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

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.

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.