20052009年英国精算师考试ct8 历年真题及答案解析.pdf

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) = 1011 1/12= 1010
(ii) Downside semi-variance of R = 1011 upside semi-variance of U; the
upside semi-variance of U is by symmetry 1/24 so downside semi-variance of
R is 1010.
(iii) P(R < 100,000) = P(U > ) =
(iv) If VaR5%(R) = t then P(R t) = , so
P(300,000 500,000U t) = P(U > + (t / 500,000)) = 5%,
hence (since P(U > x) = 1 x), (t / 500,000)) = , so
t = 500,000 () = 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) = = .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 = , B = and C = .
Finally, solving
ri r0 = i(rM r0), we get rA = , rB =