Quote:
The Holding period return in year one is ($89 - $100+ $1) / $100 = -10.00%
The holding period return in year two is ($98 - $89 +$1) / $89 = 11.24%
the time weighted return is [{1+ (-0.1000)}{1+.1124}]^1/2 = .06%
The second calculation seems inappropriate for two reasons.
First, you calculate the hpr as though you held only a single stock where in fact you got a porftolio of 4 stocks over the second period. As a result the amounts invested over specific periods are very different.
Secondly, you left out the dividends which are assumed to be reinvested over the second period so in the second calculation you should divide by $90 ($89 plus $1 dividend) instead of $89. The amount invested over the second period is $90 (assuming you got only one stock).
My alternative solution is the following.
Unforunately, the problem is not formulated precisely and the solution is not so straigthforward as it seems. The thing concerns the exact time of dividend payments. The solution provided above is based on the assumption that at the end of year one the investor bought 3 additional shares AFTER she received the dividend on the single stock she had owned, which is not necesarily true.
Following strictly the problem the investor buys first three additional shares (that is BEFORE the dividend payment) so that at the time of dividend payments she has four (not one) stocks in her portfolio. Therefore the total dividend payment is $4 instead of $1.
Those dividend payments diminish your loss at the end of year one so that your HPR for year one is 0.93 instead of 0.90.
And the HPR for year two is:
1. Market Value (MV) of the portfolio at year 1 (after the stock purchase and the dividend payment)
4*89 + 4*1 = 360
Notice that over the second period you invest an amout of cash four times bigger than that over the first period.
2. MV at year 2
4*98 + 4*1 = 396
HPR = (396/360) - 1 = 0.10
Total return: (0.93*1.10)^(1/2) = 1.01143; (1.14% per year)
Please correct me if I am wrong.