Calculating Returns Refer to Table 10.1 in the text and look at the period from 1973 through 1980.
- a. calculate the average return for Treasury bills and the average annual inflation rate (consumer price index) for this period.
- b. calculate the standard deviation of Treasury bill returns and inflation over this period.
- c. calculate the real return for each year. What is the average real return for Treasury bills?
- d. Many people consider Treasury bills to be risk-free. What do these calculations tell you about the potential risks of Treasury bills?
(a)
To determine: The returns
Introduction:
The term return refers to a profit or gain made on an investment that is usually expressed in terms of percentage or dollars. The percentage total return shows the overall performance and efficiency of the amount invested.
Answer to Problem 22QP
Solution: The average return for t-bills over the period of time is 7.75%.
Explanation of Solution
Given information:
The returns of t-bills are 0.0729, 0.0799, 0.0587, 0.0507, 0.0545, 0.764, 0.1056, and 0.1210. The inflations are 0.0871, 0.1234, 0.0694, 0.0486, 0.0670, 0.0902, 0.1329, and 0.1252.
The formula to calculate the real return by using fisher equation:
Compute the real return of 1973:
Hence, the real return for the year 1973 is 0.0131.
Compute the real return of 1974:
Hence, the real return for the year 1974 is -0.0387.
Compute the real return of 1975:
Hence, the real return for the year 1975 is -0.0100.
Compute the real return of 1976:
Hence, the real return for the year 1976 is 0.0020.
Compute the real return of 1977:
Hence, the real return for the year 1977 is -0.0117.
Compute the real return for the year 1978:
Hence, the real return for the year 1978 is -0.0127.
Compute the real return for the year 1979:
Hence, the real return for the year 1979 is 0.0241.
Compute the real return for the year 1980:
Hence, the real return for the year 1980 is -0.0037.
(b)
To determine: The returns
Introduction:
The term return refers to a profit or gain made on an investment that is usually expressed in terms of percentage or dollars. The percentage total return shows the overall performance and efficiency of the amount invested.
Answer to Problem 22QP
The variance for t-bills is 0.000616 and the standard deviation is 2.48%. The
variance for inflation is 0.000971 and the standard deviation is 3.12%.
Explanation of Solution
The formula to calculate the arithmetic average return:
Where,
R refers to average return,
T refers to number of returns
Compute the arithmetic average return:
The formula to calculate the variance for t-bills:
Where,
“T” refers to the total number of returns,
“R” refers to the return of each year,
“
Compute the variance for t-bills:
Hence, the variance for t-bills is 0.000616.
The formula to calculate the standard deviation:
Compute the standard deviation for t-bills:
Hence, the standard deviation for t-bills is 2.48%.
Compute the variance for inflation:
Hence, the variance for inflation over the period is 0.000971.
Compute the standard deviation for inflation:
Hence, the standard deviation for inflation over the period is 3.12%.
(c)
To determine: The returns
Introduction:
The term return refers to a profit or gain made on an investment that is usually expressed in terms of percentage or dollars. The percentage total return shows the overall performance and efficiency of the amount invested.
Answer to Problem 22QP
The average observed risk premium is -1.40%.
Explanation of Solution
Compute the average observed risk premium:
(d)
To determine: The returns
Introduction:
The term return refers to a profit or gain made on an investment that is usually expressed in terms of percentage or dollars. The percentage total return shows the overall performance and efficiency of the amount invested.
Answer to Problem 22QP
Treasury bills have no risk.
Explanation of Solution
Since, there is only an enormous small possibility of the government defaulting, treasury bills have no risk or modest default risk. The calculation shows that there is a risk of inflation. The actual purchasing power of the investment has declined over time even though the return is positive.
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Chapter 10 Solutions
UPENN: LOOSE LEAF CORP.FIN W/CONNECT
- Consider the following table for the period from 1973 through 1980. Inflation 8.80% 12.20 7.01 4.81 6.77 9.03 13.31 12.40 Year 1973 1974 1975 1976 1977 1978 1979 1980 T-bill return 6.93% 8.00 5.80 5.08 5.12 7.18 10.38 11.24 a. Calculate the average return for Treasury bills and the average annual Inflation rate (consumer price Index) for this period. Note: Do not round Intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. b. Calculate the standard deviation of Treasury bill returns and Inflation over this time period. Note: Do not round Intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. c. Calculate the real return for each year. Note: A negative answer should be indicated by a minus sign. Do not round Intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16. d. What is the average real return for Treasury bills? Note: A negative answer…arrow_forwardof interest? The exact real rate? 10. Inflation and Nominal Returns Suppose the real rate is 1.8 percent and the inflation rate is 3.7 percent. What rate would you expect to see on a Treasury bill? 11. Nominal and Real Returns An investment offers a total return of 12 percentarrow_forwardIf the risk-free rate is 2.2 percent, the inflation rate is 1.9 percent, and the market rate of return is 6.8 percent, what is the amount of the risk premium on a U.S. Treasury bill?arrow_forward
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