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Unformatted text preview: I L QUESTION] (22 points) ﬂ ’3 tie/V Cg ’ : 3('0\ ' You have the following single indeé ﬂTfegression information on two securities: Securi A Security B ] ( { at” A g 'f I
(X B )7 "‘ " W 0“ “‘l I 1
RA=1%+2Rm+eA 'RB=l%+1RM+eB J
O'CE Residual standard deviation = 0.20 i Residual stande deviation = 0.40 l
R—squa e = 0.90 : F A
few mg a) What is the variance of Security A? (3 points)
pi: QA’Gul 46“; 4034*: 3‘19 (mH 0.036 — ________ = 0‘4 c u .
35961114 G‘(€A» %M‘+o.z‘ 0t4GM 0056 074": 0.0‘] a 67:5 emu We»: 1‘10.04)+ on‘: 0.4 v GM: M
b) What is the systematic variance of Security A? (3 points) Gama“: fume): 0.36 c) What is the variancc of the market index? (3 points)
GM 1: Oloﬁ L.“ d) What is the variance of Security B? (3 points)
= How) + 0.43 = 0‘13 e) What is the covariance between Securities A and B? (3 points) gaVLEA.Rn)=ﬁ~u<p6‘M*: (2)0)(0‘04): (MB "V" i) What is the correlation between Securities A and B? (3 points) twain P a \ 9' “a ‘
€A9=é® 8=__D__‘B____;*—{_::—~:jo,5‘6q
A 5 Oil
g) What is the covariance between Security A and the market index? (2 points)
CUVMMQM): 39346;“: (.17: ; $06)); 0J8 [1/
h) What is the Rsquare of the regression of Security B on the market index? (2 points)
"‘ 4 0'7“ 2 _
R=‘—:—‘~ =oae'~~
(3‘8 OJJ;
PageZ ’z 1 Fina‘I_Morning
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a. a L. .1 >' Tognd'ﬁi‘vq:lglﬁa
of 5 ’6',“ ‘1" 0? (e, R12
‘ I c . ‘»._ QUESTION 2 (20 points) ' Assume that the returns of secuties in the economy areﬂﬁven b ources of risk (systematic factors). The riskfree rate is The [able below provides information on thesethree factors and the betas of two well diversiﬁed portfolio 9». n @with respect to these factors. _ ELM— (‘9
Factor Expected Rate Actual Rate [3; ' [3Q _ __ of Change of Chan e i___ﬁ__J'
I Industrial production I a 2% 3% i 1.2 0.6 ' “30‘4"
! Inﬂation ! 6% 4% .' 0.6 033‘ i M9413, O
; Oilprices 3% ___ 2%  1.4 0.7 l / 9"
a) What should the exgected return of portfolio P be if this portfolio is fairly; priced? (4 points)
‘ EU’pl: H + FP,PP1* FREE. ‘ ﬁring = ‘i’z’z+'.2 ‘, ’a‘ Mr" '4” 19/0 I“ I
b) What is the unexpected return of portfolio P if its idiosyncratic return is O? (4 points) AF! 4'GP34\F§ cm
.. Mme/M— ll(3~13 +0.6tq.~—t‘,\* :... J.” .3 ,_P__H:f&‘: _SJ. .. _ ‘ l
c) Portfolio Q has an expected return 0 7.1%. What is Portfolio Q’s alpha?
Is Portfolio Q over or underpriced? ' (4 points) Requnrpd Emu = H‘" 8MP: + 69$?” mars: 4% +0th v/u+~o.ax w. + 9.; yaw/o
6m»); 8x €ch W'hlm sat,4 n: l . . , ouev ﬁned '.
d) What if: the arbitrage strategy hat canbgituploimi'shiiiigpi’iéing? =saline the stegs and show what the arbitrage proﬁts are given the actual returns of the factors given above. @wints) at a» la. 3 1/0 2 Tcolrzed _.
