# Portfolio risk, return and standard deviation

See the attached file.

Question 1:

a) Is it possible to increase return and decrease risk of a portfolio at the same time?

b) Why do investors buy common stocks instead of investing all their money in bonds and t bills.

Question 2:

Use the attached table table to answer -

A) If the investor allocates 30% of his money to Scott Corp. and the remaining 70% to Bill Corp and the correlation of returns of the 2 stocks is 0.5, what is the expected returns and standard deviation of the portfolio?

B)Explain what happens to the expected returns and standard deviation when you reallocate your portfolio and invest 50% in each stock.

© BrainMass Inc. brainmass.com October 24, 2018, 6:23 pm ad1c9bdddfhttps://brainmass.com/economics/bonds/portfolio-risk-return-standard-deviation-39512

#### Solution Preview

Answers in the attached file.

Quest 1)

a) Is it possible to increase return and decrease risk of a portfolio at the same time?

Yes, through the process of diversification. If we hold a portfolio which has a single stock in it, we can reduce the risk and increase the return by adding another stock which has a higher expected return and has zero correlation with the earlier stock. For example suppose we have a stock A which has a expected return of 10% and a standard deviation ( a measure of risk) of 15%. To this ...

#### Solution Summary

The solution explains the risk and return of a portfolio and the change when portfolio composition is changed.

Security Market Line, Mean variance criteria, Portfolio return, Portfolio beta, Portfolio standard deviation, Beta of stock,

mean-variance criteria, dominance, SML,

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

View Full Posting Details