Homework 5

Homework 5 - Finance Homework 5 Winter 2011 ARE 171A A....

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Unformatted text preview: Finance Homework 5 Winter 2011 ARE 171A A. Havenner As always, rates are annual effective unless otherwise noted. Calculating the initial statistics (average returns and their variances) very carefully will make this assignment easier. Use T-1=9 in the denominator when calculating the variance. You may wish to use software such as Excel to do some problems, or they can be done with a calculator and graph paper. We will use these data for the next homework assignment, so be sure to save them. You should also photocopy this week’s assignment before turning it in, since it may be helpful for next week’s assignment also. 1. Risk and Return of Individual Assets: Several of our students have secretly been in business, and their companies have been trading publicly for a while. With the long-awaited overthrow of communism in Poland, Chris, Karolina, Malwina, and Samantha established Walesa Memorial Enterprises, a highly successful import— export business trading under the symbol WME. In the meantime, Rishal and Rohin began an equally successful string of luxury resorts trading under R&R. Ten years of data on percent returns for WME and R&R are given below: D_ate_ WME R R we WME R&R 2001 3.97 7.77 2006 10.90 18.93 2002 10.90 16.56 2007 6.49 15.04 2003 8.74 11.83 2008 14.23 5.24 2004 10.36 12.84 2009 14.23 21.46 2005 9.28 7.94 2010 7.12 14.53 [5] 1) Based on these data, what is the expected return on WME? What is the expected return on R&R? [8] ii) What is the variance of the return for WME? The standard deviation? Do the same calculations for R&R. (Remember to use T-1=9 in the variance denominator.) [8] iii) What is the covariance of WME returns with R&R returns? What is the correlation of the two returns? Write out the formulas you use explicitly. 2. Portfolio Risk and Return, Two Assets: [5] i) What is the risk and return of a portfolio with no WME stock and all R&R stock? No R&R stock and all WME stock? (Use the standard deviation -— not the variance -— to characterize risk.) [20] ii) Evaluate the risk and return for each of the weight combinations below: WME: 0 .1 .7 .8 .9 1 R&R: 1 .9 .3 .2 .1 0 Carry four digits beyond the zeros. Table your results, with the two columns of weights next to the column of portfolio standard deviation (risk) next to the portfolio expected returns. [10] iii) Plot the expected risks and returns tabled above. Use graph paper (plot carefully) or software (e.g., 2007 Excel’s "Insert/ Scatter/ Scatter with smooth lines" or 2003 Excel’s "Chart/ XY plot'”. Be sure that risk is on the horizontal axis and return is on the vertical axis; for 2007 Excel that means risk must be a column to the left of return. [10] iv) On both the table and the graph, identify both the feasible set and the efficient set. Do they differ? Why or why not? (I have not mentioned a risk free asset, so assume that none is available.) [5] v) What proportion of WME would you hold? Why? Do we know what another investor would hold? Why or why not, briefly? [5] vi) Is it possible for the feasible set to be backward bending when the correlation between asset returns is positive, i.e., when 9,7 > 0, or is it necessary for of}. to be zero or negative? Use the numbers in the example you have just done in the parts above to show how your answer applies in this case. 3. Two Fund Separation for the Individual Investor: Suppose your portfolio consists entirely of the two risky assets above and a riskless asset that pays 4.037%. The tangency of the borrowing and lending line with this portfolio of risky assets is at .6 in WME and .4 in R&R and pays 11.06% with a standard deviation of 3.17%. [12] i) If your attitude toward risk implies that you are prepared to tolerate a standard deviation of 4.7%, what is the maximum expected return that you can achieve if you cannot borrow or lend? You can answer this question either graphically by showing this point on a reproduction of your graph from above, or computationally by setting up the variance of the portfolio equation and solving for the weights on WME and R&R (remember that the weights sum to one). State clearly which you are doing. If you do it computationally, mark the point on your graph. [12] ii) What is your optimal strategy if you can borrow or lend at the risk free rate and are prepared to tolerate a standard deviation of 4.7%? (Show this point on the graph in part i) above, along with the borrowing and lending line.) What is the maximum expected return that you can achieve at this risk? (Calculate this return, do not just take it from the plot.) What are the portfolio investment shares necessary to implement this strategy? 1 This 2003 command is from my memory, so it may not be completely correct. We want an X-Y scatterplot (with a smoothed line connection if available), in any event. The risk must be the horizontal or X axis (abcissa), and the portfolio and CML returns must be the vertical or Y axis (ordinate). ...
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This note was uploaded on 02/27/2012 for the course ARE 171A taught by Professor Whitney during the Spring '08 term at UC Davis.

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Homework 5 - Finance Homework 5 Winter 2011 ARE 171A A....

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