Problem 10-8 Risk Premiums [LO 2] Consider the following table for a period of s

Question

Problem 10-8 Risk Premiums [LO 2] Consider the following table for a period of six years. Returns Year Large-Company Stocks U.S. Treasury Bills Year 1 – 15.09 % 7.37 % Year 2 – 26.59 8.03 Year 3 37.31 5.95 Year 4 24.01 5.47 Year 5 – 7.32 5.49 Year 6 6.65 7.76

Requirement 1: Calculate the arithmetic average returns for large-company stocks and T-bills over this time period. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Arithmetic average returns Large-company stock 3.16 % T-bills 6.68 %

Requirement 2: Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Standard deviation Large-company stock 24.25 % T-bills 1.17 %

Requirement 3: Calculate the observed risk premium in each year for the large-company stocks versus the T-bills.
(a) What was the arithmetic average risk premium over this period? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Risk premium -3.52 %
(b) What was the standard deviation of the risk premium over this period? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) Risk premium standard deviation %

Explanation / Answer

Year   U.S Stock(X) Treasury Bill(Y) x-x y-   (x-x)^2 (y-)^2                                         1                        15.09                     7.37       (4.4050)                0.69          19.40           0.48                                         2                        26.59                     8.03         7.0950                1.35          50.34           1.83                                         3                        37.31                     5.95       17.8150              (0.73)        317.37           0.53                                         4                        24.01                     5.47         4.5150              (1.21)          20.39           1.46                                         5                          7.32                     5.49    (12.1750)              (1.19)        148.23           1.41                                         6                          6.65                     7.76    (12.8450)                1.08        164.99           1.17                      116.97                   40.07           (0.00)                0.00        720.73           6.88 Requirement 1 Treasury Bill-   116.97/6        6.6783 % Mean/ 6 Arithmetic Mean 40.07/6     19.4950 % Requirment 2 Standard Deviation Treasury Bill-   720.73     24.8464 Arithmetic Mean 6.88        2.5845 Requirement 3- a) Arithmetic Average Risk Premium   (Rm-Rf) 116.97-40.07           76.90 (Rm-Rf)/6           12.82 B) Standard Deviation of Risk Premium 24.8464/6              4.14 2.5845/6         0.4308 (Rm-Rf)/6           12.82 B) Standard Deviation of Risk Premium 24.8464/6              4.14 2.5845/6         0.4308

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