a)
To determine: The arithmetic average for large-company stocks and Treasury bills.
Introduction:
Arithmetic average return refers to the returns that an investment earns in an average year over different periods.
a)
Answer to Problem 8QP
Answer:
The arithmetic average of large-company stocks is 3.24%, and the arithmetic average of Treasury bills is 6.55%.
Explanation of Solution
Explanation:
Given information:
Refer to Table 10.1 in the chapter. Extract the data for large-company stocks and Treasury bills from 1973 to 1978 as follows:
Year |
Large co. stock return | T-bill return |
Risk premium |
1973 | –14.69% | 7.29% | –21.98% |
1974 | –26.47% | 7.99% | –34.46% |
1975 | 37.23% | 5.87% | 31.36% |
1976 | 23.93% | 5.07% | 18.86% |
1977 | –7.16% | 5.45% | –12.61% |
1978 | 6.57% | 7.64% | –1.07% |
Total | 19.41% | 39.31% | –19.90% |
The formula to calculate the arithmetic average return:
Where,
“∑Xi” refers to the total of observations,
“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),
“N” refers to the number of observations.
Compute the arithmetic average for large-company stocks:
The total of the observations is 19.41%. There are 6 observations.
Hence, the arithmetic average of large-company stocks is 3.24%.
Compute the arithmetic average for Treasury bill return:
The total of the observations is -39.31%. There are 6 observations.
Hence, the arithmetic average of Treasury bills is 6.55%.
b)
To determine: The standard deviation of large-company stocks and Treasury bills.
Introduction:
Variance refers to the average difference of squared deviations of the actual data from the mean or average.
Standard deviation refers to the deviation of the observations from the mean.
b)
Answer to Problem 8QP
Answer:
The standard deviation of large-company stocks is 24.11%, and the standard deviation of Treasury bills is 1.24%.
Explanation of Solution
Explanation:
Given information:
Refer to Table 10.1 in the chapter. The arithmetic average of Treasury bills is 6.55%. Extract the data for large-company stocks and Treasury bills from 1973 to 1978 as follows:
Year |
Large co. Stock return | T-bill return |
Risk premium |
1973 | –14.69% | 7.29% | –21.98% |
1974 | –26.47% | 7.99% | –34.46% |
1975 | 37.23% | 5.87% | 31.36% |
1976 | 23.93% | 5.07% | 18.86% |
1977 | –7.16% | 5.45% | –12.61% |
1978 | 6.57% | 7.64% | –1.07% |
Total | 19.41% | 39.31% | –19.90% |
The formula to calculate the standard deviation of the returns:
“SD(R)” refers to the standard deviation of the return,
“X̅” refers to the arithmetic average,
“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),
“N” refers to the number of observations.
Compute the squared deviations of large-company stocks:
Large-company stocks | |||
Actual return |
Average return(B) |
Deviation (A)–(B)=(C) |
Squared Deviation (C)2 |
(A) | |||
−0.1469 | 0.0324 | −0.1793 | 0.0321485 |
−0.2647 | 0.0324 | −0.2971 | 0.0882684 |
0.3723 | 0.0324 | 0.3399 | 0.115532 |
0.2393 | 0.0324 | 0.2069 | 0.0428076 |
−0.0716 | 0.0324 | −0.104 | 0.010816 |
0.0657 | 0.0324 | 0.0333 | 0.0011089 |
Total of squared deviation | 0.05813 | ||
Compute the standard deviation of the return:
Hence, the standard deviation of large-company stocks is 24.111%.
Compute the squared deviations of Treasury bill:
Treasury bill | |||
Actual return |
Average Return (B) |
Deviation (A)–(B)=(C) |
Squared Deviation (C)2 |
(A) | |||
0.0729 | 0.0655 | 0.0074 | 0.00005 |
0.0799 | 0.0655 | 0.0144 | 0.00020736 |
0.0587 | 0.0655 | -0.0068 | 0.00004624 |
0.0507 | 0.0655 | -0.0148 | 0.00021904 |
0.0545 | 0.0655 | -0.011 | 0.000121 |
0.0764 | 0.0655 | 0.0109 | 0.00011881 |
0.000154 |
Compute the standard deviation:
Hence, the standard deviation of Treasury bills is 1.24%.
c)
To determine: The arithmetic average and the standard deviation of observed risk premium.
Introduction:
Arithmetic average return refers to the returns that an investment earns in an average year over different periods.
Standard deviation refers to the deviation of the observations from the mean.
c)
Answer to Problem 8QP
Answer:
The arithmetic average is −3.32%, and the standard deviation is 24.92%.
Explanation of Solution
Explanation:
Given information:
Refer to Table 10.1 in the chapter. Extract the data for large-company stocks and Treasury bills from 1973 to 1978 as follows:
Year |
Large co. stock return | T-bill return |
Risk premium |
1973 | –14.69% | 7.29% | –21.98% |
1974 | –26.47% | 7.99% | –34.46% |
1975 | 37.23% | 5.87% | 31.36% |
1976 | 23.93% | 5.07% | 18.86% |
1977 | –7.16% | 5.45% | –12.61% |
1978 | 6.57% | 7.64% | –1.07% |
Total | 19.41% | 39.31% | –19.90% |
The formula to calculate the arithmetic average return:
Where,
“∑Xi” refers to the total of observations,
“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),
“N” refers to the number of observations.
The formula to calculate the standard deviation:
“SD (R)” refers to the standard deviation of the return,
“X̅” refers to the arithmetic average,
“Xi” refers to each of the observations from X1 to XN (as “i” goes from 1 to “N”),
“N” refers to the number of observations.
Compute the arithmetic average for risk premium:
The total of the observations is (-19.90%). There are 6 observations.
