The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows:

Dividend Stock price
Boom $2.00 $50
Normal economy $1.00 $43
Recession $0.50 $34

a) Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely.

b) Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%.

Explanation:

a. Calculate the expected holding-period return and standard deviation of the holding- period return. All three scenarios are equally likely.

1/3 = 0.3333

Boom Holding Period Return - HPR

HPR =  = (50 – 40 + 2)/40 = 0.3

Normal HPR=(43 – 40 + 1)/40 = 0.1

Recession HPR = (34 – 40 + 0.5)/40 = -0.1375

Expected Return =(0.3333*0.3)+(0.3333*0.1)+(0.3333*-0.1375)=0.1+0.0333-0.0458 = 0.0875

Var(r) = sd^2 = sum of  p(s)[r(s)-E(r)]^2

Var(r) = (0.3333)[(0.3)-0.0875]^2 + (0.3333)[(0.1)-0.0875]^2  + (0.3333) +[-.1375-.0875]^2 =

Var(r)= 0.0151+ 0.0001 + 0.0169 = .0321

Sd(r)= sd square root = square root of 0.0321 = 0.1791

b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%.

Expected return = (0.5)(0.0875) + (0.5)(0.04) = 0.0438 + 0.02 = 0.0638

Sd = (0.5)(0.1791) = 0.0896

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