# Solutions 10-8-18

**Topics:**Standard deviation, Arithmetic mean, Variance

**Pages:**3 (455 words)

**Published:**February 8, 2013

RISK AND RETURN: LESSONS FROM MARKET HISTORY

8. We will calculate the sum of the returns for each asset and the observed risk premium first. Doing so, we get:

YearLarge co. stock returnT-bill returnRisk premium

1973–14.69%7.29%(21.98%

1974–26.477.99–34.46

197537.235.8731.36

197623.935.0718.86

1977–7.165.45–12.61

1978 6.57 7.64 –1.07

19.41%39.31%–19.90%

a.The average return for large company stocks over this period was:

Large company stock average return = 19.41% /6

Large company stock average return = 3.24%

And the average return for T-bills over this period was:

T. T-bills average return = 39.31% / 6

U. T-bills average return = 6.55%

V.

b.Using the equation for variance, we find the variance for large company stocks over this period was:

Variance = 1/5[(–.1469 – .0324)2 + (–.2647 – .0324)2 + (.3723 – .0324)2 + (.2393 – .0324)2 + (–.0716 – .0324)2 + (.0657 – .0324)2] Variance = 0.058136

And the standard deviation for large company stocks over this period was:

Standard deviation = (0.058136)1/2

Standard deviation = 0.2411 or 24.11%

Using the equation for variance, we find the variance for T-bills over this period was:

Variance = 1/5[(.0729 – .0655)2 + (.0799 – .0655)2 + (.0587 – .0655)2 + (.0507 – .0655)2 + (.0545 – .0655)2 + (.0764 – .0655)2]

Variance = 0.000153

And the standard deviation for T-bills over this period was:

Standard deviation = (0.000153)1/2

Standard deviation = 0.0124 or 1.24%

c.The average observed risk premium over this period was:

Average observed risk premium = –19.90% / 6

Average observed risk premium = –3.32%

The variance of the observed risk premium was:

Variance = 1/5[(–.2198 –...

Please join StudyMode to read the full document