w P ifat‘rf/ — ph‘ceri Q3 Weir  (Jvrmoi El atrium032 19??“me
arbTeraae SW13” 1 1. guy P and 5‘5." an gem“ (lncmnfqf—G 1. 13079) + (3F 5F. + gphaF1+gP§DF3 H ‘w. .v 3) = 849/0
marsM q\I&/o+ 0.6 gig) + o.‘>,é£Lm+o’a 0.3”]. :drbi‘ﬁﬂae profrt F inal_Moming _ QUESTION3 (20 points) raj.» "  Suppose you are looking at your pension savings and compare your actual performance to that of a
benchmark mutual fund portfolio you could have invested in. The information on your performance
and that of the benchmark are ided below g mural” 4. . . 1
Stocks I 15% 0.6 jl 0.4 ‘ 12% I I .' T  Corporatebonds II 10%_ 1 _ 0.3 J, 0.4 L _ _8%_ l
I. 1‘ I Treasuries 5% J1 0.1 M 0.2 5% I The performance attribution formula is given by: ,  m+4  use;  ——. a) Break your relative outperformance/underperl'ormance into the individual components
due to asset allocation and smn for each asset class? (12 points)
Show your calculations then ﬁll in the table below. . 9“
Asset allomh‘on I tl/Jpa  um a; 4 If
a 1’ ’xoxé — datum/o 1— (OJ—bra.) x853 r (st—UJMS‘VO
: 24—" otsw mg: lx9/0 l
2: 0.6 (IPA—um +~ 0.3(i0‘l.*b.‘«‘ 1* Galﬁ'ﬁ "a," .
= “i” 0‘6: 2.49/0 Amer 803% ~‘ 0.4kb). v. +0i‘ls: 8v «ratz 1r '5 .: Clo/o ,
\_, 3‘??? Wevpé'y'jumom‘e < p 7 0\6X'f%+OI%X'O’/u +— D‘: , a) ,1”: '2‘; D/J / git/51rd
TOTAL OUTPERFRMAN_CE '
_ 3,5, 9.10.1 agar:
# Total from Stocks ___ﬁ ﬁ _'_I_‘ota_l_ from corporatgggygsn; __Total fr_om Treasuries __
________ 1Z;.__._. ._. _ ___:'_°_'2__ ____._'_%__
Asset Security Asset Security Asset Security
‘ Allocation _ Selection Allocation , Selection Allocation Selection , liqD/o_ l¢8‘/0 ——O\Qo!, 0.60/3 —Olsola 00/0 b) What is your overall performance due to asset allocation? (3 points) 1. i  i 0/ o
c) What is your overall performance due to security selection? (3 points)
2 r 4" 0/0 l d) What is your conclusion, i.e. should you focus your efforts more on asset allocation or
secgritygelggtion? (2 points) 4e UAW57 {elf CiTon Page 4 Final_Morning QUESTION 4 (18 points) ' .f’s , V
I r
x. . ‘ A semiannual bond has a 12% annual coupon rate, a face value 331,000, and 1.5 years to maturity.
The bond is selling at a semi—annual yield~to—mat_u1:ity of 5%. ’ ’ I i iﬂ—w—f‘*ﬂ*.“4 5" .
a) You just bought this bond. What is the price that you paid? (5 points) I __ /
FM lﬁoo _/Q
q” 3 PV= $0251.15  '
fMT 60
RI 5 /, b) What is effective annual yield of the bond? (3 points) k'l.05)“'—} = \otzsefo c) Suppose that six months have passed and you have just collected the semiannual coupon on
the bond. This morning you also sold the bond. Note that a week ago, Moody’s upgraded the
bond and the market now requires a semi—annual yield to maturity of only 4%. What was your
semiannual holdingperiod return. (lOpoints)  \ \' ‘ [:V LOGO
m 1 WT 60 in": “‘7‘”
'i 4% loa¥.?l~rox?.rb
Smw annual mama Parcel WWW : H. .———. (011L335
= 0/9”” 1 Oh ' 3L 3/0
Q J? ' Page 5 F inaLMornmg QUESTION 5 (20 points)  i . , ‘ You are provided with the following information on 1,2, and 3year zerocoupon bonds: —————— y'——‘_—m_'———T
Year II Price of ' Spot One year .
