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The risk and the return of an investor can be reduced by adding a risk-free Treasury...

The risk and the return of an investor can be reduced by adding a risk-free Treasury bill to the market portfolio. Assume that the standard deviation of the market portfolio is 14%, its expected return is 12% and that you can borrow or invest at the risk-free Treasury bill rate of 3%. If you want to reduce an investor’s risk to a target standard deviation of 5%, what percentage of your portfolio would you invest in the market portfolio?

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Answer #1

Let the weight of risky asset = w, weight of risk free asset = (1-w)

Standard deviation of portfolio = = 0.05

Where, is standard deviation of risky asset

is standard deviation of risk free asset

covri,rf is the covariance between risky and risk free asset

Since the standard deviation of risk free asset is zero and the covariance between risky and risk free asset is also zero, the target standard deviation of portfolio will be

Target standard deviation of portfolio =

0.05 =   

w = 35.71%

Therefore required percentage of investment in market portfolio to achive target standard deviation = 35.71%

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