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Unformatted text preview: /1 UNIVERSITY OF WATE R LOO Examination Please print in pen:
Waterloo Student ID Number: Winter 201 3 Times: Monday 20130211 at 17:30 to 13:20 (5:30 to 6:20PM) ACTSC 3 72 Duration: 50 minutes
Exam [0: 2578986 Sections: ACTSC 372 LEC 001 Spec1al Materlals
Instructors: WOOd Peter] Candidates may bring only the listed aids.
. Calculator SPECIAL NOTE: Please note that no questions will be answered by either the TAs or by the instructor. if you are uncertain as to how to proceed in a question, please
make the most common sense assumptions. if necessary, state the additional assumptions you feel are needed in order to answer the question. FOR EXAMINERS’ USE ONLY i ACTSC 372 Winter 2013 Midterm
© 2013 University of Waterloo Page 1 Of 8 l______ﬁ_____ ACTSC 372 Winter 20 l 3 Term Test #1 [8] l.(a) A portfolio of securities has a 1 year 95% VaR of $3 million. What does this
mean? ﬂan. [5 Q 37 dumm— ‘Ouw at” /06c,
mm ‘lJ'w 473m. (b) In practice, how do investment analysts actually compute the beta of a security? Run a rag/mam» 044 («L “LAWS a3
4’)! 8900!?“ again” 441. mar/<94. (c) In practice, people use a proxy for the market portfolio (such as an index), instead
of the “true” market portfolio as described by CAPM. Why? ”ﬂew cm, for h» WW] dtourll’m W
pawlw 1b WA MU ﬂoasiéh (d) Give the formula for the Sharpe ratio of a portfolio P. Why would anyone want to
ﬁnd this ratio? Sta 3 van W [I actual
“'77 ' CH 4 campamdzh Mac/J04»  r________,_____________———— ACTSC 372 Winter 2013 Midterm
© 2013 University of Waterloo Pagﬁ 2 Of 8 ACTSC 372 Winter 2013 Term Test #1 [9] 2. Suppose the following data is available. Assume CAPM holds. m— Standard Deviation PetroCanada Inc mam——
Market 'ortfolio (a) Find the values (i), (ii) and (iii). There is no need tojustify your answers.
0: \ t; l
(g t 1 c (c co 1 “/0 (b) Find the Traynor ratio of PetroCanada. Is this security overpriced, underpriced or correctly priced, according to CAPM?
rpft ; w :1 55%,! : 5.7/2 [5; 07
 CLE— ﬂxz g;+5.7(/a/)>7Z>LZ (shat 8/1" = glib/4. _
Silklat 112 L [01 3.) gut/El 7‘. W (e) Construct a portfolio consisting of the Market portfolio and the risk free asset that
has the same systematic risk of PetroCanada, but better returns. What is the expected return of this portfolio? 7
a#L}/ 5 4'04'6'17'0' , 6!“
F, artar 716%“? {$93 03 I‘Nk gﬁec cask/1L
5.1— l’la/kuf' fwI'MID / 3.0" 0119') ,4. 03—13—27 72 ACTSC 372 Winter 2013 Midterm
Page 3 of 8 © 2013 University of Waterloo ACTSC 372 Winter 2013 Term Test #1 [9] 3. Suppose there are 2 securities in the marketplace, A and B. Assume aA —
20%, 03 —— 10%, ,uA — 10%, [13 — 7%. and the correlation of the returns is p — —0. 5 Consider a portfolio P— — M + (1 — t)B. For what values oft is this portfolio efﬁcient? Provide a sketch of the efﬁcient frontier.
J t €902) 4 M) 0m r 2( emf“ WW)
[9 ﬂ  .219 (JG/)1.  204%!to —@6[)(/o/) + 947(341m‘ 0U: .. S!) a?” :7 5% —;l LL17
M 2') )‘Hze L1 .74 {2— 28‘s] 2. +~Ilc :o ch—d (we Wilma : ACTSC 372 Winter 2013 Midterm
© 2013 University of Waterloo Page 4 Of 8 ACTSC 372 Winter 2013 Term Test #1 _—’—_———————————— [5] 4. Assume there is a risky asset A which has an expected return on RA and a
volatility (i.e. standard deviation) 0A. Assume you construct a portfolio
P consisting of the asset A and the risk free asset (in some proportion). Let RP and
Up be the return and standard deviation of the portfolio as usual. Show that “P
RP = Tf ‘l' _(RA _Tf)
0A \§\
§
+
.2 l
\g
D ACTSC 372 Winter 2013 Midterm ‘ © 2013 University of Waterloo Page 5 Of 8 ACTSC 372 Winter 2013 Term Test #1 [9] 5. You have analyzed the returns on various securities, and you believe that they are
best modeled with a one factor APT model. More speciﬁcally, assume Rx=E+ﬁ(F—F)+6x where X [S a typical security in the market. Assume the ﬁrm speciﬁc risks are all independent from each other and from the factor. Suppose Var(F1)—  0.0025.
Suppose there are 2 securities in the market A and B, with the following data: (a) Construct a portfolio from securities A and B whose beta is 0.7. What is the
expected return of this portfolio? 4.1.” 5.0m : 0,7 “‘7! 3) 4¢J01 536:5)
RF; gal[02+5’o1U‘ 632
(b) What is the variance of the returns of the portfolio in part (a).
Wm): (M [a]; *frlp’ﬂ + gag/t #5’Ul£¢>
2 f: (fa/(Fl 4—617” mlm PM) was) 2 0.01%)? __________________..___.._._.—————————
ACTSC 372 Winter 2013 Midterm
© 2013 University of Waterloo Page 6 0f 8 l___________________ ACTSC 372 Winter 2013 Term Test #1 (c) What do you think the risk free rate is? 7:» 524—5 7/
509% ”MW ‘5’
=7 aft
b a 3h. a
1/ a’J— )5) ‘L "
7/ 7 L1
/ N ACTSC 372 Winter 2013 Midterm
© 2013 University of Waterloo Page 7 Of 8 ACTSC 372 Winter 2013 Term Test #1 _—_———_—_————— BLANK PAGE ACTSC 372 Winter 2013 Midterm
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