‘ ZeroCoupon Bond 1 Rates Forward Rates
1 i $952.38 1 (13' HQ I___ 2 3' $873.44 ie‘ '1 ® I 3 $711.78 9 . a) Calculate the spot rates for maturities 1,2, and 3, then ﬁll in the table above? (5 points) r.. L000
(3: Man“ 2 452.35 $5 305 0» '5~'/. ® l 000
,________. Hg ‘1 = 33’4’4 ammo“ : an? a» 4m luv 3
(a) ...______.. r . __ . . ,,
RH uﬂa i “9'8 ‘33” '3‘ 3‘ "r *0 a 1)) Calculate the oneyear forward rates for years 1,2, and 3, then ﬁll in the table above? (5 points) @ g °/o @ «stow: <+otow>< w» 4.1; “"2” '"l r 0.06} a). cw» l a 09
© {4 0‘1;)3 == (‘+0.0=};\ 4 'ia)
193:: ‘l ,,‘ ._.I. 0.127. 0» 11.? °/=
. 'z 23
c) Ifthe pure expectation hypothesis is correct, what price does the market expect that the price of l, . a twgﬂeag zero coupon bond (face of $1,000) will be one year from now? (5 points) t r
ts l . 00x.)
~. were. 43
I \ 0 d) If the pure expectation hypothesis is correct, what does the market expect that the price of a
twoyear 10% annual coupon bond (face of $1,000) will be one year from now? (5 points) \ i001 = $‘lé‘6 6 Page 6 F inal_Morning .4: , QUESTION 3 (30 points) , _ I. a... ' You collect the following information on two securities and the market: Expected Standard Correlation
return Deviation with market
. M
O SecuntyA 73% 40% 0.25
Security B 9.3% 35% 0.40
Market ? 20% 1.0 .\
. ,,, ’3 — r
a) Whatarethebetaspftheftwo SeczrliltiesAfndB? (6points) L1 '02:) :' R4; 7' Ukﬁ'“ ¥ /
2 _ than " [h Ediigﬁ __ EQLCA; —— V . , _ I (,_., , 1*” " 3333;; «1  K r is” x i > r: #729
at. " ’1‘ )1 47'5’51720L I J ,3 A? l. 72,52,15495‘2141 wild”;
£57.43 g: [xx7.5. Km “((5 f rt wingwr ’lsifhas‘kz k .. ' .? 9' /'.ef9’_3_gm> /%;_; T“ c’: e
9'75 17% (Km + “17.33;” +’1.____..’“[email protected]:v>
0. F4}: b) If both Securities A and B are priced correctly according to the CAPM (in equilibrium),
calculate the expected return of the Market and the riskfree rate. (6 points) (“mm73° {ﬂeafat 1 ft IERA: is 5981613
0 7.5: rg + 0.3(RM_r;)“‘@
' q'5: n; + 0»? CRM"£')'[email protected] @ 4,? ;. oﬁQR’Mwb
I. QMw‘Ze: q “0 7.8: filt OrS L4,) 1.8: C + q'rs
:9; @quiSCET’E c) If Security C has an expected return 9 and a beta of 1.5, is it over or under~priced? (41718) 1.4: ‘:"_. :‘Qf—zk'g'rt’ ’79" “"147 / ' ) —: (XC :IIAS " Eff, ‘t 4v5(RM‘;‘$)3
0<_¢' “as— [:3 + asides) 
O “a; 45, £3 .+ 43.821 6 [M45254 . Ii Paco i‘ (1) Eric is a portfolio In aer managing «$500,000 }quity portfolio with a beta oi» d an
expected return 0 He holds $10,000 of security®(described above) in his portfolio. He decides to sell all of his
holdings of security A and invest all the $10,000 in security C (described in c)).
What will the new beta of his overall portfolio be aﬁer this transaction? (10 pts)
0 ﬁg; 49.4 66: 4'4 Two: 9:39:00
40,000 Pt 89.“ 3K 40,900 C 80‘ 0.8 :33; =*a= I "n,"
Egg—L"— @%:o,09 *8: = .
l J g  [0.04 + 0.029.} 5'. 4,4 — £9,03a=—‘—> . E _ ‘1. \,\2_
wk \5l r
gm: §¥(bl)’é%i( 6) Is Eric’s new portfolio over or underpriced? Explain why this is n_o_t surprising, (4 p15) 5. . : {EL
0 E}, 3 AR  :24 E32“ + oaﬁ EBB" EVan ffi'Q'lZX?)
" .1 :2 43.01 " + i. YS:D&
 4.93 — 0,45 + 0.3 a :: [43,051 ‘1
«X: 43.05 — [3 + 4.998 *(451 3)]
oar. 43533" E New]
o(= 0.93% O. s on dag] 010' O _ ...
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 Spring '12
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