# homework1f09ans - Econ 434 Professor Ickes Fall 2009...

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Econ 434 Professor Ickes Fall 2009 Homework Assignment #1: Answer Sheet This assignment is due on Tuesday, September 15, at the beginning of class (or sooner). 1. Consider the following returns data for two economies, Macrodonia and Microdonia: Panel A −−−−−−−−−−−−−−−−−−−−−−− Panel B −−−−−−−−−−−−−−−−−−−−−−−−− Year Macrodonia % Microdonia % x % y % Return % Risk % 1994 9 . 52 8 . 11 0 0 0 1 3 . 38 23 . 15 1995 56 . 76 9 . 4 9 01 3 . 85 21 . 53 1996 6 . 22 1 . 1 8 02 4 . 31 20 . 52 1997 36 . 62 5 . 3 7 03 4 . 77 20 . 2 1998 14 . 31 0 . 7 6 04 5 . 24 20 . 61 1999 12 . 56 7 . 7 5 05 5 . 72 1 . 71 2000 42 . 6 28 . 6 4 06 6 . 17 23 . 4 2001 0 . 5 34 . 0 3 07 6 . 64 25 . 56 2002 12 . 1 13 . 9 2 08 7 . 12 8 . 09 2003 12 . 4 . 5 1 09 7 . 57 30 . 89 average 13 . 38 18 . 03 0 100 18 . 03 33 . 90 standard deviation 23 . 15 33 . 90 correlation 0 . 127 (a) Calculate the average return and the standard deviation of returns for each country over this period (use a calculator or an excel spreadsheet,whichhasabui lt-informu laforthis, or the excel program I provided for the class in my lecture). Also calculate the correlation of returns across the countries. The latter is denoted by ρ ij . brief answer see table. (b) The expected return for a portfolio with two assets is given by R p = xR i + yR j .L e t i be Macrodonia and j be Microdonia, and let x be the share of the portfolio invested in Macrodonia assets, and y the share in Microdonia assets. Calculate the expected returns for each of the ten portfolios given by the weights in panel B of the table. brief answer see table. (c) Ther isko faport fo l ioisg ivenbyitss tandarddev iat ion , σ . For a portfolio of two assets this is given by the formula: σ P = ³ x 2 σ 2 i + y 2 σ 2 j +2 xy σ i σ j ρ ij ´ 1 2 Use this formula to calculate the riskiness of each of the ten portfolios in panel B of the table(remember the excel program). brief answer see table. 1

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12 13 14 15 16 17 18 19 15 17 19 21 23 25 27 29 31 33 35 R e t u r n Standard Deviation Set of Feasible Portfolios MinimumVariancePortfolio 70% Macrodonia 30% Microdonia Setof EfficientPortfolios Figure 1: (d) Using your calculations of the risk and return of the ten portfolios make a graph of the feasible set of portfolios. Which portfolio has the minimum risk? (e) Label the e cient set of portfolios in your graph. Explain why a portfolio that is comprised only of home assets would be a poor choice for residents of either country. brief answer A portfolio comprised of %100 Macrodonia assets has R p =13 . 38 and σ p =23 . 15 . Th i si sno te cient — you could get a higher return with the same amount of risk. For example, 40% Microdonia 60% Microdonia yields R p =16 . 17 and has the same level of risk. A portfolio comprised of all Microdonia assets would be optimal only for investors who did not care about risk, only return. If an investor was risk neutral her indi f erence curves would be horizontal (can you explain why) and thus would hold only Microdonia assets. An investor that was risk averse would choose a portfolio somewhere on the e cient frontier, but most likely a diversi f ed portfolio.
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## This note was uploaded on 01/11/2012 for the course ECONOMICS 434 taught by Professor Staff during the Fall '11 term at Pennsylvania State University, University Park.

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homework1f09ans - Econ 434 Professor Ickes Fall 2009...

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