Question

# What is the standard deviation of a stock that has a 10 percent chance of earning...

What is the standard deviation of a stock that has a 10 percent chance of earning 18%, a 10 percent chance of making 11%, a 40 percent chance of making 5%, and a 40 percent chance of making 22%?

• A. 7.95%

• B. 13.70%

• C. 7.78%

• D. 13.05%

You have \$250,000 to invest in two stocks. Stock A has an expected return of 15% and stock B has an expected return of 8%. How much must you invest in each stock to have a portfolio with an expected return of 13%?

• A. \$216,667 in Stock A and \$33,333 in Stock B

• B. \$96,154 in Stock A and \$153,846 in Stock B

• C. \$178,571 in Stock A and \$71,429 in Stock B

• D. \$134,615 in Stock A and \$115,385 in Stock B

Which of the following will be true about the return and standard deviation of a portfolio?

• A. The return of a portfolio will be the weighted average of the returns in the portfolio, but the standard deviation will be less than the weighted average of the standard deviations in the portfolio.

• B. The return and standard deviation of a portfolio will be the weighted average of the returns and standard deviations in the portfolio.

• C. The return and standard deviation of a portfolio will be less than the weighted average of the returns and standard deviations in the portfolio.

• D. The return of a portfolio will be less than the weighted average of the returns in the portfolio, but the standard deviation will be the weighted average of the standard deviations in the portfolio.

Solution:

1.Calculation of standard deviation

Mean=Probabilty*Return

=0.10*18%+0.10*11%+0.40*5%+0.40*22%=13.7%

 Probability(P) Return(%) Deviation=Return-Mean(D)(%) (D^2)*P 0.10 18 4.3 1.849 0.10 11 -2.7 0.729 0.40 5 -8.7 30.276 0.40 22 8.3 27.556 Sum of (D^2)*P 60.41%

Standard deviation=SQRT(Sum of (D^2)*P)

. =SQRT(60.41%)=7.77%

Therefore correct answer is option c

2.Calculation of amount to be invested on each stock

Expected return of portfolio=Stock'A return*Weight of Stock A+Stock'B return*Weight of Stock B

Let the amount invested in Stock A is X,thus amount incvested in stock B is \$250,000-X

13%=15%*(X/\$250,000)+8%*(\$250,000-X/\$250,000)

0.13=0.15X/250,000+(20,000-.08X)/250,000

0.13=(0.07X+20,000)/250,000

X=178,571

Thus amount invested to be invested in stock A is \$178,571 and Stock B is \$71,429(\$250,000-\$178,571)

Therefore correct answer is Option C

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