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Unformatted text preview: Aids:
Time:
Room: Examiner: ACTSC 372 — WINTER 2009
MIDTERM EXAM  Feb 6 2009 NAME: Nona SoLuTioms
I.D.:
Calculator
1230—120 pm
MC2054/MC4063/MC1085
M. R. Hardy
Question Maximum Mark
1 12
2 12
3 16
Total 40 / 35 1. i [12 marks] (a) Show that 2 xi is a valid utility function: and state whether it is a risk
averse, risk neutral or risk seeking utility function. (b) Derive an expression for the absolute risk aversion for the utility function = 16%. . t II, S.
Ma u'm: if“ 70 230 um i, . “1.4 “Mb Lulu» Ii
n ‘l;
6% MA : _v~/(_’ﬂ ; .L . 2“ __ J_
whl ‘Hm 1" L“ (c) An individual faces the following loss X: 1000 w. probability 0.001
X = 100 W. probability 0.100
0 W. probability 0.899 Calculate the maximum premium the individual would pay for full insurance
in respect of this loss if her wealth is 2000 and her utility function is = 55%. (d) Without any further calculation, state with reasons what the eﬂect on the maximum premium would be if the initial wealth were increased. ., Ill
“(‘0’ (x) = E[“("°‘)‘Yl =7 QOOOQ'l; 1000‘, 0.00! 4} Hon ,oJ + zoool'Ho‘Z‘lc'
=3 1000—6 5 “We'll =7 CUM1% “ "l Sinu AKA L. DEczEAsmq, 49¢ «hum H L McLYrLMuu‘n p. oleaua‘lAa 4‘: 0b DLI—kk. C\ DOM (hue/m.
3‘ Wham/m 42¢ wait)“ 57E[x]=u.o ._ OO—
W‘vﬁk t “.0 M kl 7 llm Shut “(at so it. ?NMC\MM 9°‘i& 2. [12 marks] A portfolio of investments contains 200 shares of security A and 100 shares of security
B. The cost of the shares is $15 per share for security A and $18 per share for security B. Possible rates of return of each security for three possible states of the world are
given in the table: State of Probability of Rate of Return Rate of Return the world state occurring asset A asset B
1 1/3 13% 11%
2 1/2 9% 10%
3 1/6 6% 9% (a) Calculate the standard deviation of return of security A. (b) Calculate the covariance of the two asset returns. 1 .1.
‘L 1. ' ‘ 1..
(“3 (0'13 * i * 0'0“ ‘1 * °'°" *  (043 + oo‘x +0.0; 3 1 s 3 L T— ; (wuss)
= (0000 6H) 1 \ I OOqu% 1‘7 EIRneb]: Oonll * cohol3 * 0.091004 :O_oo”,I // 3 I e
E [(241] deg) ; o.o°1%33x otoiu‘! : woman; COV: 0,ooo\b‘t‘H (C) Calculate the portfolio weights, 11:1 and 9:2 for this portfolio.
(d) Calculate the expected return on the portfolio. (e) Calculate the standard deviation of the portfolio. C0 TL forHolco L. 200 ska/“l A 41* $1; YVSLJC
+ 100 n u 6 at“; In, sLue. ToM portlolfo Vllw " 4300  ' ‘ ' 9C .: O~3¥§
?roPo(‘l'wnw ml A—J, 04,7.) 1 £00 /l4?; I./L,v1./LL : 0.0qq58 \ 1‘ (a) 6* ~ (2061+ 2mm Wt Cw (New
Y' ' ‘ 2 2— 1.
= I 0.000%L + 031S*0.00684
(0.615 t L + 2* (New, oS‘H‘ o.oooltﬁ*m> 0
: Liosl (03 f: [16 marks] A pension fund manager is considering two mutual funds: one is the stock fund
while the other is the long—term government and corporate bond fund. The pension fund manager is given the following information: Expected Return Standard Deviation
Bond fund 0.06 0.12 Stock fund 0.12 0.20
Correlation between the fund returns is 0.30 (a) Write down the mean return vector, u, and the covariance matrix. (b) Write down the Lagrangian function that you would minimize to derive the
minimum variance portfolio, and hence write down the three equations that you could solve to give the minimum variance portfolio weights x1 and 2:2. 0.0,..1.‘ 9.0041
0.09 I: "A. 1/;
041 0.0011. 0.0% 21.11. 6—7. "" 3‘ (1H 11' A (c) You are given that the minimum variance portfolio is: min 1 —1
:c : (#2482 e
and that
24 _ 76.31 —13.74
_ —13.74 27.47 Calculate the minimum variance portfolio weights. (d) You are further given that the efficient frontier portfolios satisfy * . * —1.5
:c 2mmm+Tz* where z =
1.5 If you are seeking an efﬁcient portfolio that yields an expected return of 13%,
calculate the standard deviation for that portfolio, and write down the portfolio
weights. Cc) " : (oi5’! in mm: “810‘ i 2,
Ze ‘343 M o.\1°\°\ (e) Comment on any practical problems that may arise in using this portfolio. (f) Explain brieﬂy the impact of adding a risk free asset to this portfolio. «mm. m N w. h m x "ﬁlm MllL “7* 4‘L Lt Dru/l JC tolwlvt a. Nb" . “l [M
NW at“, 1L” M aplww M A Ky Lawn 0L)“ “93 mwkﬁmmt— ,low '9’“ (“’3 ...
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 Winter '09
 MARYHARDY
 minimum variance portfolio, fund manager

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