portfolio investment 范例

Stuhut管理团队1 · 发表于 2018-3-5 16:35:11

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Calculation Questions Question 1 A pension fund manager isconsidering three mutual funds. The first is a stock fund, the second is along-term government and corporate bond fund, and the third is a T-bill moneymarket fund that yields a sure rate of 5.5%. The probability distributions ofthe risky funds are: file:///C:/Users/Administrator/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpgThe correlation between the fundreturns is .15. 1. Tabulate and draw the investment opportunity set of the two riskyfunds. Use investment proportions for the stock fund of 0% to 100% inincrements of 20%. What expected return and standard deviation does your graphshow for the minimum-variance portfolio? Parameters to Opportunity set = E(r Stock) = 15%, E(r Bonds)= 9%, SD (Stock)= 32%, SD(Bonds) =23%, Correlation= .15

	Bonds	Stocks
Bonds	529	110.4
Stocks	110.4	1024

The Minimum Variance:Wmin(Stock) = SD2(Bonds) – Covariance(Bonds, Stock) / SD2(Stock)+ SD2(Bond) – 2*(Covariance Bond, Stock) = 529 – 110.4 / 1024+529 – 2*(110.4)Wmin(Stock) =0.3142Therefore Wmin(Bonds) = 1-0.3142 =0.6858 The Minimum Variance Portfolio mean and StandardDeviation:E(r) minimum = 0.3142(15) + 0.6858(9) = 10.89%Standard Deviation = (W2 (Stock)*SD2(Stock)+W2 (Bond)*SD2(Bond)+2W(stock)*W(bond)Covariance (Stock, Bond))1/2 =(0.31422(1024)+0.68582(529) + 2(0.3142)(0.6858)(110.4))1/2 =19.94%

% in stocks	% in Bonds	Expected Return	Standard Deviation
0	100	9	23
20	80	10.2	20.37	Min Variance
31.42	68.58	10.89	19.94
40	60	11.4	20.18
60	40	12.6	22.5	Tangency Portfolio
70.75	29.25	13.25	24.57
80	20	13.8	26.68
100	0	15	32

file:///C:/Users/Administrator/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png 2. Draw a tangent from therisk-free rate to the opportunity set. What does your graph show for theexpected return and standard deviation of the optimal risky portfolio? E(r) SDMin Variance 11% 20%Tangency 13% 25%file:///C:/Users/Administrator/AppData/Local/Temp/msohtmlclip1/01/clip_image006.png3. What is the Sharpe ratio of thebest feasible CAL? Ws = (E(rs) - rf) *SD2b - (E (rb)– rf)* Cov*(rs, rb)/ (E(rs) – rf) + E(rb )- r ]* SD2s - [E(rs)- rf+E(rb ) rf ]*Cov(rs ,rf ) =(15-5.5)*529-(9-5.5)*110.4/(15-5.5)*529+ (9-5.5)*1024 – (15-5.5+9-5.5)*110.4 =4,639.1/7,143.3 =0.6494Wb =0.3506Mean and Standard Deviation of the optimal risky portfolio:E(rp) = 0.6494*(15) + 0.3506 *(9) = 12.90%SDp =(0.64942(1024)+0.35062(529) + 2*(0.6494)(0.3506)(110.4))1/2 = 24.39% Sharpe Ratio:=E(rp)- Rf / Standard Deviation Portfolio= 12.90-5.5/24.39=0.30344. Suppose now that your portfoliomust yield an expected return of 12% and be efficient, that is, on the bestfeasible CAL. a. What is the standard deviationof your portfolio?E (rc)= (rf+ E(rp) – rf/ Standard Deviation portfolio)*Standard Deviation = 5.5 + 0.3034 *SD12% =5.5 +0.3034 *SD SD=11.34%  b. What is the proportion invested in the T-billfund and each of the two risky funds? E(rc) = (l − y)* rf + yr * (rp) = rf + y* [E(rp)− rf] = 5.5 + y*(12.90-5.5) E(rc) =12% 12-5.5 = 12.90y - 5.5y6.5 =7.4yY =6.5/7.4Y =0.8784, and1-Y= 0.1216, the proportion of T-bill fund.Proportion Invested:In Stocks in a complete portfolio = 0.8784* 0.6494 =0.5704In Bonds in a complete portfolio = 0.8784 *0.3506 = 0.30805. If you were to use only the tworisky funds and still require an expected return of 12%, what would be theinvestment proportions of your portfolio? Compare its standard deviation tothat of the optimal portfolio in the previous problem. What do you conclude? 12 = 15ws +9*(1-ws)12 = 15ws + 9 –9ws12 =9 + 6wsws = 0.5 So the proportions are 50% invested in the stock fund and50% in the bond fund.The Standard Deviation of this portfolio is:=((0.52*1,024) + (0.52*529) + (2* 0.5* 0.5 * 110.4))1/2=21.06%