I.) Q4/2006 Fund Normal Fund Class Weight Position Return Return US Equities 0.50 0.40 7.30 6.70 International Equities 0.40 0.20 12.05 10.40 Bonds 0.05 0.25 0.75 1.24 T-Bills 0.05 0.15 1.20 1.25 Total 1.00 1.00 Returns: (in percent) Normal Position Your Fund Your Alpha Alpha due to Active Asset Allocation US Equities International Eq Bonds T-Bills Total Alpha due to Active Security Selection US Equities International Eq Bonds T-Bills Total Attributed Alpha II.) 2006 Fund Normal Fund Class Weight Position Return Return US Equities 0.50 0.40 12.11 15.79 International Equities 0.40 0.20 17.00 19.14 Bonds 0.05 0.25 1.50 2.44 T-Bills 0.05 0.15 1.25 1.44 Total 1.00 1.00 Returns: (in percent) Normal Position 2.) Consider this return data. Your Fund You are the portfolio manager, and your client is upset. She notes that you Your Alpha underperformed in every asset class. Alpha due to Active Using return attribution show her you Asset Allocation are worth your 1% fee. US Equities International Eq Bonds T-Bills Total Alpha due to Active Security Selection US Equities International Eq Bonds T-Bills Total Attributed Alpha III.) 2002 Fund Normal Fund Class Weight Position Return Return US Equities 0.50 0.40 -20.00 -22.10 International Equities 0.40 0.20 -13.00 -15.64 Bonds 0.05 0.25 12.00 10.27 T-Bills 0.05 0.15 2.50 1.70 Total 1.00 1.00 Returns: (in percent) Normal Position Your Fund Your Alpha Alpha due to Active Asset Allocation US Equities International Eq Bonds T-Bills Total Alpha due to Active Security Selection US Equities International Eq Bonds T-Bills Total Attributed Alpha
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J. P. Morgan Asset Management publishes information about financial investments. Over the past 10 years, the expected return for the S&P 500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a Core Bonds fund was 5.78% with a standard deviation of 2.13% (J. P. Morgan Asset Management, Guide to the Markets, 1st Quarter, 2012). The publication also reported that the correlation between the S&P 500 and Core Bonds is -0.32. You are considering portfolio investments that are composed of an S&P 500 index fund and a Core Bonds fund. a. Using the information provided, determine the covariance between the S&P 500 and Core Bonds. Round your answer to two decimal places. If required enter negative values as negative numbers. b. Construct a portfolio that is 50% invested in an S&P 500 index fund and 50% in a Core Bond fund. Round your answers to one decimal place. r = x + y In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places. Expected return % Standard deviation % c. Construct a portfolio that is 20% invested in an S&P 500 index fund and 80% invested in a Core bond fund. Round your answers to one decimal place. r = x + y In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places. Expected return % Standard deviation % d. Construct a portfolio that is 80% invested in an S&P 500 index fund and 20% invested in a Core bond fund. Round your answers to one decimal place. r = x + y In percentage terms, what is the expected return and standard deviation for such a portfolio? Round your answers to two decimal places. Expected return % Standard deviation % e. Which of the portfolios in parts (b), (c), and (d) above has the largest expected return?
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a) You currently have all of your ÂŁ1,000,000 wealth invested in an aggressive portfolio of UK stocks which has a beta of 1.3. You are concerned that this is too risky a position. You can also invest (both long and short) in a defensive UK stock portfolio which has a beta of exactly 0.3. You wish to reallocate your wealth so that some is invested in the aggressive portfolio and the rest in the defensive portfolio and so that your overall beta is 0.5. What are your portfolio weights on the aggressive asset and the defensive asset? (10 marks) b) A market consists of only two stocks, X and Y. The market cap of X is $3bn and that of Y is $7bn. X has an expected return of 10% and a return standard deviation of 32%. Y has an expected return of 8% and a standard deviation of 20%. Their return correlation is 0.25. i) What is the expected return on the market and the return standard deviation of the market? (10 marks) ii) What are the CAPM betas of X and Y? (10 marks) c) Assume that you believe in the Capital Asset Pricing Model. You believe that you have, through extensive research, identified a stock that plots below the Security Market Line. What does this imply for whether or not it is fairly priced? How would you exploit this situation? [Write no more than 5 sentences in your answer.] (10 marks)
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Part 2: Investment Allocations An investor has selected the following asset types in his portfolio. The expected return for each asset type has been estimated by using the historical data: Expected Returns Bonds 7% High tech stocks 12% Foreign stocks 11% Call options 14% Put options 14% Gold 9% Table 5: Expected returns of Investments The following table indicates the covariance matrix of the assets’ returns. Each diagonal entry is the variance of an asset and non-diagonal entries are the covariances between any pairs of assets. Bonds High tech stocks Foreign stocks Call options Put options Gold Bonds 0.001 0.0003 -0.0003 0.00035 -0.00035 0.0004 High tech stocks 0.009 0.0004 0.0016 -0.0016 0.0006 Foreign stocks 0.008 0.0015 -0.0055 -0.0007 Call options 0.012 -0.0005 0.0008 Put options 0.012 -0.0008 Gold 0.005 Table 6: The Covariance matrix of assets’ returns (i) Suppose that our investor wishes to invest $10,000 in this portfolio. Determine how he should allocate this investment to the individual assets in his portfolio in order to have a minimum baseline expected return of 11%, and at the same time, at a minimum risk. (ii) Let the solution pair be denoted by (r, e), where “r” denotes the minimized risk and “e” denotes the expected portfolio return after the problem is solved. Use successive values of 10%, 10.5%, 11%, 11.5%, 12%, 12.5%, 13% and 13.5% as the baseline return values to obtain eight pairs of solutions (r, e). Plot “e” versus “r”. Explain whether there exists a pattern in this plot. In other words, explain, in your opinion, the type of mathematical relationship that “r” and “e” may have.
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