- Calculare the arithmetic average returns for large-company stocks and T-bills

Question

- Calculare the arithmetic average returns for large-company stocks and T-bills over this time period.

- Calculate the standard deviation of the returns for large-company stocks and T-bills over this time period.

- 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?

(b) What was the standard deviation of the risk premium over this period?

Returns Year Large-Company Stocks (X) U.S. Treasury Bills 1 -15.79% 7.51% 2 -26.80% 8.10% 3 37.45% 6.09% 4 24.15% 6.17% 5 -7.60% 5.56% 6 6.79% 7.97%

Explanation / Answer

a. Arithmetic average of returns of stock = (-15.79% -26.80% + 37.45% + 24.15% -7.60% + 6.79%)/6 = 3.03%

Average of return of T-bill = (7.51% + 8.10% + 6.09% + 6.17% + 5.56% + 7.97%)/6 = 6.90%

b.

Std dev = Square root (sum of square of difference between values and average/(n - 1))

note: n-1 is for unbiased std. dev. n would give biased std. dev.

c. Risk premium = Stock return - t-bill return

d. Arithmetic average of risk premium = (-23.30% -34.90% + 31.36% + 17.98% -13.16% -1.18%)/6 = -3.87%

Large-Company Stocks (X) X - average Squared -15.79% -18.82% 0.035431788 -26.80% -29.83% 0.089002778 37.45% 34.42% 0.118450694 24.15% 21.12% 0.044591361 -7.60% -10.63% 0.011306778 6.79% 3.76% 0.001411254 Sum of square 0.300194653 Sum of square/5 0.060038931 Std. Dev 0.245028428

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