# Problem 11-10: Calculate expected return and standard deviation of portfolio

Consider the information on the attached spreadsheet.

a. Your portfolio is invested 35% each in A and C, and 30% in B. What is the expected return of the portfolio?

b. What is the variance of this portfolio? The standard deviation?

Problem 11-10

Rate of Return, if State Occurs

Probability of

State of Economy State of Economy Stock A Stock B Stock C

Boom 0.3 0.3 0.45 0.33

Good 0.4 0.12 0.1 0.15

Poor 0.2 0.01 -0.15 -0.05

Bust 0.1 -0.2 -0.3 -0.09

#### Solution Preview

... = 0.115

E(RC) = (0.3)*(0.33) + (0.4)*(0.15) + (0.2)*(-0.05) + (0.1)*(-0.09)

= 0.099 + 0.06 - 0.01 - 0.009

= 0.14

Step 2

Combine the three expected returns according to their weights to get the expected return on the portfolio.

n

E(P) =  WiE(Ri) where W = weight

i = 1

= (0.35)*E(RA) + (0.3)*E(RB) + (0.35)*E(RC)

= (0.35)*(0.12) + (0.3)*(0.115) + (0.35)*(0.14)

= 0.042 + 0.0345 + 0.049

= 0.1255 (ANS)

Step 3

Find the variance and standard deviation for each stock

n

2 =  (ki - k)2Pi where k = expected return

...