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# Calculating expected return and drawing the CAL

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1
Asset Expected Return Standard Deviation Weight
X 15% 22% 0.5
Y 10% 8% 0.4
Z 6% 3% 0.1

What is the expected return on this three -asset portfolio?

6. True or False and Explain
You can construct a portfolio with a Beta of .75 by investing .75 of the budget in T-Bills and the remainder in the market portfolio?

For Problems 19-23, assume that you manage a risky portfolio with an expected rate of
return of 17% and a standard deviation of 27%. The T-bill rate is 7%.
19. a. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill
money market fund. What is the expected return and standard deviation of your
client's portfolio?
b. Suppose your risky portfolio includes the following investments in the given
proportions:
Stock A 27%
Stock B 33%
Stock C 40%
What are the investment proportions of your client's overall portfolio, including the
position in T-bills?
c. What is the reward-to-variability ratio (S) of your risky portfolio and your client's
overall portfolio?
d. Draw the CAL of your portfolio on an expected return/standard deviation diagram.
What is the slope of the CAL? Show the position of your client on your fund's CAL.

#### Solution Preview

1
Asset Expected Return Standard Deviation Weight
X 15% 22% 0.5
Y 10% 8% 0.4
Z 6% 3% 0.1

What is the expected return on this three -asset portfolio?

The expected return = Sum (Expected return X weight)
Expected return = 15%X0.5 + 10%X0.4 + 6%X0.1 = 12.1%

2. Karen Kay

a. Alpha = Forecasted Return - Expected return
We calculate the expected return using CAPM
Expected return = Risk Free Rate + (Market return - risk free rate ) X beta
Stock X
Expected Return = 5% + (14%-5%) X 0.8 = 12.2%
Alpha = 14%-12.2% = 1.8%
Stock Y
Expected Return = 5% + (14%-5%) X 1.5 = 18.5%
Alpha = 17%-18.5% = -1.5%

b. (i) Stock X should be recommended since it has a positive alpha and the beta is lower than the beta of Stock Y. A positive alpha means that the stock plots above the Security Market Line and so the price is expected to rise. A low beta would result in risk reduction of the portfolio
(ii) Stock Y is recommended since it has a higher forecasted return and a ...

#### Solution Summary

The solution explains how to calculate the expected return of a portfolio, reward to variability ratio and constructing the Capital Allocation Line (CAL)

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