Question

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 $2.80 $48 Normal Economy 1.80 43 Recession .90 34 a) calculate the expected holding-period return and standard deviation of the holding period return. all three scenarios are equally likely. (Do not round up intermediate calculations. round your answers to 2 decimal places.) Expected return .... standard deviation ... 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 5%. (do not round up intermediate calculations. round your answers to 2 decimal places.) Expected return .... standard deviation ...

Answer 1

Answer:

Explanation:

(a) HPR = Ending Price - Beginning Price + Cash Dividend / Beginning Price

a. The holding period returns for the three scenarios are:

Boom: (48 - 40 + 2.8)/40 = 0.27 = 27%

Normal: (43 - 40 + 1.8)/40 = 0.120 = 12.0%

Recession: (34 - 40 + .90)/40 = -0.1275 = -12.75%

= [(1/3) × 0.27] + [(1/3) × 0.120] + [(1/3) × (-0.1275) =0.08750 or 9%

Variance = [(1/3) × (0.27 - 0.08750)^2] + [(1/3) × (0.120 - 0.08750)^2] + [(1/3) × (-0.1275 - 0.08750)^2] = .026863

Std. Dev = Sq. Rt .026863 = .16390 = 16.39%

(b) E(r) = (0.5 × 8.75%) + (0.5 × 5%) = 6.88%

σ = 0.5 × 16.39% = 8.19%

Thanks