Question

Suppose you have a portfolio that includes two stocks. You invested 60 percent of your total fund in a stock that has a Beta equal to 3.0 and the remaining 40 of your funds in a stock that has a Beta equal to 0.5. What is the Portfolio Beta?

1. a)            Stock F has a Beta Coefficient equal to 2. If the Risk-Free Rate of Return equals 4 per-

cent and the Expected Market Return equals 10 percent, what is stock F’s Required Rate of Return?

2.             A portfolio’s Expected Return is 12%, its Standard Deviation is 20%, and the Risk-Free Rate is 4%. Which of the following would make the greatest increase in the Portfolio’s Sharpe

                Ratio?

1. An increase of 1% in Expected Return.
2. A decrease of 1% in Risk-Free Rate
3. A decrease of 1% in its Standard Deviation

Answer 1

1. Calculation of portfolio beta

particulars	beta	weights	weighted beta
stock 1	3.0	0.60	1.8
stock 2	0.5	0.40	0.2
TOTAL			2.0

The portfolio beta equals 2.0

2. Calculation of required return of stock F

formula:

Required rate of return = risk free return + beta of stock * ( market return - risk free return)

= 4% + 2 * ( 10% - 4% )

= 16 %

3. Calculation of Sharpe ratio of portfolio

Sharpe Ratio = ( portfolio expected return - risk free return )/ standard deviation of portfolio

= (12% - 4% ) / 20%

= 0.40

situation i : increase in expected return by 1%

Sharpe Ratio = ( portfolio expected return - risk free return )/ standard deviation of portfolio

= (13% - 4% ) / 20%

= 0.45

situation ii: decrease in risk free return by 1%

Sharpe Ratio = ( portfolio expected return - risk free return )/ standard deviation of portfolio

= (12% - 3% ) / 20%

= 0.45

situation iii: decrease in standard deviation by 1%

Sharpe Ratio = ( portfolio expected return - risk free return )/ standard deviation of portfolio

= (12% - 4% ) / 19%

= 0.42

The higher the portfolio return higher is the sharp ratio therefore increase in portfolio return by 1% will make greatest increase in the sharp ratio.

In the above question the decrease in 1% of risk free return will have the same effect as increase in expected return by 1%