Question

You invest $100 in a risky asset with an expected rate of return of 15% and a standard deviation of 15% and a T-bill with a rate of return of 5% (and a standard deviation of 0).

6. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 13%?

A) 20% and 80% B) 25% and 75% C) 80% and 20% D) 75% and 25%

7. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 8%?

A) 67% and 33% B) 53% and 47% C) 27% and 73% D) 47% and 53%

8. A portfolio that has an expected return of 23% is formed by

A) borrowing $40 at the risk-free rate and investing the total amount ($140) in the risky asset. B) borrowing $80 at the risk-free rate and investing the total amount ($180) in the risky asset. C) borrowing $60 at the risk-free rate and investing the total amount ($160) in the risky asset. D) borrowing $85 at the risk-free rate and investing the total amount ($185) in the risky asset.

9. The slope of the CAL formed with the risky asset and the risk-free asset is equal to

A) 0.5667. B) 0.6667. C) 0.7667 D) 0.4667.

Answer 1

6. Suppose you invest x amount in risky investment and (100-x) in risk free invest

So, x*15%/100+(100-x)*5%/100=13%

or, 0.15x+5-0.05x=13

or, 0.10x=8

or,x=80

You will invest $80 in risky asset and (100-80)=$20 in risk free asset. Option C is correct.

7.

Say, X amount of money must be invested in risky asset and (100-x) into risk free asset

So, X*15%/100+(100-X)*0%=8%

or, 0.15X=8

or, X= 8/0.15=53.33 or 53(Approx)

So, to get 8% standard deviation of the portfolio you will invest 53% in risky asset and (100%-53%)=47% in risk free asset.

8.

Say, you need to borrow X amount of money at risk free rate and invest (100+X) into the risky asset to get 23% expected return.

So, Expected return= (100+X)*15%-X*5%=23

or, 15+0.15X-0.05X=23

or, 0.10X=8

or, X=80

So, you need to borrow $80 at risk free rate and invest (100+80)=$180 into the risky asset to get expected return of 23%.

9.

When standard deviation is 0 (i.e. all money is in risk free investment), the expected return is=5% and when standard deviation is 15% (I.e. all money is in risky investment), then expected return=15%

So, slope of CAL= (15%-5%)/(15%-0%)=10%/15%=0.6667

Hence, slope of CAL is 0.6667. Option B is correct.