Question

Here are some historical data on the risk characteristics of Bank of America and Starbucks.

	Bank of America	Starbucks
β (beta)	1.57	.83
Yearly standard deviation of return (%)	35.80	21.00

Assume the standard deviation of the return on the market was 23.0%. (Use decimals, not percents, in your calculations.)

     

a. The correlation coefficient of Bank of America's return versus Starbucks is .30. What is the standard deviation of a portfolio invested half in each stock? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation             %

b. What is the standard deviation of a portfolio invested one-third in Bank of America, one-third in Starbucks, and one-third in risk-free Treasury bills? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation             %

c. What is the standard deviation if the portfolio is split evenly between Bank of America and Starbucks and is financed at 50% margin, that is, the investor puts up only 50% of the total amount and borrows the balance from the broker? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation             %

d-1. What is the approximate standard deviation of a portfolio comprised of 100 stocks with betas of 1.57 like Bank of America? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation             %

d-2. What is the approximate standard deviation of a portfolio comprised of 100 stocks with betas of .83 like Starbucks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation             %

Answer 1

a)23.31%
b)15.54%
Here we ignored treasury bill since the standard deviation of treasury bill is 0
c)Here since we are keeping only 50% and borrowing rest 50% the standard deviation is going to double as the risk is also high and it is =2*23.31%=46.62%
d)Here the portfolio will be well diversified since we have 100 stocks and portfolio standard deviation depends on the average covariance of securities in the portfolio(beta)
standard deviation=beta*market standard deviation
=1.57*23%=36.11%
d2)=0.83*23%=19.09%