Chapter 8 Business Finance Study guide
Which of the following correlation coefficients (CorrAB) 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 (CorrAB) 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. Additional Learning 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.
Assume you have the following assets, expected returns, and betas: Asset Expected returns Beta A 16% 1.2 B 14% 1.0 C 21% 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
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. E(Rj) = Rf + Bj(E(Rm) - Rf) where; E(Rj) = required return or expected return Rf = risk-free rate Bj = Beta of sercurity j E(Rm) = expected return on the market So, substituting the numbers into the formula yields; E(Rj) = 4% + 1.6(12% - 4%) = 16.8%
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%. To determine the risk premium you need to use the CAPM formula below; E(Rj) = Rf + Bj(E(Rm) - Rf) where; E(Rj) = required return or expected return Rf = risk-free rate Bj = Beta of sercurity j E(Rm) = expected return on the market Bj(E(Rm) - Rf) = risk premium for security j So, substituting and solving you get; 15% = 6% + risk premium, so after subtracting 6% from each side you get; Risk premium = 9% Additional Learning The CAPM makes evaluating an asset's risk very easy. You can look at an asset's beta and immediately determine the asset's risk. For this reason you need to make sure you understand all the components of the CAPM.
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.
A stock's holding period return represents:
the total return earned over a specific period through buying and selling an asset.
The __________ indicates the tendency of historical returns to be different from their average and how far away from the average they tend to be.
variance
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. Additional Learning 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.
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: So for Hobo Hats the return is; Additional Learning Note that the return is comprised of the dividend yield and the capital gains yield for Hobo stock. While in this case it is also an annual return you need to make sure you always compare returns for equivalent holding periods. In other words do not compare a 6-month holding period return to a 12-month holding period return. This type of comparison is not appropriate.
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.
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. Additional Learning 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.
__________ 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.
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. 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. Additional Learning 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:
mean and standard deviation. The normal distribution is a symmetrical distribution that is described by its mean and standard deviation. Normal distributions can be fully described by only two values; a mean 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 mean, and 95% of the time the observed values will fall within plus or minus two standard deviations of the mean. Because of this property you can accurately describe a normally distributed set of data with a mean and standard deviation. The standard deviation is the square root of the variance so both of those are a measure of risk. The compound return and the realized return are both return measures but neither is the appropriate return to use when describing a normal distribution. Additional Learning 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 equity market risk premium is the:
return of equities over T-bills. The equity market risk premium is the return of equities over T-bills. The equity 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.
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. Additional Learning 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. Additional Learning 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 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.
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.
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. Additional Learning 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.
