refresher-risk & return (1)-20130709-142408

7/29/2019 Refresher-Risk & Return (1)-20130709-142408

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Risk & Return- Refresher

1. Unicom is a regulated entity serving Northern Illinois. The following table lists thestock prices (beginning of the year) and dividends (during the year) of Unicom from1989 to 1997.

Year 1989 1990 1991 1992 1993 1994 1995 1996 1997

Price ($) 36.1 33.6 37.8 30.9 26.8 24.8 31.6 28.5 24.25

Dividend ($) 3 3 3 2.3 1.6 1.6 1.6 1.6 1.6

i. Estimate the average annual return you would have made on yourinvestment at beginning of 1989.

ii. If you were investing in Unicom today, would you expect the historicalstandard deviations and variances to hold? Explain.

2. Suppose shares of ABC ltd and XYZ ltd trade at the same price today. Over the next 3years, returns on the common stock of ABC ltd and XYZ ltd show the following

trends:

Returns/Year Year 1 Year 2 Year 3

ABC (%) 25 -20 10XYZ (%) 10 -15 20

i. Would the share prices of ABC and XYZ be same after 3 years?ii. Calculate the CAGR for ABC and XYZ.

3. The economy of a country may experience rapid growth or moderate growth orrecession. The following table illustrates the probability of the three outcomes along

with the respective stock market returns.

State of economy Probability Stock market return (%)

Rapid growth 0.2 25Moderate growth 0.6 15

Recession 0.2 -15

i. Calculate the expected stock market returns and the standard deviation ofreturns.


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4. Suppose the returns of the Moonshine Company Ltd are normally distributed. Themean return is 20% and the standard deviation of the return is 10%. Determine the

range of returns in which about2/3 of the Companys returns fall.

5. You have been asked to analyze the standard deviation of a portfolio composed ofthe following three assets:

Investment Expected return (%) Standard deviation (%)Sony Corporation 11 23

Tesoro Petroleum 9 27Storage Technology 16 50

You have also been provided with the correlations across the three investments.

Investment Sony Tesoro Storage Tech

Sony 1 -0.15 0.2

Tesoro -0.15 1 -0.25

Storage Tech 0.2 -0.25 1

Estimate the variance of the portfolio, equally weighted across all assets.

6. Consider a Markowitz portfolio across a universe of 1250 assets. How manycovariances would you need to compute in order to obtain Markowitz portfolios?

7. Consider a portfolio of equally weighted securities in which the average variance ofreturn for each security is 50 while its average covariance with any other security in

the portfolio remains constant at 10. What is the expected variance of a portfolio of

20, 50, and 100 securities? How many securities need to be held before the risk of

the portfolio is only 10% more than the minimum?

8. Tim Anderson owns a combination of the optimal risky market portfolio and a risk-free asset. If the standard deviation of the optimal risky market portfolio is 20% and

the expected return on the portfolio is 10%. Consider the following situations to

advise Tim on his portfolio composition. (Proportion of wealth invested between

the market portfolio and the risk-free asset.)

i. If Tim desires a portfolio with no standard deviation.ii. If Tim desires a portfolio with no more than 20% standard deviation.

iii. If Tim desires a portfolio with a standard deviation of 10%.


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9. John Nelson intends to borrow a sum equivalent to 20% of his portfolio to beinvested in a risky portfolio that lies on the Capital Market Line (CML). If the slope of

the CML is 0.48 and the return of the optimal risky market portfolio is 20% with a

standard deviation of 25%, calculate the returns derived by John if the borrowing

cost exceeds the risk free lending rate by 2%.

10.A security that lies on the Security Market Line (SML) is represented by thecoordinates (0.25, 0.11) represented in the standard (x, y) convention. If the market

returns are 20%, determine the slope and the Y-intercept of the SML.

11.Gamma Natural Resources (GNR), an iron ore miner, buys a large but privately heldiron ore miner in Australia. As a result of the cross-border acquisition of a private

company, GNRs standard deviation of returns is reduced from 50% to 30% and its

correlation with the market falls from 0.95 to 0.75. Assume that the standarddeviation and return of the market remain unchanged at 25% and 10%, respectively

and that the risk-free rate is 3%.

i. Calculate the beta of GNR stock and its expected return before theacquisition.

ii. Calculate the expected return after the acquisition.12.You invest 20% of your money in the risk-free asset, 30% in the market portfolio

and 50% in Green Apple, a British firm that has a beta of 1.5. Given that the risk-free

rate is 3% and the market return is 15%, calculate the portfolio beta and expected

return.

13.A French pension fund has employed three investment managers, each of whom isresponsible for investing in one-third of all asset classes so that the pension fund

has a well-diversified portfolio. Consider the following information about the

managers.

Manager Return (%) Alpha Beta

A 10 0.2 1.1B 11 0.1 0.7C 12 0.25 0.6

Risk-free rate 3


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Calculate:

i. Expected returnii. Sharpe ratio*iii. Treynor ratio*iv. Jensens alpha

Optional. Not in the curriculum.

14.A British investor is holding FTSE 100 index, which is her version of the market. Shethinks that three stocks, X, Y, and Z, which are not part of the FTSE 100 index, are

undervalued and should form a part of her portfolio. She has the following

information about the stocks, the FTSE 100 index and the risk-free rate.

Stocks/Index Expected return (%) Standard deviation (%) BetaX 15 30 1.5

Y 18 25 1.2Z 16 23 1.1

FTSE 100 12 18 1Risk-free rate 2 0 0

i. Calculate Jensen alpha for X, Y, and Z.ii. Nonsystematic variance for X, Y, and Z.iii. Should any of the three stocks be included in the portfolio? If so, which stock

should have the highest weight in the portfolio?

refresher-risk & return (1)-20130709-142408

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