# Portfolio Risk and Return, Beta, Standard deviation

1) Consider the following three investments:

Security Expected return Standard deviation

J 0.12 0.4

K 0.14 0.4

L 0.13 0.5

M 0.12 0.3

Using the mean-variance criteria, identify whether one security dominates or whether there is no dominance for each pssible pair of securities

2) Tor Johnson has identified the following securities for a portfolio:

Security Amount invested Expected Return Beta

A $1,000 0.10 0.75

B 5000 0.15 1.20

C 1500 0.12 0.90

D 2500 0.16 1.30

Compute the expected return of the portfolio. Compute the beta of the portfolio.

3) Stock X has a standard deviation of return of 0.6 and stock Y has a standard deviation of 0.4. The correlation of the two stocks is 0.5. Compute the standard deviation of a portfolio invested half in X and half in Y.

4) The expected standard deviation of market returns is 0.20. Maria Houseman has the following four stocks:

Standard deviation of market returns= 0.20

Security Standard deviation Correlation with market

A 0.30 0.70

B 0.75 0.30

C 0.45 0.50

D 0.50 0.16

Compute the beta of each stock

5) The rate of treasury bills is 4% and the equity risk premium is 10%. Use the SML to estimate the return on each of the stocks in problem 4.

6) Maria has decided to invest $5,000 in each of the stocks in 4). Compute the expected return on the portfolio and the portfolio beta.

Please see attached file

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#### Solution Preview

Please see the attached file.

1 Standard deviation Expected return

J 0.4 0.12

K 0.4 0.14

L 0.5 0.13

M 0.3 0.12

If we plot the expected return against the standard devition we see that

J has a standard deviation of 0.4 and expected return of 0.12

K has a standard deviation of 0.4 and expected return of 0.14

Thus K has a higher return for the same risk (standard deviation)

K dominates J

2 Amount invested Expected Return Beta

A $1,000 0.10 0.75

B 5000 0.15 1.20

C 1500 0.12 0.90

D 2500 0.16 1.30

Return of portfolio

r p=summation of wi* ri = w1* r1 + w2*r2+w3r3+w4r4+---

Beta of portfolio

beta p=summation of wi* beta i= w1* beta 1 + w2*beta 2+ w3beta 3 + w4beta 4+---

Amount invested Expected Return Beta

A $1,000 0.10 0.75

B 5000 0.15 1.20

C 1500 0.12 0.90

D 2500 0.16 1.30

Amount invested "weights

(wi)" "Expected Return

(ri)" wi* ri "Beta ...

#### Solution Summary

Calculates Portfolio return, Portfolio beta, Portfolio standard deviation, Beta of stock etc.

1) Which security (A or B) has the least total risk? __________________

2) Which security (A or B) has the least systematic risk? __________________

3) Which security (A or B) has the greatest diversifiable risk? ____________________

4) What is the portfolio beta if you invest 35% in A, 45% in B and 20% in the risk-free asset?

Problem 2 (Chapter 13) Please use the following information to answer the following questions. The return on the risk-free asset is 4% and the return on the market is 14%.

Security Standard Deviation Beta

A 20% 1.2

B 25% 0.8

1) Which security (A or B) has the least total risk? __________________

2) Which security (A or B) has the least systematic risk? __________________

3) Which security (A or B) has the greatest diversifiable risk? ____________________

4) What is the portfolio beta if you invest 35% in A, 45% in B and 20% in the risk-free asset?

5) What is the portfolio expected return if you invest 35% in A, 45% in B and 20% in the risk-free asset?

6) What is the portfolio expected return if you invest 140% in A and the remainder in the risk-free asset via borrowing at the risk-free interest rate?

7) If you forecast the expected rates of returns for both Security A and security B, you get 14%. Which security should you buy/sell/hold as a result?