Ch 7 Practice

0247 00100 variance r 00115 00065 covmsft ibm 000375

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Unformatted text preview: d the return on 30 day US T-Bills: July 29th 1988 - Dec 31st 2011 Microsoft IBM Mean r 0.0247 0.0100 Variance r 0.0115 0.0065 Cov(MSFT, IBM) 0.00375 rf, Dec 31st, 2011 0.0002 (a) Assume that an investor has the mean-variance utility function over expected portfolio returns and portfolio risk: ) in the risk free asset and a fraction in a risky portfolio (portfolio of 2 risky Suppose that they invest fraction ( assets). When allocating funds in the risky portfolio, they invest fraction ( ) in IBM and fraction in MSFT. Calculate the optimal proportion of funds they allocate in the risk free asset, in IBM and in MSFT. Assume For the remaining parts, Consider a portfolio consisting of the risk free asset and Boeing stock only and suppose you don’t know the value of . (b) For what value of will an investor allocates all her funds into IBM stocks? (c) For what value of will an investor allocates more than her funds into IBM stocks? (d) For what value of will an investor allocates less than her funds into IBM stocks? (7.5) Consider the following table of returns and probabilities for two risky assets A and B: State Rate of Return A Rate of Return B Probability Strong 10% 5% 0.3 Normal 5% 20% 0.4 Weak 10% 5% (a) Calculate the expected return and risk of asset A. (b) Calculate the expected return and risk of asset B. 6 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (c) Calculate the expected covariance of asset A and asset B returns. (d) Suppose you want to construct a portfolio consisting of assets A and B that minimizes the expected risk. Suppose a proportion of the portfolio is in asset A and proportion ( ) is in asset B. Calculate the (the proportion of portfolio in asset A) -- which minimizes risk of a portfolio of assets A and B. (e) Given the allocation in part (d), will portfolio risk be impacted more by higher riskiness of asset A or asset B? Show all calculations. (7.6) The following table contains Motorola’s and Research in Motion’s (RIM) Closing Monthly Price, Monthly Returns, and Monthly Capital Gains in 2010: Motorola Stocks Research in Motion (RIM) Stocks Date (M/D/Year) Closing Monthly Price Returns Capital Gains Closing Monthly Price Returns Capital Gains 1/29/2010 \$ 6.15 -0.207474 -0.207474 \$ 62.91 -0.068551 -0.068551 2/26/2010 \$ 6.76 0.099187 0.099187 \$ 70.88 0.126687 0.126687 3/31/2010 \$ 7.02 0.038462 0.038462 \$ 73.97 0.043595 0.043595 4/30/2010 \$ 7.07 0.007123 0.007123 \$ 71.19 -0.037583 -0.037583 5/28/2010 \$ 6.85 -0.031117 -0.031117 \$ 60.69 -0.147493 -0.147493 6/30/2010 \$ 6.52 -0.048175 -0.048175 \$ 49.26 -0.188334 -0.188334 7/30/2010 \$ 7.49 0.148773 0.148773 \$ 57.53 0.167885 0.167885 8/31/2010 \$ 7.52 0.004005 0.004005 \$ 42.84 -0.255345 -0.255345 9/30/2010 \$ 8.53 0.134309 0.134309 \$ 48.69 0.136555 0.136555 10/29/2010 \$ 8.16 -0.043376 -0.043376 \$ 56.92 0.169029 0.169029 11/30/2010 \$ 7.66 -0.061275 -0.061275 \$ 61.83 0.086261 0.086261 12/31/2010 \$ 9.07 0.184073 0.184073 \$ 58.13 -0.059842 -0.059842 (a) True or false: neither Motorola nor RIM paid a monthly dividend in 2010? Give a brief explanation and provide a formula to justify your answer. The following table contains the return on 30-day US Treasury Bills issued on December 31st 2010 as well as Motorola and RIM’s average monthly returns; variance of monthly returns; and the covariance of Motorola’s and RIM’s monthly returns for the period February 26th, 1999 to December 31st, 2010: 30 Day U.S. T-Bill Return (Dec 31st 2010) 0.00081 The following figures are for the period February 26th, 1999 to December 31st, 2010 Average Motorola Monthly Returns Variance of Motorola Monthly Return Average RIM Monthly Returns Variance RIM Monthly Returns Covariance of Motorola and RIM Monthly Returns 0.002616887 0.013877326 0.054275605 0.052027303 0.012945617 7 ECO 204 Chapter 7: Practice Problems & Solutions for Economics of Financial Portfolio Allocation in ECO 204 (this version 2012-2013) University of Toronto, Department of Economics (STG). ECO 204, S. Ajaz Hussain. Do not distribute. (b) Are Motorola stocks riskier than RIM stocks, or the other way around? Give a brief explanation and justify your answer by calculating the risk premium for each stock. An investor has the following mean-variance utility function over expected portfolio returns [ ] and portfolio variance where is a parameter reflecting the investor’s “attitude towards risk”: (c) Suppose this investor wants to invest in a portfolio consisting of US 30-day T-Bills and RIM stocks. Derive a formula for the optimal fraction of this portfolio that will be in US 30-day T-Bills and RIM stocks and calculate the value of the parameter for which the investor invests 100% of her portfolio dollars into RIM stocks. Show all calculations and state all assumptions. (d) Suppose . Suppose this investor wants to invest in a portfolio consisting of US 30-day T...
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