MBA 570x Homework 1 Due 9/24/2014 Solution

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1 MA 570x Homework 1 Due 9/24/2014 olution Individual work: 1. Quetion related to Chapter 11, T Why do you think i a fund of fund market for hedge fund, but not for mutual fund? Anwer: Invetor can inexpenively recreate diverification by inveting in variou mutual fund. Mot invetor do not have the amount of capital needed to invet in multiple hedge fund to achieve diverification. In addition, while mutual fund are very tranparent about their invetment trategie (which are relatively traight forward) and there i an entire indutry dedicated to providing invetor with analyi of mutual fund, hedge fund are much more opaque about their invetment activitie and their trategie are more eoteric. A a reult, the cot/reward ratio for a fund of hedge fund i much higher than for a fund of mutual fund. 2. Quetion related to Chapter 12: a. During the height of the financial crii in late 2008, the yield curve flattened and the yield on the 30-year Treaury bond reached a then-all-time low of 2.52%. A a hedge fund manager, uppoe you think the market ha overreacted and will eventually correct itelf, leading to a teepening in the yield curve. What trade might you execute in a long/hort trategy to take advantage of the ituation? Anwer: hort the 30-year Treaury; long the 1-year Treaury. b. Why did convertible arbitrage trategie perform o poorly in 2008? In thi trade, hedge fund go long the convertible, and hort the underlying tock. When the temporary hort-ban wa intituted in late 2008, trader could no longer hedge their poition by horting tock. A the tock market fell, convertible value dropped, and the inability to manage hort poition compounded the lo. 3.1 Chapter 7 (KM): 5 uppoe that your client decide to invet in your portfolio a proportion y of the total invetment budget o that the overall portfolio will have an expected rate of return of 16%. a. What i the proportion y? y* (1-y)*0.08 = olve the above: y = 0.8 b. What are your client invetment proportion in your three tock and the T-bill fun? tock 1: 0.8*0.25 = 0.2 tock 2: 0.8*0.32 = 0.26 tock 3: 0.8*0.43 = 0.34 Rik free aet: = 0.2

Mot invetor do not have the amount of capital needed to invet in multiple hedge fund to achieve diverification.

2 c. What i the tandard deviation of the rate of return on your client portfolio? 0.28*0.8 = 22.40% 3.2 Chapter 7 (KM): 7 You client degree of rik averion i A=3.5. a. What proportion, y of the total invetment hould be inveted in your fund? y* = ( )/(0.01*3.5* ) = 0.36 b. What i the expected value and tandard deviation of the rate of return on your client optimized portfolio? 0.36*18% *0.08 = 11.60% tandard deviation of the portfolio = 0.36*28 = 10.08% 4. Chapter 8 (KM): 1, 6 1. A penion fund manager i conidering three mutual fund. The firt i a tock fund, the econd i a long-term government and corporate bond fund, and the third i a T-bill money fund that yield a rate of 8%. The probability ditribution of the riky fund i a the following: tock fund () ond fund () Expected return tandard deviation 20% (E( r )) 30% ( ) 12% (E( r )) 15% ( ) What are the invetment proportion in the minimum-variance portfolio of the two riky fund, and what i the expected value and tandard deviation of it rate of return? 2 cov( r r ) E, E w (page 214, footnote 4) min cov( r, r ) E E Uing the above information, we find the weight of the minimum variance portfolio in the tock fund i 0.17 and the weight in the bond fund i E(r p ) = 12* *0.17 = 13.36% w w 2 w w = p Thu, σ p =13.92% 6. You require that your portfolio yield an expected return of 14%, and that it be efficient on the bet feaible CAL. a. what i the tandard deviation of your portfolio? Obtaining the weight for optimal riky portfolio baed equation (8.7) on page 221. You get weight in bond i 0.548; and the weight in tock i w w 2 w w = p We have: σ p =16.514% b. what i the proportion inveted in the T-bill fund and each of the two riky fund? E(r p ) = 0.548* *20 = 15.6%;

What i the expected value and tandard deviation of the rate of return on your client optimized portfolio? 0.36*18% + 0.64*0.08 = 11.60% tandard deviation of the portfolio = 0.36*28 = 10.08% 4.

