Question

can someone help me do this without using excel?

3. (30 points) - Rate of returns for A and B companies in different states of nature are provided in the following table: State of nature Probability Rate of return on A's share (% Rate of return on B's share (%) 10 Weak Average Strong Very strong 0.3 0.5 0.1 0.1 a. Find the expected retum on companies Gamma and Theta shares. b. Calculate the standard deviation of retum for both shares. c. If an investor invests 80% in Gamma share and 20% in Theta share, find the expected retum and the standard deviation of return on this portfolio.

Answer 1

Date: Page no A Companies dac: x-1C Prox² Eralentility (P) Return (in %) (x) 3 - 4 10 - 10.9 3.1 7.1 10.1 35.643 4.805 5.041 10.201 17 "Expected Return (5C) = 6.97. Variance (E Pd xe?) = 55.69 (-3x(-4) +•5x10•1X14 +:X17) (EPx9c) 6 Standard - Variance = √55.69 = 7.46% Deinatian

B Campanies 4.7 . dy=y- Pdy? ce Return (im) (4) a - 2 .7 2.187 - .7 7 2.3 .245 .529 8.649 14 9.3 Variance (EPd x°) - 11.61 aj Expected Return (1) = 4.7%. (.3x2 + 5x4 t. 71 x 7+ • 1x14) - CEP x 2 b) Standard – Denialian Variance = 11.61 = 3.41%

Now Calculation of Returns Conariance between A and B dy Px dx xdy Eralentility dx (P) O -10.9 - 2.7 .3 .5 L - .7 3.1 7.1 10.) 8.829 - 1.085 1.633 9.393 2.3 9.3 Cauariance (Elxdxxdy) - 18.77

c) Crinen Weight of stock I Weight of Stock Af A Campanie (WA) = 80 (80%) of B Campanie (WB) = 20 (20%) Expected Return - Expected Return & WA + Expected Return x WB of fortfalia of a companie of B Companie - 7 4.7.7.X.2 6.94 x 8 6.46 %.

Standard - Deviation Standard Deciatian X WA)+/ Standard Deristian x WB] of a companie I cof B Companie 1 + 2x Couariance between x WA X WB Stock's -|(7:46x:8)+(3.41x.2) + 2x18.77 x.8x:2 وہا.

A Campanie B Campanie (Theta) (Gamma) 4.7% a) Expected Return b) Standard Deviation 6.90% 7.46% 3.41%. Portfalia expected Return Standard Deuiatians 6.467. 6.49%