Test 1 SOLN - /1 UNIVERSITY OF WATE R LOO Examination...

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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 2013-02-11 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. _ Silk-lat 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 0-3 I‘Nk gfiec cask/1L 5.1— l’la/kuf' fw-I'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‘ 6-32 (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 © 2013 University of Waterloo ...
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