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# Portfolio Risk and Return, Beta, Standard deviation

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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.

\$2.19

## 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?

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