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Portfolio Return and Beta

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Jamie Peters invested $100,000 to set up the following portfolio 1 year ago. (see attachment for table).
a. Calculate the portfolio beta on the basis of the original cost figures.
b. Calculate the percentage return of each asset in the portfolio for the year/
c. Calculate the percentage return of the portfolio on the basis of original cost, using income and gains during the year.
d. At the time Jamie made his investments, investors were estimating that the market return for the coming year would be 10%. The estimate of the risk-free rate of return averaged 4% for the coming year. Calculate an expected rate of return for each stock on the basis of its beta and the expectations of market and risk-free returns.
e. On the basis of the actual results, explain how each stock in the portfolio performed relative to those CAPM-generated expectations of performance. What factors could explain these differences?

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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

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