You have $800,000 invested in a complete portfolio that consists of a portfolio

Question

You have $800,000 invested in a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets.

E(rp)=12.00%

?p =7.00%

T-Bill rate=3.6%

Proportion of T-Bill in the complete portfolio: 20%

Proportion of risky portfolio P in the complete portfolio: 80%

Composition of P:

Stock A                 40%

Stock B                 25%

Stock C                 35%

Total                      100%

What is the expected return on your complete portfolio?

What is the standard deviation of your complete portfolio?

What are the dollar amounts of Stocks A, B, and C, respectively, in your complete portfolio?

If your degree of risk aversion is A=4, is your complete portfolio optimal? (assuming P is the optimal risky portfolio)

Explanation / Answer

Total investment = 800,000

Amount in t-bills = 20% of 800,000 = 160,000

Amount in risky assets = 800,000 - 160,000 = 640,000

Interest on t-bills = 3.6% of 160,000 = 5,760

Return on portfolio = 7% (given) = .07*640,000 = 44,800

Thus, expected return = interest on t-bills+return on stocks = 5,760+44,800 = 50,560

rate of return = 50,560/800,000 = 6%

Dollar amount of stocks:

Stock A = 40% . P amount = 640,000. Thus A = .4*640,000 = 256,000

Stock B = .25*640,000 = 160,000

Stock C = .35*640,000 = 224,000

Degree of risk aversion = 4 (beta)

Using CAPM = risk free rate+beta*(market return - risk free rate)

3.6%+4(7-3.6) = 3.6+13.6 = 17.2%

As, return on portfolio is less than return per CAPM, it is not an optimal portfolio

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