Question

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

	Bank of America	Starbucks
β (beta)	1.51	.90
Yearly standard deviation of return (%)	31.9	17.5

Assume the standard deviation of the return on the market was 18%. (Use decimals, not percents, in your calculations.)

     

a. The correlation coefficient of Bank of America's return versus Starbucks is .38. 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 1.51 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 .90 like Starbucks? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Standard deviation             %

Answer 1

Given,

The correlation coefficient of Bank of America's return versus Starbucks is .38. &

Particulars	Bank of America	Starbucks
β (beta)	1.51	0.90
Yearly standard deviation of return (%)	31.9	17.5

Also, the standard deviation of the return on the market was 18%

1) Now we are to calculate the Standard Deviation when ratio of weights of the stock is equal i.e. 50% in Bank of America & 50% in Starbucks. The standard deviation is also known as the Portfolio risk. Standard deviation (σ) is found by taking the square root of variance .The variance is calculated

Portfolio Risk= w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*Cov(R_A, R_B)
Where: w_A and w_B are portfolio weights, σ²(R_A) and σ²(R_B) are variances and
Cov(R_A, R_B) is the co-variance.

the calculation be expressed in the following manner:-

= (.50)²*(.319)²+(.50)²*(.175)²+2(.50)(.50)*(.38)

=.250+.102+.250+.031+.190=0.823

Therefore, Portfolio Variance = .823, Std Deviation in this case would be =0.9072 . Therefore the Std Deviation expressed in percentage will be 90.72%