The stock of Business Adventures sells for $40 a share. Its likely dividend payo

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:

  

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

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%.

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

Explanation / Answer

a.

Holding-period return = (Income received from Investment + Ending Value - Beginning Value) / Beginning Value

Standard deviation of holding-period return -

Mean of Xi = [0.5 + 0.2 + (0.275)] / 3 = 0.14167

Mean of (Xi - Mean)2 = [0.1284 + 0.0034 + 0.01778] / 3 = 0.04986

Standard deviation = 0.04986 = 0.22329

b.

Expected Return of portfolio invested half in Business Adventures and half in Treasury bills

                Therefore, E(R) = w1R1 + w2R2 + w3R3 + .... + wnRn

                                       = (0.5) * (0.5) + (0.5) * (0.2) + (0.5) * (-0.275) + (0.5) * (0.04)

                                       = 0.2325

Variance = (0.5) (0.5 - 0.25)2 + (0.5) (0.2 - 0.1)2 + (0.5) (-0.275 - 0.1375)2 + (0.5) (0.04 - 0.02)2

                  = 0.03125 + 0.005 + 0.08508 + 0.0002

              = 0.12153

Standard deviation = 0.12153 = 0.3486

Beginning Value Ending Value Income Received HPR Boom $40 $52 $8 0.5 Normal economy $40 $44 $4 0.2 Recession $40 $34.5 ($5.5) (0.275)

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