Chapter 3 Risk and Return Overview
Which of the following correlations represents the strongest relationship between two variables?
Correlation = -1.00 Rationale: The strongest relationship exists at +1 and -1. The weakest relationship is at zero.
Pablo has $1 million saved for retirement. He expects to retire in 15 years. His retirement fund is expected to earn a nominal rate of 9%, and the inflation rate is estimated at 3%. How much money (in millions) should Pablo have when he retires, in real dollars?
$2.3m Rationale Real return = (1.09/1.03)-1 = 5.8252%FV = $1m x (1.058252)^15 = $2.34mAlternatively, on a financial calculator enter:PV = ($1,000,000)N = 15i= 5.8252PMT = 0Solve for FV = $2,337,957
Uncle Robbie, who lives in Kenner, Louisiana, bought a Treasury bond on the secondary market that has 10 years until maturity and a 2% coupon payment, paid semi-annually. Which of the following risks is he subject to?
Reinvestment rate risk. Rationale Uncle Robbie's bond is subject to reinvestment rate risk. The bond is not subject to default risk as it is a Treasury security.
Based on a normal distribution, 95% of all outcomes for investment returns should fall within approximately:
Two standard deviations.
A commercial bank owns a portfolio of fixed income securities with a market value of $810 million. The bank is concerned about a spike in inflation during the coming month, citing a potential energy shortage. A surge in oil and natural gas price would place significant downward pressure on the value of the portfolio. The risk management measure most likely to help the bank is:
Value at risk. Rationale While beta and standard deviation are excellent risk management measures, they are designed to identify long-term risks and variability. They reveal very little about short-term risk. Value at risk, however, was developed as a result of the 1987 crash to help banks manage the potential losses during market downturns, especially over shorter terms.
What are the two sources of return from an investment?
Yield and Capital Gain Yield + Capital Gain = Total Investment Return
Amelia bought Acme, Inc. for $40 per share two years ago. Today, Acme is trading at $72 per share. What is the annualized return for Amelia?
34.16% Rationale Annualized return = (1.8)^1/2 -1 = 34.16%
Security Y has the following returns over five years: 3%, 6%, 0%, 6%, and 3%. What is the mean return and the standard deviation (sample) for Security Y?
Mean of 3.6% and standard deviation of 2.5%. Rationale The mean equals 3.6% and the standard deviation equals 2.51%. To calculate standard deviation using the formula: The differences are: 0.6, 2.4, 3.6, 2.4, and 0.6 The differences squared are: 0.36, 5.76, 12.96, 5.76, 0.36. Sum of differences equals: 25.2. Divided by 4: 6.3 Square root = 2.51 Alternatively, standard deviation can be calculated on a financial calculator using the ∑+ key.
The "doctor" describes himself as a "swinging for the fences" type of investor. He invests in 1 stock ABC that has a beta of 0.75 and concludes that he is only taking 3/4 of the risk of the market. Is he right?
No, beta only measures systematic risk. Rationale: Beta only measures systematic risk. Since the doctor has only one stock, he has a lot of unsystematic risk as well. Therefore, he is incorrect.
Which of the following statements is correct? a. The coefficient of variation is equal to average return divided by standard deviation. b. Correlation and R2 range from -1 to +1. c. The covariance between assets A and B is equal to the standard deviation for A times the standard deviation for B divided by the correlation between A and B. d. None of the above are correct.
None of the above are correct. Rationale The coefficient of variation measures risk per unit of return, so it is calculated as the standard deviation of a security divided by it's average return. The correlation between two assets does range from -1 to +1, but R2 has a range of only 0 to +1. The covariance for two assets can be calculated as the standard deviation of asset A, multiplied by the standard deviation of asset B, multiplied by the correlation between the assets.
Portfolio C has a standard deviation of 20% and a correlation with the market of 0.9. If the standard deviation of the market is 18%, what is the beta for C?
1.00 Rationale Beta equals the standard deviation of the portfolio times the correlation divided by the standard deviation of the market: (0.2 x 0.9)÷ 0.18 = 1.00.
Stan invested in the Great Growth mutual fund 5 years ago. His returns were 60%, -20%, 10%, 0% and 25%, respectively. What was the geometric average return over the five years?
12% Rationale [(1+ 60%) x (1+ -20%) x (1 + 10%) x (1 + 0%) x (1 + 25%)] ^ 1/ 5 - 1= 11.97%.
Marjorie invested in the Hyper Growth mutual fund five years ago. Her returns were 26%, -10%, 15%, 3%, and 31%, respectively. What was his arithmetic average return over the five years?
13% Rationale: [26% -10% + 15% + 3% + 31%] ÷ 5 = 13%.
Assume that an American's investment in the stock of a French company yielded a nominal rate of return of 18% in the past 12 months. Assume also that the Euo was worth $0.20 at the start of the period and $0.25 at the end of the period. In this case, the true rate of return for the investor was:
47.5% Reason: [1.18*(0.25/0.20)]-1 The euro increased in value during the holding period. If the investor started with $100 and the euro was 0.20 per USD, then the investor could exchange their $100 for 500 Euros. The investment then grew by a nominal rate of 18% (500 EU x 1.18 = 590 EU). To bring the Euros back to dollars when the euro is now worth 0.25 per USD (590 x 0.25 = $147.50). Therefore, the investor's return was more than the nominal 18%
Consider a firm with assets of $200 and equity of $200. This firm issues $50 in debt with a 10% annual interest rate to repurchase $25 in equity and to invest $25 into the business. The first year after issuing the debt, the firm has $18 in operating income. Compute the firm's return on equity, ignoring tax.
