Solve for the optimal fraction of this portfolio that

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Unformatted text preview: -Bills and a “risky” asset that is the “optimal” composite blend of Motorola and RIM stocks. Solve for the optimal fraction of this portfolio that will be in US 30-day T-Bills, Motorola and RIM stocks. Show all calculations and state all assumptions. Hint: ❶ Construct the optimal “blend” of Motorola and RIM stocks ❷ Construct a portfolio of US 30 day T-bills and the “blended risky asset”. (e) Suppose . Suppose this investor wants to invest in a portfolio consisting of US 30-day T-Bills and a “risky” asset which is that composite blend of Motorola and RIM stocks which minimizes the risk of the “risky” asset. Solve for the optimal fraction of this portfolio that will be in US 30-day T-Bills, Motorola and RIM stocks. Show all calculations and state all assumptions. Hint: ❶ Construct that “blend” of Motorola and RIM stocks which minimizes the risk of the “blended risky asset” ❷ Construct a portfolio of US 30 day T-bills and the “blended risky asset”. Optional questions: The following questions are not required, but you are encouraged to attempt them. They will you in applying probability concept. (7.7) The following table contains three risky assets and a risk free asset Asset 1 return Asset 1 variance Asset 2 return Asset 2 variance Asset 3 return Asset 3 variance Covariance (Asset 1, Asset 2) 0.02500 0.02600 0.04300 0.03862 0.05600 0.05200 0.00091 8 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. Covariance (Asset 2, Asset 3) Covariance (Asset 1, Asset 3) Risk free asset return 0.00130 0.00052 0.00300 (a) Which of two risky assets you will choose to construct a portfolio that has minimum risk and highest return to risk ratio? (b) Which of two risky assets and the risk free asset you will choose to construct the optimal portfolio that has the highest return to risk ratio? Assume the mean-variance utility function of the form . (7.8) You are the Chief Financial Officer (CFO) at Super Corp. the following information is given to you to calculate next month return and associated risk. November October September August $ 190.07 $ 193.49 $ 186.94 $ 189.64 (a) Find return for the month of December. Assume price change occur with equal probability and no dividend payment. (b) [Optional] Find next week’s return. Assume price change occur with probability of (.10, .25, .35, .30). Now assume return is continuous and return distribution is given by () { (c) [Optional] Find next month’s return and variance. Assume . [please show all work]. 9 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. Solutions (7.1) For this question you’ll need to download data for a “risk free asset” and two “risky assets”: US 3-month T-Bills and Dell and Boeing stocks. Here’s what you need to do to get data on US 3-month T-Bills and Dell and Boeing stocks: Go to http://dc1.chass.utoronto.ca/ and then CRSP (if you’re off campus you’ll need to log in with your UTORid) Go to Advanced search Choose Monthly tables (this is because daily tables, by definition, do not contain dividend yields) Search for Keywords “Dell Boeing” (string in company name, and match any keywords) Select Dell and Boeing and “copy to my companies list” In Select one or more companies ”Select all” and continue In “Monthly Tables” select: Lowest bid price, highest ask price, closing price, volume shares traded, Returns, and Returns without dividends In “Output format” select “MS Excel Ready” and continue The Excel spreadsheet will contain Boeing data from Sept 29th 1934 onwards and Dell data from June 30th 1988 onwards, both until December 31st 2011. In a separate worksheet, download 3-month US T-bill daily interest rates from Federal Reserve St. Louis http://research.stlouisfed.org/fred2/series/TB3MS/downloaddata?cid=116 . Transform this data from percentages into “out of 100” decimal places Create a single worksheet with Boeing, Dell and T-Bill interest rates data from June 30th 1988 onwards. Arrange individual stock data in the following order: Volume, High price, Low price and closing price. (a) Use Excel’s built in “stock chart tool” to plot Dell and Boeing’s Volume, High price, Low price and Closing price. Answer Please see Excel Model Chapter 7.1. (b) The return on an asset between time and ⏟ is defined as: ⏟ CRSP gives the “holding period return” (i.e. ) and “return without dividends” (i.e. capital gains). Calculate Dell and Boeing’s dividend yield and dividend for each month in the sample. What do you notice about Dell’s dividends (Finance and accounting majors: read this article)? Answer Please see Excel Model Chapter 7.1. Dividend Yield (or gain) is calculated as: Dividend Yield = Return – Return without Dividend Once we have dividend yield, the...
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This note was uploaded on 03/20/2014 for the course ECON 204 taught by Professor Ajazhussain during the Fall '09 term at University of Toronto- Toronto.

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