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2-Answer - 09/10 ( 1 Rate of return in yen for the period...

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09/10 The University of Hong Kong Department of Statistics and Actuarial Science STAT 2309 The Statistics of Investment Risk (First Semester 2009 2010) Problem Sheet 2 Suggested Solution 1. Rate of return in yen for the period from January 2 to April 20: (5003+253.2)/5064 – 1 = 3.80% Rate of return in yen for the period from April 20 to December 31: 6014/5003 – 1 = 20.21% Total rate of return in yen = (1+3.80%)*(1+20.21%) – 1 = 24.77% FX return from January 2 to April 20 = 0.008/0.0079 – 1 = 1.27% FX return from April 20 to December 31 = 0.007/0.008 – 1 = -12.5% Total rate of return in dollar = (1+3.80%)*(1+1.27%)*(1+20.21%)*(1-12.5%) – 1 = 10.56% 2.
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09/10 3. (a) μ = (0.5)(-5%) + (0.5)(20%) = 7.5% ߪ = [ (0.5)(-5%) 2 + (0.5)(20%) 2 – (7.5%) 2 ] 0.5 = 12.5% μ = (0.5)(-7%) + (0.5)(22%) = 14.5% ߪ = [ (0.5)(7%) 2 + (0.5)(22%) 2 – (14.5%) 2 ] 0.5 = 7.5% ߪ ஺஻ = E[ ܴ ܴ ] – E[ ܴ ] E[ ܴ ] E[ ܴ ܴ ] = (0.5)(-5%)(7%) + (0.5)(20%)(22%) = 2.025% ߪ ஺஻ = 2.025% - (7.5%)(14.5%) = 0.9375% Portfolio 1: ݔ = 0.25, ݔ = 0.75 μ = (0.25)(7.5%) + (0.75)(14.5%) = 12.75% σ 2 = (0.25) 2 (12.5%) 2 + (0.75) 2 (7.5%) 2 + 2(0.25)(0.75)(0.9375%) = 0.7656% σ = 8.75% Portfolio 1 involves investing 25% of the total wealth in Asset A and the remaining 75% of the wealth in Asset B.
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