Question

Question 2 An investor has a certain amount of money available to invest now. Two alternative portfolio selections are available. The estimated profits of each portfolio under each economic conditions are indicated in the following pay-off table: Event Portfolio Selection Portfolio Selection Economy declines +$1000 -$2000 No change +$ 1500 +$2000 Economy expands +$3000 +$5000 Based upon his own past experience the investor assigns the following probability to each condition: P (Economy declines) = 0.20 P (No change) 0.70 P (Economy expands) 0.10 Determine the best portfolio selection for the investor according to the (i) (ii) expected return on each portfolio. Standard deviation of the returns on each portfolio.

Answer 1

Solution: . Part (7) Given Information Event Economy Declines No change Economy Expands Portfolio selection Portfolio Selection 'B' A + $ 1000 + $ 1500 ! - $ 2000 + $ 2000 i.+ $ 5000 . 000 P ( Economy Declines) = 0.20 p (No change) . P ( Economy Expands) - 0.10 Part (1): Expected Return on each portfolio A & B: The Expected return of a portfolio is -obtained by multiplying each asset's weight in the portfolio by it's expected return, then: adding all those fiqures together. :: Expected return of portfolio A is ERA = $ 1000 x 0.20 + $ 1500 x0.70+ $3000X 0.0 = $ 200 + $1050 + $ 300 TERA - $ 1550

Expected Return of portfolio Bis ERB : - $ 2000 ¥0-20 + $ 2000 x0.70 + $ 5000X010 - $ 400 + $ 1400 + $ 500 ERB = $ 1500 $1550 Answer:. • Expected return on Portfolio 'A' is and on portfolio 'B' is $ 1500. • since E RA > E-RB • Therefore portfolio A is better. Part (11): Standard deviation of portfolio A isi Expected return(x); $. 1550 (as per. Part ()). Standard deviatrone) } P(x; -7) = 0.2(1000 - 1550) + 0.7 (1500 - 1550) 2 +0.1(3000 - 1550 - 50-(-550)7 0.7(-50)*+ 0.1(1450)2 - 10.2 x 3,0 2,500 +0.7x2500 + 0.1 x 21,02,500 - 560,500 + 1750 +210250 i SDA-1272500: SDA - 522.0153

of portfolio B 15: Expected Return (X)B- andard deviation of return of portfolio cted Return (7), = $ 1500 (as per part (1)) Standard deviation (0)Ë P (X; - x)? - 10.21-2000-1500)?+ 0.7 (2000-1500)+ 0.1(5000-1500) - 10.2(-3500)?+0.7 (500)+0.1(3500) = 10.2 x 122,50,000+0.7 x ,50,000+ 0.1 x 129,50,000 = 124,50,000+ 1,75,000 + 19,25,000 = 38,50,000 S.Dg : 1962.149 Answer: • The Standard deviation of return of portfolio A (CA) is 522.0153 and Standard deviation of return of Portfolio B (OB) is 1962,142. • since og >OA :,: Portfolio A is Better