I’m done the first book (ethics and quant) and have spent the last week practicing it. Statistics was my killer during the undergrad, much more than anything else on level 1, so I’m really trying to get that stuff down. Monday I’m moving on to econ which I majored in so hopefully I can get through it in a week or less and be right on schedule. (so I’m done 3 study sessions)
I “started” on July 1st, but it wasn’t until probably 2 weeks ago that I started to actually get on it on a regular basis. I’m not too worried, but I’m thinking there’s no more time to slack off anymore either.
The way that I think about it is that time weighted return is an extension of money weighted return (i.e. IRR). Essentially, I break it down into the following steps:
STEP1: calculate year over year IRR
Year 0 to Year 1 IRR = x
Year 1 to Year 2 IRR = y
Step 2: calculate time weighted return
(1+time weighted return) ^ total time = (1+x)(1+y)
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.
You are absolutely wrong in assuming dividends and solving the question.
There is a very big difference btw MWR and TWR and that is TWR (Time Weighted Return) is not affected by the timings of the cash flows (Whereas MWR is affected by timings.) So assuming dividends received before or after new purchases etc etc in TWR is totally irrelevant.
Second: solving second year return is totally ok either you assume that you have 4 shares with four dividends or 1 share with 1 dividend (because higher or lower cashflows don’t affect the TWR & your investment is related with same stock).