Question

The expected return of the market portfolio is 14 percent with a standard deviation of 25 percent. The risk-free rate is 6 percent. What is the weight of the market portfolio in an efficient portfolio with a standard deviation of 30 percent?

A) 120%

B) 83.33%

C) 20%

D) 16.78%

Answer 1

An efficient portfolio is one in which the return is maximum for a given level of risk , or , the risk is minimum for a given level of return.

Note:- Standard Deviation is used as a measure of Risk for calculating the effecient portfolio.

The Risk-Free asset giving 6% return is always assumed to carry zero risk , meaning standard deviation is 0.

Hence, for an efficient portfolio with standard deviation = 30%, weight of Market Portfolio is calculated as below:-

30% = Weight * Standard Deviation of Market Portfolio

30% = Weight * 25%

Weight = 30% / 25% = 1.2 times or 120%

Hence, the correct answer is option A) 120%

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