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### 2009homework#5solution

Course: H ADM 222, Fall 2009
School: Cornell
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Word Count: 571

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___________________________________ NetID: Name: _______________________ HADM 2222 Fall 2009, Prof. Q. Ma Homework assignment #5 [Due 10 a.m. Wednesday November 4, 2009, Statler 435 drop box] 1. Consider the following information State Probability X Z_ Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10% What is the standard deviation of a portfolio with an investment of \$6000 in X and \$4000 in Z? Solution:...

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___________________________________ NetID: Name: _______________________ HADM 2222 Fall 2009, Prof. Q. Ma Homework assignment #5 [Due 10 a.m. Wednesday November 4, 2009, Statler 435 drop box] 1. Consider the following information State Probability X Z_ Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10% What is the standard deviation of a portfolio with an investment of \$6000 in X and \$4000 in Z? Solution: Portfolio weights are 60% and 40% for assets X and Z, respectively. Rp is (13%, 9.6%, 7%) in (boom, normal, recession). For example, Rp for Boom = 60% * 15% + 40% * 10%= 13%. E(Rp)= .25(13%)+.60(9.6%) + .15(7%) = 10.06%. Variance=.00036924; standard deviation = 1.92%. 2. You have \$10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 15 percent and Stock Y with an expected return of 10 percent. If your goal is to create a portfolio with an expected return of 12.2 percent, how much money will you invest in Stock X? In Stock Y? Solution: Here we are given the expected return of the portfolio and the expected return of each asset in the portfolio, and are asked to find the weight of each asset. We can use the equation for the expected return of a portfolio to solve this problem. Since the total weight of a portfolio must equal 1 (100%), the weight of Stock Y must be one minus the weight of Stock X. Mathematically speaking, this means: E(Rp) = .122 = .15wX + .10(1 wX) We can now solve this equation for the weight of Stock X as: .122 = .15wX + .10 .10wX; wX = 0.44. So, the dollar amount invested in Stock X is the weight of Stock X times the total portfolio value, or: Investment in X = 0.44(\$10,000) = \$4,400; and the dollar amount invested in Stock Y is: Investment in Y = (1 0.44)(\$10,000) = \$5,600 3. Based on the information below, calculate the expected return and standard deviation for the two stocks: State of Probability of Rate of Return if State Occurs Economy State of Economy Stock A Stock B Recession .15 .06 -.20 Normal .60 .07 .13 Boom .25 .11 .33 Solution: E(RA) = .15(.06) + .60(.07) + .25(.11) = .0785 or 7.85% E(RB) = .15(.2) + .60(.13) + .25(.33) = .1305 or 13.05% !A2 =.15(.06 .0785)2 + .60(.07 .0785)2 + .25(.11 .0785)2 = .00034;!A = (.00034)1/2 = 1.85% !B2 =.15(.2 .1305)2 .60(.13 + .1305)2 + .25(.33 .1305)2 = .02633; !B = (.02633)1/2 =16.23% Prof. Q. Ma, HADM 2222 Fall 2009 1/2 Name: ___________________________________ NetID: _______________________ 4. What are the portfolio weights for a portfolio that has 100 shares of Stock A that sell for \$40 per share and 130 shares of Stock B that sell for \$22 per share? Solution: The portfolio weight of an asset is total investment in that asset divided by the total portfolio value. First, we will find the portfolio value, which is: Total value = 100(\$40) + 130(\$22) = \$6,860. The portfolio weight for each stock is: WeightA = 100(\$40)/\$6,860 = .5831; WeightB = 130(\$22)/\$6,860 = .4169 5. Consider the following information about Stocks I and II: State of Economy Probability of Rate of Return if State Occurs State of Economy Stock I Stock II Recession .25 .09 -.30 Normal .50 .42 .12 Irrational exuberance .25 .26 .44 What are the expected returns and standard deviations of the two stocks? Solution: E(RI) = .25(.09) + .50(.42) + .25(.26) = .2975 or 29.75% !I2 = .25(.09 .2975)2 + .50(.42 .2975)2 + .25(.26 .2975)2 = .01862; !I = (.01862)1/2 = 13.65% E(RII) = .25(.30) + .50(.12) + .25(.44) = .0950 !II2 = .25(.30 .0950)2 + .50(.12 .0950)2 + .25(.44 .0950)2 = .06908; !II = (.06908)1/2 = 26.28% 6. Consider the following information: State of Probability of State of Economy Economy Boom .20 Good .40 Poor .30 Bust .10 Rate of Return if State Occurs Stock A Stock B Stock C .30 .45 .33 .12 .10 .15 .01 -.15 -.05 -.06 -.30 -.09 a. Your portfolio is invested 30 percent each in A and C, and 40 percent in B. What is the expected return of the portfolio? Solution: Boom: E(Rp) = .30(.3) + .40(.45) + .30(.33) = .3690 or 36.90% Good: E(Rp) = .30(.12) + .40(.10) + .30(.15) = .1210 or 12.10% Poor: E(Rp) = .30(.01) + .40(.15) + .30(.05) = .0720 or 7.20% Bust: E(Rp) = .30(.06) + .40(.30) + .30(.09) = .1650 or 16.50% And the expected return of the portfolio is: E(Rp) = .20(.3690) + .40(.1210) + .30(.0720) + .10(.1650) = .0841 or 8.41% b. What is the standard deviation of the portfolio? Solution: !p2 = .20(.3690 .0841)2 + .40(.1210 .0841)2 + .30(.0720 .0841)2 + .10(.1650 .0841)2 = .03029; !p = (.03029)1/2 = .1741 or 17.41% Prof. Q. Ma, HADM 2222 Fall 2009 2/2
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Chapter 5 E Energy Quick Quizzes 1. (c). The work done by the force is , where is the angle between the direction of the force and the direction of the displacement (positive xdirection). Thus, the work has its largest positive value in (c) where , the wo
UCSD - MATH - 11
Andrew Eskander Math 11L April 18, 2008 Lab 3 1. The equation of the regression line is BMR = 157 + 0.187 * Mass.Sca t t e r pl ot of BMRv sMa ss9000 8000 7000 6000 BMR 5000 4000 3000 2000 1000 0 0 10000 20000 Ma ss 30000 40000 500002. The regression l
UCSD - MATH - 11
Andrew Eskander Math Lab 11 June 6, 2008 Lab #8 1.Sca t t e r pl ot of HT9 v sHT2155 150 145 140 HT9 135 130 125 120808590 HT295100Re si dua l sVe r susHT2( r esponseisHT9) 105 Re sidua l05 10808590 HT295100The regression equation is HT
UCSD - MATH - 11
Andrew Eskander Michael Gustin English 1 28 October 2008 Week 1 Writing Assignment: Racism and the College Campus Provided the racism within college campuses, minorities struggle to perform academically, get involved socially, as well as utilize the resou
UCSD - MATH - 11
Andrew Eskander Math 11L April 18, 2008 Lab 3 1. The equation of the regression line is BMR = 157 + 0.187 * Mass.Sca t t e r pl ot of BMRv sMa ss9000 8000 7000 6000 BMR 5000 4000 3000 2000 1000 0 0 10000 20000 Ma ss 30000 40000 500002. The regression l
Punjab Engineering College - ENGR - 12H1
University of Florida - FIN - 4504
Topic3:TradingFIN4504 AaronGubinOverview Primaryvs.SecondaryMarkets PrivateCompanies IPOsvs.SEOs Trading SecuritiesMarketRegulationA.Gubin,FIN45042Primaryvs.SecondaryMarkets PrimaryMarket SecondaryMarketA.Gubin,FIN45043PrivateCompanies Financi