering two securities. Security A has a historical average annual return of 7% and a standard deviation of 3%. Security B has a historical average annual return of 7% and a standard deviation of 9%. From this information you can conclude that Security B is more risky than Security A. Both securities have the same return but security B is much riskier than security A since it has a higher standard deviation. Standard deviation measures dispersion around the mean for normally distributed securities and a higher number represents greater risk.
You purchased Hobo Hats stock last year for $60 a share. Today, you received $2 a share dividend and immediately sold the stock for $63. Your realized return, or holding period return, was _________.
8.33% You purchased Hobo Hats stock last year for $60 a share. Today, you received $2 a share dividend and immediately sold the stock for $63. Your realized return, or holding period return, was 8.33%. To compute a holding period return you use the following formula: rt = (Ct + Pt - P(t-1)) / P(t-1) So for Hobo Hats the return is: rt = ($2 + $63 - $60) / $60 = .0833 or 8.33% In order to compare holding period returns you need to make sure the holding period is identical. It is not a valid comparison to compare a percentage return for a stock held two years to a percentage return for a stock held six months.
Over the past 20 years, the average annual return for ShortStop Baseball Gear has been 9% and the standard deviation has been 4%. Given this information you know that the:
95% prediction interval is from 1% to 17%. Over the past 20 years, the average annual return for ShortStop Baseball Gear has been 9% and the standard deviation has been 4%. Given this information you know that the 95% prediction interval is from 1% to 17%. The properties of the normal distribution tell us that 95% of the time the observed values will fall within plus or minus two standard deviations of the mean. Given that two standard deviations are 8% (i.e. 2 x 4%) then the prediction interval is between 1% (i.e. 9% - 8%) and 17% (i.e. 9% + 8%), or between 1% and 17%. Since the standard deviation is the square root of the variance, the variance had to be 16%2. Taking the square root then yields a standard deviation of 4%. And, given what we know about ShortStop's past returns we should expect them to be close to the average annual or mean return and be about 9% next year.
__________ risk is the only risk that matters to investors with broadly diversified portfolios.
Systematic Systematic risk is the only risk that matters to investors with broadly diversified portfolios. Systematic risk can also be called non-diversifiable risk or market risk. Systematic risk is the risk that an investor must assume that impacts the overall market or system. This type of risk cannot be eliminated through diversification so is the only relevant risk. Unsystematic risk, asset-specific risk, and unique-risk are all terms for the type of risk that can be eliminated through diversification. For this reason it is also called diversifiable risk. This type of risk should not be a factor since investors can eliminate it and therefore asset returns will typically not compensate investors for this type of risk in an efficient market.
Firm-specific risk is the:
diversifiable risk of an asset. Firm-specific risk is the diversifiable risk of an asset. This is the component of risk that is unique to a specific firm that does not affect other firms. Efficient diversification can eliminate this type of risk. When looking at an asset in isolation the standard deviation measures the total risk of the asset which includes both diversifiable and non-diversifiable components. We make a critical distinction between the risk that can be eliminated and the risk that must be held by the investor. In an efficient market investors will only be compensated for the non-diversifiable risk since they can eliminate firm-specific risk through diversification.
An investor's required rate of return should be a function of the:
risk-free rate of return plus a risk premium for the stock's systematic risk. An investor's required rate of return should be a function of the risk-free rate of return plus a risk premium for the stock's systematic risk. In an efficient market investors will only be compensated for the systematic risk since they can diversify and eliminate the unsystematic risk. Therefore the required return should be the risk-free rate plus some additional amount to reward the investor for taking on the systematic risk. The systematic risk premium should factor in the expected inflation rate since inflation impacts all securities. The systematic risk premium can differ from stock to stock. Keep in mind that a recession may hurt all firms but some firms will be hurt more than others.
The beta of a portfolio is the:
slope of the risk-return line, or the CAPM risk measure. The beta of a portfolio is the slope of the risk-return line, or the CAPM risk measure. When you plot returns on the Y-axis and risk on the X-axis and fit a line through those returns the slope of that line will be the beta which is the relevant measure of risk according to the CAPM. The standard deviation of returns is a measure of risk but it measures total risk instead of the systematic risk measured by beta. The excess returns of the market portfolio over the risk-free return are known as the market risk premium which is a measure of return and not risk. The CAPM and beta make it very easy to immediately understand a security's risk and the impact it will have on a portfolio of assets. Since the beta of the market is equal to 1 any beta above 1 is higher risk than the overall market and should generate higher returns than the market. Conversely any beta below 1 indicates lower risk than the overall market and should generate below market returns.
The __________ indicates the tendency of historical returns to be different from their average and how far away from the average they tend to be.
standard deviation The standard deviation indicates the tendency of historical returns to be different from their average and how far away from the average they tend to be. An asset with a high standard deviation has returns that fluctuate more than an asset with a low standard deviation. Taking the square root of the variance gives you the standard deviation which is more commonly seen as a measure of dispersion around the mean for any normal distribution.
The risk of a portfolio is best described as the:
standard deviation of expected portfolio returns. The risk of a portfolio is best described as the standard deviation of expected portfolio returns. Standard deviation is a measure of dispersion about the mean for normally distributed assets. Since portfolio returns approximate a normal distribution the portfolio standard deviation is a good measure of portfolio risk. The market risk premium is the excess return over the risk-free rate and it is a return measure that identifies the amount of return investors receive for assuming risk. Neither are measures of risk.