7.4% Rationale ROE = ($18 OI - $5 interest) ÷ $175 = 0.07429Interest expense = $50 × 0.10 = $5Equity is $200 - $25 after the repurchase = $175
Portfolio A has a weighted beta coefficient of 1.5 and Portfolio B has a weighted beta coefficient of 0.9. With these assumptions, which of the following statements is correct?
Assuming the market were to drop by 5%, Portfolio B should drop less than Portfolio A. Rationale Since Portfolio A's beta is higher than B's, any change in the market should result in a larger change for A compared to B.
Bunny has only one stock in her investment portfolio. The beta of the stock is 0.7. Bunny assumes that her investment portfolio is only 70% as risky as the market. Which is the correct response?
Bunny is wrong because beta only measures systematic risk and having only one stock in a portfolio inherently has unsystematic risk. Rationale One stock has a high level of unsystematic (diversifiable) risk.
Which of the following statements regarding the standard deviation of a distribution is least accurate? a.The standard deviation is a measure of a distribution's dispersion around its mean. b. Investors use the standard deviation of a security's returns as a measure of risk. c. Distributions with a higher arithmetic mean also have a higher standard deviation. d. The variance of a distribution is its standard deviation squared.
Distributions with a higher arithmetic mean also have a higher standard deviation. Rationale: The standard deviation of a distribution measures its level of dispersion, so it is possible to have a high mean return, but a small standard deviation if the distribution is clustered around the mean. Option c is therefore the least accurate statement. The standard deviation is used as a risk measure and can be squared to give the variance.
Which of the following a systematic risk? a. country risk b. exchange rate risk c. executive risk d. business risk
Exchange rate risk Reason: all others are considered unsystematic risk which can be minimized through diversification
Which of the following statements concerning risk and return is not correct? a.Inflation risk, or purchasing power risk, is the variability in securities returns caused by a decline in the purchasing power of the invested dollars. b. Total return = yield + price change c. Exchange rate risk is the risk that currency fluctuations will cause an adverse effect on the return from an investment. d. Market risk includes a wide range of factors, including business cycles, changes in interest rates, global conflicts, as well as changes in consumer preferences.
Inflation risk, or purchasing power risk, is the variability in securities returns caused by a decline in the purchasing power of the invested dollars. Rationale inflation risk is not associated with the variability in securities returns. Rather, it is the decline in purchasing power of the amounts invested.
Which of the following is (are) correct regarding average returns? a. The geometric mean is a better measure of an investor's effective return over several periods than the arithmetic mean. b. The arithmetic mean is the average return for a series of returns and will always be less than or equal to the geometric mean. c. Both a and b. d. Neither a nor b.
The geometric mean is a better measure of an investor's effective return over several periods than the arithmetic mean. Rationale Option b is incorrect as the arithmetic mean will always be greater than or equal to the geometric mean.
What is the most accurate definition of risk?
The uncertainty of future returns
The geometric mean of a set of holding period returns for security is used to calculate: 1. The time-weighted return 2. The dollar-weighted return 3. The IRR
Time-weighted return Reason: the time-weighted return is calculated as the geometric mean of the HPR. The $-weighted return is the IRR of the CF into and out of a security. As such, it is dependent on the amount invested in a security in each period
Which of the following statements concerning risk and return is not correct? a. Market risk includes a wide range of factors, including business cycles, change in interest rates, global conflicts, as well as changes in consumer preferences b. Total return = Yield + Capital Gain c. Exchange rate risk is the risk that currency fluctuations will cause an adverse effect on the return from an investment d. Liquidity risk is a more significant risk for securities such as Treasury bills
liquidity risk is a more significant risk for securities such as Treasury Bills Reason: treasury bills are extremely liquid
Bubba, who lives in Scotland, invested £1 million in IBM, a U.S. company, trading at a market value of $85 per share. The conversion rate for pounds to dollars was £1 to $1.65 at the time of the investment. Assume that after two years, the stock doubles in price and he sells the stock when the conversion rate for pounds to dollars is £1 to $2.00. How much is his gain in pounds?
£0.65 million. Rationale The initial investment of £1 million at an exchange rate of $1.65 will buy $1.65 million. If the market price of the share doubles, so will the value of the dollar investment, hence Bubba will have $3.3 million ($1.65 x 2) at the end of the two-year period. The exchange rate on the date of sale has moved to $2.00 per £1, so the sales proceeds will be £1.65 million ($3.3 million divided by 2). Bubba has therefore turned his initial £1 million into £1.65 million and gained £0.65 million. The percentage gain can also be calculated using the nominal yield (100%) and the currency movement. The foreign currency (USD) weakened against GBP, it takes $2 to buy £1 at the date of sale but only $1.65 initially. This means at the date of sale $1 buys £0.50 (1/$2) and initially $1 bought £0.606 (1/$1.65). USD has therefore weakened by 17.50% [(0.5/0.606) - 1]. Bubba's gain is therefore [(1 + 100%) x (1 - 17.50%)] - 1 = (2 x 0.825) - 1 = 65%. R2