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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%
