Your investment portfolio consists of $10, 000 invested in only one stock-Micros

Question

Your investment portfolio consists of $10, 000 invested in only one stock-Microsoft. Suppose the risk-free rate is 4%, Microsoft stock has an expected return of 14% and a volatility of 36%, and the market portfolio has an expected return of 12% and a volatility of 19%. Make sure to round all intermediate calculations to at least Jive decimal places. Under the CAPM assumptions, What alternative investment has the lowest possible volatility while having the same expected return as Microsoft? What is the volatility of this investment? What investment has the highest possible expected return while having the same volatility as Microsoft? What is the expected return of this investment? What alternative investment has the lowest possible volatility while having the same expected return as Microsoft? To create an alternative investment that has the lowest possible volatility while having the same expected return as Microsoft, we use the following strategy: What investment has the highest possible expected return while having the same volatility as Microsoft? To create an alternative investment that has the highest possible expected return while having the same volatility as Microsoft, we use the following strategy:

Explanation / Answer

1)

a.

under the CAPM assumption the market portfolio is efficient, A Leveraged position in the market portfolio has the highest expected return of any portfolio for a given volatility, and the lowest volatility for a given expected return, that is, one can achieve the same expected return as Microsoft by holding a leveraged position in the market portfolio .W and 1-Wm the risk free asset:

W(Rp) = Wm(ERf)+(1-w)fRf

Setting this equal to 14% and solving for the weight in the market portfolio gives, Wm = 1.9

Portfolio with the lowest volatility that has the same return as Microsoft has $ 10,000 X1.9 = $19,000 invested in the market portfolio and borrows $ 19,000- $10,000 = $ 9000 at the risk free rate.

The Volatility portfolio

Op = 1.9Om

Note that this the lower than the volatility of Microsoft alone

b.

Under CAPM assumption the market portfolio is efficient. A leveraged position in the market portfolio has the highest expected return of any portfolio for a given volatility, and the lowest volatility for a given expected return. That is, one can have the same volatility as Microsoft by holding a leveraged position in the market portfolio Wm, 1-Wm, in the risk free asset such that

Op = 0.36 = WmOm

=0.36 =Wm0.19

Wm = 0.36/0.19 = 1.894737

So the portfolio with the highest expected return that has the same volatility as Microsoft invests $10,000 X 1.894737 =18,947 in the market portfolio and borrows $ 18947-$ 10,000= $8,947 at the risk free rate.

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