Question

In: Finance

Consider 3 stocks: A with E(RA)= 15% and SD(RA)=20%, B with E(RB) =14% and SD(RB)=24% and...

Consider 3 stocks: A with E(RA)= 15% and SD(RA)=20%, B with E(RB) =14% and SD(RB)=24% and C with E(RC)=18% and SD(RC)=30%. The risk free rate RF= 6%,

1. which stock would you combine with the risk free to form a portfolio?

2. write the equation of Capital market line

3. If you consider that your target risk is 15%, what would be the composition of your final portfolio?

Expert Solution

1.

In general, we would like to have highest return per unit risk. So if we have to select one stock, we would select the stock with highest Sharpe ratio.

Sharpe ratio = (Stock return - Risk free return) / Stock standard deviation

Using this formula, we get the following values:

As the Sharpe ratio for A is highest, so it offers highest return per unit risk. So we will select stock A.

2.

The slope of the capital market line is given by:

Wher E(Rm) is expected return on market portfolio and is the standard deviation of market portfolio.

Since our market portfolio comprises of one stock only which is stock A, so the slope will be equal to the Sharpe ratio:

= (15% - 6%) / 20%

= 0.45

So the equation will be:

E (Rj) = 0.06 + 0.45*

3.

If W is the weight of stock A in the final portfolio, then the portfolio risk can be written as W * SD(RA)

Portfolio risk = W * SD(RA)

15% = W * 20%

W = 15% / 20%

= 0.75

So our final portfolio should have 75% of capital invested in stock A and remaining 25% invested in the risk free asset.

jeff jeffy answered 1 year ago

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