The stock of Business Adventures sells for $50 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 $3.00 $60
Normal economy 1.20 58
Recession .75 49
Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely.

Solution :

Holding Period return is given by :

Holding period return

Now the holding the period return for the various cases :

Boom

Ending stock price = $ 60

Beginning stock price = $ 50

Dividend income = $ 3

Hence, holding period return is

                                                      = 0.26

So, the holding period return = 26%

Normal economy

Ending stock price = $ 58

Beginning stock price = $ 50

Dividend income = $ 1.2

Hence the holding period return

                                                      = 0.184

So, the holding period return = 18.4%

Recession

Ending stock price = $ 49

Beginning stock price = $ 50

Dividend income = $ 0.75

Hence the holding period return

                                                      = -0.005

So, the holding period return = -0.5%

As all the cases, the probability is same = 0.333

Therefore, the expected holding period return is :

The expected holding period return = (0.333 x 0.26) + (0.333 x 0.184) + (0.333 x -0.005)

                                                           = 0.8658 + 0.06127 - 0.00166

                                                           = 0.149515

Therefore, the expected holding period return = 14.95%

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