Hence, the arithmetic average of risk premium is −3.32%.
Compute the squared deviations of risk premium:
Risk premium | |||
Actual return (A) |
Average Return (B) |
Deviation (A)–(B)=(C) |
Squared deviation |
(C)2 | |||
-0.2198 | -0.0332 | -0.1866 | 0.034820 |
-0.3446 | -0.0332 | -0.3114 | 0.096970 |
0.3136 | -0.0332 | 0.3468 | 0.120270 |
0.1886 | -0.0332 | 0.2218 | 0.049195 |
-0.1261 | -0.0332 | -0.0929 | 0.008630 |
-0.0107 | -0.0332 | 0.0225 | 0.000506 |
0.062078 |
Compute the standard deviation:
Hence, the standard deviation of risk premium is 24.92%.
d)
To determine: Whether the risk premium can be negative before and after the investment.
Introduction:
Arithmetic average return refers to the returns that an investment earns in an average year over different periods.
Variance refers to the average difference of squared deviations of the actual data from the mean or average.
Standard deviation refers to the deviation of the observations from the mean.
d)
Explanation of Solution
Explanation:
The risk premium cannot be negative before the investment because the investors require compensation for assuming the risk. They will invest when the stock compensates for the risk. The risk premium can be negative after the investment, if the nominal returns are very low compared to the risk-free returns.
Want to see more full solutions like this?
Chapter 10 Solutions
ESSENTIALS OF CORPORATE FINANCE (LL)
- Over a certain period, large-company stocks had an average return of 12.79 percent, the average risk-free rate was 2.62 percent, and small-company stocks averaged 17.61 percent. What was the risk premium on small-company stocks for this period?arrow_forwardYou’ve observed the following returns on SkyNet Data Corporation’s stock over the past five years: 19 percent, 24 percent, 11 percent, −9 percent, and 13 percent. Suppose the average inflation rate over this period was 3.6 percent and the average T-bill rate over the period was 4.1 percent.a. What was the average real return on the company’s stock?b. What was the average nominal risk premium on the company’s stock?arrow_forwardAssume the average return on utility stocks was 8.9% over the past 40 years. �If the average return on Treasury bills was 3.8% over that period, what is the historical risk premium for utility stocks?arrow_forward
- Assume these are the stock market and Treasury bill returns for a 5-year period: Year Stock Market Return (%) T-Bill Return (%) 2016 13.0 0.2 2017 21.0 0.8 2018 -6.2 1.8 2019 29.8 2.1 2020 20.6 0.4 Required: What was the risk premium on common stock in each year? What was the average risk premium? What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)arrow_forwardAssume these are the stock market and Treasury bill returns for a 5-year period: Required: a. What was the risk premium on common stock in each year? b. What was the average risk premium? c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.) Complete this question by entering your answers in the tabs below. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.) Note: Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.arrow_forwardHistorical stock returns show that small - company stocks produced an average return of 17.4 percent, inflation averaged 3.1 percent, U.S. Treasury bills returned an average 3.8 percent, and long - term corporate bonds returned 6.2 percent. What was the risk premium on small - company stocks for that period?arrow_forward
- Over a certain period, large-company stocks had an average return of 12.19 percent, the average risk-free rate was 2.50 percent, and small-company stocks averaged 17.13 percent. What was the risk premium on small-company stocks for this period? Multiple Choice 9.69% 11.70% 14.63% 19.63% 4.94%arrow_forwardYou’ve observed the following returns on Barnett Corporation’s stock over the past five years: –25.5 percent, 14 percent, 31 percent, 2.5 percent, and 21.5 percent. The average inflation rate over this period was 3.25 percent and the average T-bill rate over the period was 4.3 percent.What was the average real risk-free rate over this time period? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)Average real risk-free rate % What was the average real risk premium? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)Average real risk premium %arrow_forwardPlease include the excel formula You’ve observed the following returns on Pine Computer’s stock over the past five years: 8 percent, −12 percent, 14 percent, 21 percent, and 16 percent. Suppose the average inflation rate over this period was 3.1 percent and the average T-bill rate over the period was 3.9 percent. What was the average real return on the company’s stock? What was the average nominal risk premium on the company’s stock over this period? Input area: Year Returns 1 8% 2 -12% 3 14% 4 21% 5 16% Average inflation 3.10% Average T-bill rate 3.90% (Use cells A6 to B13 from the given information to complete this question. You must use the built-in Excel function to answer this question. Make sure to use the “sample” Excel formula.)…arrow_forward
- Assume these are the stock market and Treasury bill returns for a 5-year period: Year Stock Market Return (%) T-Bill Return (%) 2013 36.00 0.22 2014 15.40 0.22 2015 −5.20 0.22 2016 17.00 0.09 2017 26.00 0.11 Required: a. What was the risk premium on common stock in each year? b. What was the average risk premium? c. What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)arrow_forwardAmong the following types of investments, small-company stocks, large-company stocks, long-term corporate bonds, long-term government bonds, and U.S. Treasury bills, small-company stocks had a risk premium of 13.2 percent for the past 90 years. What does the term "risk premium" mean? Is the risk premium on small-company stocks considered to be relatively high or relatively low when compared to other investment classes? Explain why.arrow_forwardAssume these are the stock market and Treasury bill returns for a 5-year period: Year Stock Market Return (%) T-Bill Return (%) 2016 13.0 0.2 2017 21.0 0.8 2018 -6.2 1.8 2019 29.8 2.1 2020 20.6 0.4 Required: What was the risk premium on common stock in each year? What was the average risk premium? What was the standard deviation of the risk premium? (Ignore that the estimation is from a sample of data.)-- expressed in % (NOTE: 11.31% is incorrect)arrow_forward
- EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENTIntermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning