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# Finance Questions and Expected Returns for Stocks

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Use the following expectations on Stocks X and Y to answer questions 9 through 11 (round to the nearest percent).

Bear Market Normal Market Bull Market
Probability 0.2 0.5 0.3
Stock X -20% 18% 50%
Stock Y -15% 20% 10%

9. What are the expected returns for Stocks X and Y?
10. What are the standard deviations of returns on Stocks X and Y?
11. Assume that of your \$10,000 portfolio, you invest \$9,000 in Stock X and \$1,000 in Stock Y. What is the expected return on your portfolio?

5. Abigail Grace has a \$900,000 fully diversified portfolio. She subsequently inherits ABC Company common stock worth \$100,000. Her financial advisor provided her with the following forecasted information:

Risk and Return Characteristics
Expected Standard Deviation
Monthly Returns of Monthly Returns
Original Portfolio 0.67% 2.37%
ABC Company 1.25 2.95

The correlation coefficient of ABC stock returns with the original portfolio returns is 0.40
a. The inheritance changes Grace's overall portfolio and she is deciding whether to buy the ABC stock. Assuming Grace keeps the ABC stock, calculate the:

i. Expected return of her new portfolio which includes the ABC stock.
ii. Covariance of ABC stock returns with the original portfolio returns.
iii. Standard deviation of her new portfolio which includes the ABC stock.

6. Consider the following information regarding the performance of a money manager in a recent month. The table presents the actual return of each sector of the manager's portfolio in column (1), the fraction of the portfolio allocated to each sector in column (2), the benchmark or neutral sector allocations in column (3), and the returns of sector indexes in column (4).

(1) (2) (3) (4)
Actual Actual Benchmark Index
Return Weight Weight Return

Equity 2.0% 0.70 0.60 2.5% (S&P 500)
Bonds 1.0 0.20 0.30 1.2 (Aggregate Bond index)
Cash 0.5 0.10 0.10 0.5

a. What was the manager's return in the month? What was her over- or underperformance?
b. What was the contribution of security selection to relative performance?
c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contribution equals her total "excess" return relative to the bogey.

15. A portfolio manager summarizes the input from the macro and micro forecasts in the following table:

Micro Forecasts

Asset Expected Return (%) Beta Residual Standard
Deviation (%)

Stock A 20 1.3 58
Stock B 18 1.8 71
Stock C 17 0.7 60
Stock D 12 1.0 55

Macro Forecasts

Asset Expected Return (%) Standard Deviation (%)
T-bills 8 0
Passive equity portfolio 16 23

a. Calculate expected excess returns, alpha values, and residual variances for these stocks.
b. Construct the optimal risky portfolio.
c. What is Sharpe's measure for the optimal portfolio and how much of it is contributed by the active portfolio? What is the M2?

#### Solution Summary

This solution is comprised of a detailed explanation to answer what are the expected returns for Stocks X and Y, what are the standard deviations of returns on Stocks X and Y, what is the expected return on your portfolio, calculate the expected return of her new portfolio which includes the ABC stock, covariance of ABC stock returns with the original portfolio returns.
and standard deviation of her new portfolio which includes the ABC stock.

\$2.19

## Suppose the expected returns and standard deviations of stocks A and B are

Please note the attachment and complete problems in Excel.

Thank you!

Suppose the expected returns and standard deviations of stocks A and B are E(RA) = 0.17,
E(RB) = 0.27, StdDevA = 0.12, and StdDevB = 0.21, respectively.

a. Calculate the expected return and standard deviation of a portfolio that is composed of
35 percent A and 65 percent B when the correlation between the returns on A and B is 0.6.

b. Calculate the standard deviation of a portfolio that is composed of 35 percent A and
65 percent B when the correlation coefficient between the returns on A and B is -0.6.

c. How does the correlation between the returns on A and B affect the standard deviation
of the portfolio?

Suppose the expected return on the market portfolio is 14.7 percent
and the risk-free rate is 4.9 percent.
Morrow Inc.stock has a beta of 1.3 Assume the capital-asset-pricing model holds.

a. What is the expected return on Morrow's stock?

b. If the risk-free rate decreases to 3.7 percent, what is the expected return on Morrow's
stock?

A portfolio that combines the risk-free asset and the market portfolio has an expected return
of 22 percent and a standard deviation of 5 percent. The risk-free rate is 4.9 percent, and
the expected return on the market portfolio is 19 percent. Assume the capital-asset-pricing
model holds.
What expected rate of return would a security earn if it had a 0.6 correlation
with the market portfolio and a standard deviation of 3 percent?

Suppose you have invested \$50,000 in the following four stocks:

Security Amount Invested Beta
Stock A \$10,000 0.7
Stock B 15,000 1.2
Stock C 12,000 1.4
Stock D 13,000 1.9

The risk-free rate is 5 percent and the expected return on the
market portfolio is 18 percent.
Based on the capital-asset-pricing model, what is the expected return on the above
portfolio?

You enter into a forward contract to buy a 10 -year, zero-coupon bond that will be issued in
one year.The face value of the bond is \$1,000 , and the 1 -year and 11 -year spot interest rates
are 4 percent per annum and 9 percent per annum, respectively. Both of these interest rates
are expressed as effective annual yields (EAYs).

a. What is the forward price of your contract?

b. Suppose both the spot rates unexpectedly shift downward by 1 percent.
What is the price of a forward contract otherwise identical to yours?

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