Question

The expected return of Culver is 14.4 percent, and the expected return of Larkspur is 22.4 percent. Their standard deviations are 9.4 percent and 22.4 percent, respectively, and the correlation coefficient between them is zero. What is the expected return and standard deviation of a portfolio composed of 25 percent Culver and 75 percent Larkspur? (Round intermediate calculations to 6 decimal places, e.g. 31.212564 and final answers to 2 decimal places, e.g. 15.25%.) The expected return % Standard deviation of portfolio % What is the expected return and standard deviation of a portfolio composed of 75 percent Culver and 25 percent Larkspur? (Round intermediate calculations to 6 decimal places, e.g. 31.212564 and final answers to 2 decimal places, e.g. 15.25%.) The expected return % Standard deviation of portfolio % Would a risk-averse investor hold a portfolio made up of 100 percent of Culver?

Answer 1

Scenario 1:

Weight of Culver W1 = 25%

Weight of Larkspur W2 = 75%

So,

Expected return of the portfolio = .25*14.4% + .75*22.4%

Expected return of the portfolio = 20.40%

Standard deviation of the portfolio = (W1^2*SD1^2 + W2^2*SD2^2 + 2*W1*W2*COV12)^.5

If correlation coefficient is zero, then covariance will also be zero.

So,

Standard deviation of the portfolio = (.25^2*.094^2 + .75^2*.224^2 + 0)^.5

Standard deviation of the portfolio = 16.96%

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Scenario 2:

Weight of Culver W1 = 75%

Weight of Larkspur W2 = 25%

So,

Expected return of the portfolio = .75*14.4% + .25*22.4%

Expected return of the portfolio = 16.40%

Standard deviation of the portfolio = (W1^2*SD1^2 + W2^2*SD2^2 + 2*W1*W2*COV12)^.5

If correlation coefficient is zero, then covariance will also be zero.

So,

Standard deviation of the portfolio = (.75^2*.094^2 + .25^2*.224^2 + 0)^.5

Standard deviation of the portfolio = 9.00%

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No, risk averse investor will not hold a portfolio, full of 100% Culvar stocks as it has higher standard deviation than the portfolio of 75% Culvar and 25% Larkspur stocks.

So, risk averse investor will choose to go for the portfolio of 75% Culver and 25% Larkspur stocks, because it has lowest standard deviation or risk profile and return level is also higher than only Culvar stock.