Question

State of Nature	Probability	Investment A Return	Investment B Return
I	0.25	6%	15%
II	0.4	9%	12%
III	0.35	5%	-3%

Given the above information on two investments A and B, calculate the statistics below. The correlation coefficient between A and B is 0.6472. Note that since the correlation is given, you

do not have to do the long calculation for covariance, just use the shortcut

s AB

= r ABs As B .

1. Expected Return for Investment A

6.85%

1. Standard Deviation for Investment A

1.80%

1. Expected Return for Investment B

7.50%

4. Standard Deviation for Investment B

7.79%

5. The covariance between A and B

6. The expected return for a portfolio consisting of 60% A and 40% B

7. The standard deviation of a portfolio consisting of 60% A and 40% B.

Answer 1

ANSWER A of Expected Retwin = { returns x probability = (6 x 0.25] + [9 x 0.40] + (5 x 0.35] Investment A - 1.5 + 3.6 + 1.75 = 6.85 %. ie. 6.85% Returns Retwens - AR (Retan - €8) prob (Relwn-ER] x arab -0.85 2.15 - 1.85 0.7225 0.25 0.180625 4.6225 0.40 1.849 3.4225 0.35 1.197875 VARIANCE = 3.2275 {n} Std. Deviation - 1.7965% ie. JUARIANCE

Ç Expected Return = of = Investment B = E Returns x probability (15 x 0.25 + [12 x 0.40) + (-3 x 0.35 3.75 + 4.8 + (-1.05) 7.5 % e 7.5% Retuans Rotwens med (Retan - Ge] prob (Retin-eĚx prab 15 7.5 0.25 12 4.5 -10.5 56.25 20.25 10.25 14.0625 0.40 8.1 0.35 38.5875 VARIANCE = 60.75 Deviation = 7.7942%. ie. JUARIANCE 트 COVARIANCE R = Co-relation as X TA x re - 0.6472 x 1.7965 7.7942 - 9.0623 E ER of Portfolio - (Era x Weight ) + (ER x Weight) = (6.85 x 0.6 ) + (1.5 x 0.4) = 4.11 + 3 = 7.11 %