3 15.6% = 8%*w %*(1-w) w: weight in the rik free aet = the ret in tock and bond fund 5.1 Chapter 24 (KM): 3 A manager buy three hare of tock today, and then ell one of thoe hare each year for the next three year. Hi action and the price hitory of the tock are ummarized below. The tock pay no dividend: Time Price Action 0 90 uy 3 hare ell 1 hare ell 1 hare ell 1 hare a. calculate the time-weighted geometric average return on thi portfolio. b. Calculate the time-weighted arithmetic average return on thi portfolio. c. Calculate the dollar-weighted average return on thi portfolio. olution: a. Time Cah flow Holding period return 0 3 ( $90) = $270 1 $100 (100 90)/90 = 11.11% 2 $100 0% 3 $100 0% Time-weighted geometric average rate of return = ( ) 1/3 1 = = 3.57% b. Time-weighted arithmetic average rate of return = (11.11% )/3 = 3.70% The arithmetic average i alway greater than or equal to the geometric average; the greater the diperion, the greater the difference. c. Dollar-weighted average rate of return = IRR = 5.46% [Uing a financial calculator, enter: n = 3, PV = 270, FV = 0, PMT = 100. Then compute the interet rate, or ue the CF 0 = 300, CF 1 =100, F 1 =3, then compute IRR]. The IRR exceed the other average becaue the invetment fund wa the larget when the highet return occurred. 5.2 Chapter 24 (KM): 4 aed on current dividend yield and expected capital gain, the expected rate of return on portfolio A and are 12% and 16%, repectively. The beta of A i 0.7, while that of i 1.4. The T-bill rate i currently 5%, wherea the expected rate of return of the &P 500 index i 13%. The tandard deviation of portfolio A i 12% annually, that of i 31%, and that of the &P 500 index i 18%. a. If you currently hold a market-index portfolio, would you chooe add either of thee portfolio to your holding?

The tock pay no dividend: Time Price Action 0 90 uy 3 hare 1 100 ell 1 hare 2 100 ell 1 hare 3 100 ell 1 hare a. calculate the time-weighted geometric average return on thi portfolio. b.

4 Compare their alpha (ince alpha i relevant meaure when the portfolio i already well diverified). A i greater. (1.4% veru -0.2%) b. If intead you could invet only in T-bill and one of thee portfolio which would you chooe. Comparing harpe ratio (ince the harpe ratio i relevant meaure when the portfolio i not diverified), A i greater. (0.583 veru 0.355) 5.3 Chapter 24 (KM): 5 Conider the two (exce return) index-model regreion reult for tock A and. the rik-free rate over the period wa 6%, and the market average return wa 14%. Performance i meaured uing an index model regreion on exce return. a. Compute the tatitic for each tock A Alpha 1% 2% Appraial ratio 1/10.3 2/19.1 harpe ratio 10.6/ /24.9 Treynor meaure 10.6/ /0.8 b. Which tock i the bet choice under the following circumtance? i. Thi i the only rik aet to be held by the invetor A, baed on harpe ratio ii. The tock i to mixed with the ret of the invetor portfolio, currently compoed olely of holding in the market index fund, baed on alpha. iii. Thi i one of many tock that the invetor i analyzing to form an actively managed tock portfolio. A, baed on the Treynor meaure. 5.4 Chapter 24 (KM): 7 Conider the following information regarding the performance of a money manager in a recent month. The table repreent the actual return of each ector of the manager portfolio in column 1, the fraction of the portfolio allocated to each ector in column 2, the benchmark or neutral ector allocation in column 3, and the return of ector indice in column 4 Actual ret actual wgt benchmark wgt index ret Equity 2% % (&P) ond 1% % (alomon index) Cah a. ogey: ( %) + ( %) + ( %) = 1.91% Actual: ( %) + ( %) + ( %) = 1.65% Underperformance: 0.26% b. ecurity election: Market (1) (2) (3) = (1) (2) Differential return within market (Manager index) Manager' portfolio weight Contribution to performance Equity 0.5% % ond 0.2% % Cah 0.0% % Contribution of ecurity election: 0.39%

Comparing harpe ratio (ince the harpe ratio i relevant meaure when the portfolio i not diverified), A i greater. (0.583 veru 0.355) 5.

5 c. Aet Allocation: Market (1) (2) (3) = (1) (2) Exce weight Index Contribution to (Manager benchmark) Return performance Equity 0.10% 2.5% 0.25% ond 0.10% 1.2% 0.12% Cah 0.00% 0.5% 0.00% ummary: ecurity election 0.39% Aet allocation 0.13% Exce performance 0.26% Contribution of aet allocation: 0.13%

25% ond 0.10% 1.2% 0.12% Cah 0.00% 0.5% 0.00% ummary: ecurity election 0.

Sample Problems Chapter 9

Sample Problems Chapter 9 Sample roblem Chapter 9 Title: referred tock (olve for value) 1. Timele Corporation iued preferred tock with a par value of $7. The tock promied to pay an annual dividend equal to 19.% of the par value.