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20052009年英国精算师考试ct8 历年真题及答案解析.pdf


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20052009年英国精算师考试ct8 历年真题及答案解析.pdf
文档介绍:
Faculty of Actuaries Institute of Actuaries


EXAMINATION
September 2005
Subject CT8 Financial Economics
Core Technical

EXAMINERS REPORT


Faculty of Actuaries
Institute of Actuaries
Subject CT8 (Financial Economics Core Technical) Sept 2005 Examiners Report

1 (i) Var(R) = 500,0002 Var(U) = 2.5 1011 1/12=2.08333 1010

(ii) Downside semi-variance of R = 2.5 1011 upside semi-variance of U; the
upside semi-variance of U is by symmetry 1/24 so downside semi-variance of
R is 1.04166 1010.

(iii) P(R < 100,000) = P(U > 0.4) = 0.6

(iv) If VaR5%(R) = t then P(R t) = 0.05, so

P(300,000 500,000U t) = P(U > 0.6 + (t / 500,000)) = 5%,

hence (since P(U > x) = 1 x), 0.4 (t / 500,000)) = 0.05, so

t = 500,000 (0.35) = 175,000.

2 (i) The market portfolio is (2/7, 3/7, 2/7), so

RM = (2RA + 3RB + 2RC) / 7.

Thus

Cov(Ri, RM) = [2 Cov(Ri, RA) + 3Cov(Ri, RB) + 2 Cov(Ri, RC)] / 7.

So,

Cov(RA, RM) = [.32 + .12 + .04] / 7 = .06857

Cov(RB, RM) = 0.22/7 = .03143,

and

Cov(RC, RM) = .09/7 = .01286,

and

2
M = [2 Cov(RM, RA) + 3 Cov(RM, RB) + 2 Cov(RM, RC)] / 7 = .03674.


We conclude that A = 1.8664, B = 0.8555 and C = 0.3500.

Finally, solving

ri r0 = i(rM r0), we get rA = 0.4, rB =
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