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# sol_hw2 - University of Hong Kong Department of Economics...

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University of Hong Kong Department of Economics and Finance FINA 2802C – Investment and Portfolio Analysis First Semester: 2007-2008 Dr. Kam-Ming Wan Answers to Problem Set 2 (1) a. Six year Holding period return for i) 500 index fund = (1.099)*(1.012)*(1.374)*(1.229)*(1.332)*(1.286) - 1 = 2.217 = 221.7% ii) Total stock market index fund = (1.106)*(0.998)*(1.358)*(1.21)*(1.31)*(1.233) - 1 = 1.9296 = 192.96% iii) Small-Cap index fund = (1.187)*(0.995)*(1.287)*(1.181)*(1.246)*(0.974) - 1 = 1.1786 = 117.86% iv) Long-term Treasury Fund = (1.1725)*(0.9236)*(1.3069)*(0.9913)*(1.1508)*(1.1352) - 1 = 0.8328 = 83.28% v) Short-term Treasury Fund = (1.0691)*(0.992)*(1.127)*(1.0455)*(1.0711)*(1.0776) - 1 = 0.4423 = 44.23% b. Arithmetic average return of investment j = 1998 1998 1993 1993 6 j tj tt t R R T == = Arithmetic average return of i) 500 index fund = (9.9 +1.2+37.4+22.9+33.2+28.6)%/6 = 22.2%, By the same token, Arithmetic average of ii) Total market index = 20.25% iii) Small-cap index fund = 14.5% iv) Long-term treasury fund = 11.34% v) Short-term treasury fund = 6.37% As these are historical returns, the variance of investment j is as follows: () 2 1998 . 2 1993 . ;where is the sample mean of investment between 1993 and 1998. 1 jt j t jj RR Rj T σ = = 1

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Variance of 500 index fund = [(9.9-22.2) 2 + …+ (28.6-22.2) 2 ] / 5 = 197.156% Standard deviation of 500 index fund = 197.156% = 14.04% By the same token, Standard deviation of Total Market index fund = 13.26% Standard deviation of Small Cap index fund = 13.05% Standard deviation of Long-term Treasury fund = 13.69% Standard deviation of Short-term Treasury fund = 4.42% c. Geometric average return of investment j is 6 6 12 6 (1 ) (1 ) ... (1 ) 1 1 1,
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sol_hw2 - University of Hong Kong Department of Economics...

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