Question

Calculate the arithmetic average returns for large-company stocks and T-bills over this period. (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 the returns for large-company stocks and T-bills over this period. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c-1. Calculate the observed risk premium in each year for the large-company stocks versus the T-bills. What was the average risk premium over this period

Answer 1

Answer:

a. Arithmetic average returns for large company stocks:

= (0.0389 + 0.1414 + 0.1913 - 0.1455 - 0.3204 + 0.3737) / 6

= 4.66%

Arithmetic average returns for T-bills:

= (0.0581 + 0.0247 + 0.0370 + 0.0713 + 0.0518 + 0.0616) / 6

= 0.05075

= 5.08%

b. First find variance.

Variance of large company stock:

Variance is divided by n - 1

= {(0.0389 - 0.0466)² + (0.1414 - 0.0466)² + (0.1913 - 0.0466)² + (-0.1455 - 0.0466)² + (-0.3204 - 0.0466)² + (0.3737 - 0.0466)²} / 5

= 0.0617140

Standard deviation = √0.0617140

= 24.84%

Variance of T-bills

= {(0.0581 - 0.0508)² + (0.0247 - 0.0508)² + (0.0370 - 0.0508)² + (0.0713 - 0.0508)² + (0.0518 - 0.0508)² + (0.0616 - 0.0508)²} / 5

= 0.0002926

Standard deviation = √0.0002926

= 1.71%

c. Risk Premiums:

Year 1                                        Year 2                                      Year 3

= 3.89% - 5.81%                        =  14.14% - 2.47%                     = 19.13% - 3.70%

= -1.92%                                    = 11.67%                                    = 15.43%

 

Year 4                                        Year 5                                      Year 6

= -14.55% - 7.13%                       = -32.04% - 5.18%                  =37.37% - 6.16%

= -21.68%                                  = -37.22%                                = 31.21%

Average risk premium:

= (-0.0192 + 0.1167 + 0.1543 - 0.2168 - 0.3722 + 0.3121) / 6

= -0.42%