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Suppose a portfolio manager wishes to construct a portfolio using two securities Coll and USR. Specifically,...

Suppose a portfolio manager wishes to construct a portfolio using two securities Coll and USR. Specifically, the manger allocates $60,000 in the Coll and $30,000 in the USR. Please calculate (1) Portfolio Expected Return (2) Portfolio Standard Deviation

Economy

Prob.

T-Bills

HT

Coll

USR

MP

Recession

0.1

5.5%

-27.0%

27.0%

6.0%

-17.0%

Below avg

0.2

5.5%

-7.0%

13.0%

-14.0%

-3.0%

Average

0.4

5.5%

15.0%

0.0%

3.0%

10.0%

Above avg

0.2

5.5%

30.0%

-11.0%

41.0%

25.0%

Boom

0.1

5.5%

45.0%

-21.0%

26.0%

38.0%
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Answer #1

A1 Rate of Return if the state occurs Probability Coll State Recession Below Average Average Above Average USR 0.1 0.2 0.4 0.2 27% 13% 6% 1496 3% 41% 26% 11% 21% Calculation of Expected Return for each S Expected return is given by following formula tock: 10 12 13 Expected returm?-P 15 16 17 Expected return of Coll -Sum of product of probability and return in each state 1.00%-SUMPRODUCT(D4:D8,E4:E8) 19 Hence expected return of Coll is 1.00% Simillarly, Expected return of USR 21 9.80% 23 24 25 Coll USR Expected Return 1.00% 9.80% 27 Variance and standard deviation of stocks can be calculated as follows: Variance and standard deviation of stocks can be calculated from following formula 31 32 Variance (Var)-> p,0,-r) 35 36 37 38 39 2 Standard Deviation (σ)-D p,(y-r) Variance of Roll -Sum of product of probability and square of excces return in each state 1.74% =SUMPRODUCT(D4:D8,(E4:E8-D26)^2) 41 42 43 Standard Deviation of Roll is Sqrt (Variance of Stock A) 13.19% SQRT(D40) Simillarly Variance and Standard deviation of USR can be Calculated 47 ROLL USR 49 50 51 52 Expected Return Variance Standard Deviation 1.00% 1.74% 13.19% 9.80% 3.54% 18.82%Calculation of expected return and standard deviation of ROLL and UBS.

A1 53 54 Portfolio return can be calculated as follows: Expected portolioreturn, rp - W 57 59 Where w, and r are the weights and return of assets A Weight and returns of the stocks of the portfolio1 is as follows: 61 62 63 ROLL USR Expected Return Weights 1.00% 9.80% 66.67% 33.33% Hence Portfolio return is calculated as follows: Portfolio expected return 3.93% SUMPRODUCT(D64:E64,D63:E63) Hence Portfolio expected return is 3.93% 70 71 72 73 74 To calculate the portfolio variance and standard deviation covariance matrix is needed Co-variance between A and B can be calculated as follows: 76 Cov(A,B) 1.75%-SUMPRODUCT($DS4:SD$8,SES4:SES8-SD$26,F4:FB-E$26) 81 82 83 84 Portfolio variance is given by following formula Portfolio variance-w,ơ(%) + w,o(%) + 2(%)* (wo)Coy(A, B) where WA and we are weights of assets A and B, σΑ and Og are standard deviation of assets A and B. Given the following data: ROLL USR Expected Return Variance Standard Deviation Weight 1.00% 1.74% 13.19% 66.67% 9.80% 3.54% 18.82% 33.33% 87 91 92 93 Portfolio Variance 0.39% D90*D89)2t(E90*E89)2+2D90*E90*D80 95 Standard Deviation of Portfolio Sqrt(Var) 6.24% :SQRT(D93) 97 Hence Expected return of the portfolio Variance of Portfolio Standard Deviation of Portfolio 3.93% 0.39% 6.24% 100 101 102 Calculation of portfolio return and standard deviation.

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