The correlation coefficient is a measure of:
the degree of variation between asset returns. The correlation coefficient is a measure of the degree of variation between asset returns. Correlation tells us how much asset returns move together, or share common risks. Highly correlated assets tend to be impacted by similar events and so tend to move together and the correlation coefficient measures the strength of this relationship. The correlation coefficient ranges from -1 to +1. Any assets that are perfectly positively correlated (+1) will move in unison. Any assets that are perfectly negatively correlated (-1) will move as mirror images of one another. For example when one asset increases in price by 10%, the perfectly negatively correlated asset will fall in price by 10%. Standard deviation, not correlation, measures the total volatility in an asset's returns. The magnitude of a change can be measured with a percentage holding period return or other metrics. Asset correlations are used to help construct portfolios of assets that maximize returns for a given level of risk, or minimize risk for a given level of returns. For example, you could have two assets with the same expected return that were perfectly negatively correlated and in theory construct a portfolio that would eliminate all portfolio volatility (i.e. risk). When one asset moves up by 20% the other would move down by 20% and the volatility would cancel out.
A stock's total rate of return represents:
the total return earned over a specific period through buying and selling an asset. A stock's total rate of return represents the total return earned over a specific period through buying and selling an asset. The total rate of return includes any dividends received and the capital gains realized from buying and selling a stock. Total dividends are one component of the total rate of return. However, capital gains are also included. And you can calculate a total rate of return for a single asset or even a portfolio of assets if they were all bought and sold at the same time.
Which of the following is the best description of systematic risk?
Any risk that will impact the value of all assets simultaneously. Systematic risk is any risk that will impact the value of all assets simultaneously. Systematic risk is risk that affects the whole system. Examples of systematic risk include recessions and changes in fiscal policy or monetary policy that impact all firms in some manner. Any risk that is unique to a specific asset and can be eliminated with a large stock portfolio or sufficient diversification is unsystematic risk. Unsystematic risks can be offset with a large stock portfolio. When one firm is exposed to upside risk another will likely offset and move down, thus immunizing the portfolio against overall swings in value due to changes affecting individual firms.
Which of the following would be the best example of systematic risk?
The Federal Reserve tightens the money supply to fight inflation which causes the interest rates to rise. Of the three examples listed the best example of systematic risk is the Federal Reserve tightening the money supply to fight inflation and pushing interest rates higher as a result. Systematic risk is common risk associated with any event that impacts all stocks in some manner. When the Fed changes interest rates it will affect all firms so it is a risk associated with the entire system. The other risks are often called firm-specific, unique risk, or unsystematic risks. These risks are unrelated to other firms and unique to a specific company. Kroger's warehouse burning primarily impacts Kroger. Amazon's computer glitch impacted Amazon. Both of these events were risks unique to a specific firm. As you dig deeper into portfolio theory you will find you are able to eliminate your exposure to unsystematic risk through efficient diversification. This concept has numerous applications in finance.
The beta for a portfolio is determined by calculating:
a weighted average of individual stock betas where the weights equal the percentage invested in each stock. The beta for a portfolio is determined by calculating a weighted average of individual stock betas where the weights equal the percentage invested in each stock. The CAPM makes computing the portfolio risk much easier since it is a simple weighted average beta. For example, assume you have a total of $10,000 invested in your portfolio with $5,000 invested in Stock A with a beta of 1.2, $3,000 invested in Stock B with a beta of 2.2, and $2,000 invested in Stock C with a beta of 0.7. The portfolio beta would be; Beta portfolio = ($5,000/$10,000)(1.2) + ($3,000/$10,000)(2.2) + ($2,000/$10,000)(0.7) = .6 + .66 +.14 = 1.4. As you can see this process makes it very simple to compute a portfolio beta. Setting this up in a spreadsheet makes the process extremely fast and you can see in advance what you expect to happen to your portfolio risk if you intend to purchase or sell a particular stock.
The normal distribution is a symmetrical distribution that is described by its:
expected return and standard deviation. The normal distribution is a symmetrical distribution that is described by its expected return and standard deviation. Normal distributions can be fully described by only two values; an expected or average return in the center and a standard deviation which gives you a percentage deviation from the mean. The properties of the standard deviation are that 67% of the time the observed values will fall within plus or minus one standard deviation of the expected return, and 95% of the time the observed values will fall within plus or minus two standard deviations of the expected return. Because of this property you can accurately describe a normally distributed set of data with a expected return and standard deviation. Most financial asset returns approximate a normal distribution so the properties of the normal distribution are useful when evaluating risk and return metrics for stocks, bonds, and other financial assets.
The market risk premium is the:
return of the market over T-bills. The market risk premium is the return of the market over T-bills. The risk premium is the amount of return over and above the risk-free rate of return and T-bills are commonly used as a proxy for the risk-free rate. Corporate bonds carry risk over and above the risk-free rate of return so are not a good proxy of the risk-free return. And, variance is a measure of risk but not a measure of return.
The risk-return tradeoff principle in finance is:
the expectation of receiving higher returns for higher risk investments. The risk-return tradeoff principle in finance is the expectation of receiving higher returns for higher risk investments. Rational investors will always demand higher returns to accept higher risk and conversely are willing to accept lower returns on lower risk investments. Any investor faced with the choice between two assets with identical expected returns should always select the lower risk asset. Returns and risk are related but not in an additive manner. They measure two different components of investing that cannot be added or subtracted. If a risky asset is overpriced then its value will fall until its return is sufficient to attract investors.