Mutual funds and rate of returns

11May10

One finds many mutual funds quoting 3 year returns and 5 year returns which are very respectable and in excess of 20% at times. However there is an important consideration behind how these returns are calculated.

There are two ways of calculating returns. Time weighted and Dollar weighted (Or Rupee weighted).

Let the following scenario play out in 2 years:

Period 1 ( 1 year):

No. of unitholders in the fund: 20

Beginning Stock Price: 100 Rs

Ending Stock Price: 120 Rs

Returns: (120-100)/100= 20%

Period 2 (1 year):

No. of unitholders in the fund: 100

Beginning stock price: 120

Ending stock price: 105

Returns: (105-120)/120 = -12.5%

The mutual funds use Time weighted rate of return calculation. So, lets see how the mutual fund returns are calculated now:

Annualized Rate of Return = [(1+20%)*(1-12.5%)]^0.5 = (1.2*0.875)^0.5 = 1.025 -> 2.5%

So the average rate of return in the mutual fund is 2.5% which is advertised in the newspapers. If a person had invested 100Rs at the beginning of period 1 he would have received 100(1+2.5%)^2 at the end of 2 years.

But this is not the same as the rupee weighted rate of return (which is simply the IRR) which is calculated as follows (assuming fund is liquidated at end of 2 years):

Investments: 20*100 = 2000 Rs in beginning of period 1 and 80*120 = 9600 Rs in beginning of period 2 (where 80 is the increase in number of shareholders) and 105*100 = 10500 Rs is the end of period 2 cash flow.

IRR is calculated by solving the following: -2000-9,600/(1+IRR)+10,500(1+IRR)^2 = 0

This works out an IRR of -8%. The reason the latter is -8% whereas the former is +2.5% is that in the latter case, the rupees invested were much higher and since the MF performed badly in that year, the weighted rate of return in terms of cash flows is lower. The time weighted method does not consider the entry and exit of cash flows.

Time weighted rate of return is the better method to use when the cash flows are not controlled by the investor i.e. the investor (in this case, the fund manager) does not decide when cash enters and when it flows out. But when the investor does control the cash flows (like a personal investor like me who decides by myself when I should invest and when I should exit from a stock), rupee weighted rate of return is a better measure.

Logically the Time weighted method is a better performance indicator than the Rupee weighted for mutual funds because “the fund manager does not control the entry and exit of cash flows into their funds” .

However in this day and age when each MF company employs hundreds of marketing professionals and uses a lot of advertisements to attract funds, raise money, launch new NFOs, they do in a way “influence” the flow of money to their funds if not directly “control”. This is critical because in every bubble, the maximum money is attracted just before the bubble bursts. I do not have a link to show proof for this but it is obvious that when the sensex touched 21,000 no one predicted it to go to 8000. When it was at 21,000 every MF fund manager came on TV and shouted buy buy buy whereas when it was at 8000, all you hear is sell, dont come to the market etc. Mutual funds and the Investment Management industry (which includes the great research analysts) do play an important role in influencing entry and exit of money to fund houses. How many fund managers announced when the sensex started the downward journey to “not withdraw money now and hence realize the unrealized losses”?

It should be noted that many MFs in the dot com boom period had a time weighted return of close to 0% whereas a dollar weighted return of close to -10%. They attracted maximum capital a year before the bubble burst and invested maximum money then in all firms ending with a .com i.e. in other words they were dumbest when they had to be smartest.

Though Time weighted method is definitely the superior method for fund managers, one must remember this distinction while looking at MF performances. This is especially true of MFs which go behind the latest fad (which is almost all of them!).

Note 1: This does not pass on the blame from private investors who, in the hope of doubling money in 1 year, invest when the market is at the top or try timing the money correctly.

Note 2: PE firms do not use time weighted rate of return ideologically since they decide when to call for cash from their investors and hence control the cash flow directly.

Note 3: I learnt this important distinction from Ashish Dhawan, Chrys Cap MD, in one of his guest lectures.


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