Question

Please explain the steps to calculate the answer. thx!

1. Your investment has a 10% chance of earning a 30% rate of return, a 50% chance of earning a 10% rate of return and a 40% chance of losing 6%. What is your expected return on this investment?

2. Consider a T-bill with a rate of return of 5 percent and the following risky securities:
Security A: E(r) = 0.15; Variance = 0.04
Security B: E(r) = 0.10; Variance = 0.0225
Security C: E(r) = 0.12; Variance = 0.01
Security D: E(r) = 0.13; Variance = 0.0625
From which set of portfolios, formed with the T-bill and any one of the 4 risky securities, would a risk-averse investor always choose his portfolio?

3. You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of treasury bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14% and Y has an expected rate of return of 12%. To form a complete portfolio with an expected rate of return of 11%, you should invest __________ of your complete portfolio in treasury bills.

4. Which of the following correlations coefficients will produce the least diversification benefit?

		-0.6
		-0.3
		0.5
		0.00

5.

The standard deviation of a portfolio consisting of 30% of Stock X and 70% of Stock Y is:

Stock	Expected Return	Standard Deviation	Correlation Coefficient
X	5%	20%	0.4
Y	10%	25%

6. Stocks A and B have the following returns in each of the states given below:

	Good	Bad	Ugly
Stock A return	10%	-1%	-10%
Stock B return	2%	0%	-3%

The probability of the good state is 0.4, the probability of the bad state is 0.3 and the probability of the ugly state is 0.3. What is the covariance between the returns of A and B?

7. Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 30%. The T-bill rate is 10%. Suppose that you have a client that prefers to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. What is the investment proportion y?

Answer 1

1.Expected return on this investment is the sum of the product of the probabilities *rates of returns

(10%*30%)+(50%*10%)+(40%*-6%)=

5.6%

2.A risk-averse investor always choose

Security D: E(r) = 0.13; Variance = 0.0625

as the Coeff. Of variation from the mean is minimum as shown in the Table below

Security	Std. devn.(Variance^(1/2)	Mean or E( r)	Coeff.of variation from the MeanStd. devn/Mean
A	0.2	0.15	1.33
B	0.15	0.1	1.50
C	0.1	0.12	0.83
D	0.03125	0.13	0.24

3.Expected Return on the risky portfolio=

Sum of the weighted probable returns of X & Y

ie. (60%*14%)+(40%*12%)=

13.2%

Suppose, $ x is invested in Treasury bills such that,

(x*5%)+(1000-x)*13.2%=1000*11%

Solving for x, we get the investment in Treasury Bills as

$268

4. ANSWER: 0
At 0, the securities have no association/correlation at all.

5. Portfolio Std. devn.=Sq.Rt.of((Wt.X)^2*(SD X)^2)+((Wt.Y)^2*(SD Y)^2)+(2*Wt.X)*(Wt.Y)*(CR Coeff.)*(SD X)*(SD Y))=
Sq.Root of (0.30^2*0.20^2)+(0.70^2*0.25^2)+(2*0.30*0.70*0.4*0.20*0.25)=
ie.((0.30^2*0.20^2)+(0.70^2*0.25^2)+(2*0.30*0.70*0.4*0.20*0.25))^(1/2)=
20.65%

6..Expected Return (Stock A)=(0.4*10%)+(0.3*-1%)+(0.3*-10%)=

0.70%

Expected Return (Stock B)=(0.4*2%)+(0.3*0%)+(0.3*-3%)=

-0.10%

Co-Variance(A,B)=(0.4*(10%-0.7%)*(2%+0.1%))+(0.3*(-1%-0.7%)*(0%+0.1%))+(0.3*(-10%-0.7%)*(-3%+0.1%))

0.001707