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# Calculating the various statistical measures

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Here are the inflation rates and U.S. stock market and Treasury bill returns between 1929 and 1933: 1929 Inflation=-2, Stock Market Return=-14.5, T-Bill Return=4.8. 1930: Inflation=-6.0, Stock Market Return=-28.3, T-Bill Return=2.4. 1931: -9.5, -43.9 and 1.1. 1932: -10.3, -9.9 and 1.0. 1933: .5, 57.3 and .3.

A. What was the real retun on the stock market in each year.
B. What was the average real return?
C. what was the risk premium in each year?
D. What was the average risk premium?
E. What was the standard deviation of the risk premium?

#### Solution Preview

Please refer attached file for better clarity of tables and missing formulas.

A.  What was the real return on the stock market in each year.

Market return, r Inflation, i Real Return
(1+r)/(1+i)-1
1929 -14.50% -2% -12.76%
1930 -28.30% -6% -23.72%
1931 -43.90% -9.50% -38.01%
1932 -9.90% -10.30% 0.45%
1933 57.30% 0.50% 56.52%

B.  What was the average real return?

Market return, r Inflation, i Real Return
(1+r)/(1+i)-1
1929 -14.50% ...

#### Solution Summary

Solution describes the steps to calculate the real return, average real return, risk premium, average risk premium and standard deviation of risk premium in the given case.

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## Calculate the average return, standard deviation, coefficient of variation in the given case.

Stocks M and W have the following historical returns:

Year Stock M Stock W
2007 -19% -13.50%
2008 33% 22.75%
2009 16% 34.50%
2010 -0.30% -7.83%
2011 27% 23.30%

a. Calculate the average rate of return for each stock during the 5-year period.
b. Assume that you are planning to hold a portfolio consisting of 30% of Stock M and 70% of Stock W. What is the realized rate of return on the portfolio in each year?
c. What is the average return on the portfolio for the 5 year period?
d. What is the standard deviation of returns for each stock and for the portfolio?
e. Calculate the coefficient of variation for each stock and for the portfolio?
f. If you are a risk averse investor, assuming these are your only choices, would you prefer to hold Stock M, Stock W, or the portfolio? Why?

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