Measuring “Skill” and Earning “Return”.

As an investor, this one is going to be a tough call. You want to invest Rs 10,000 today in a mutual fund. Where should you invest? Should you invest in the fund that has given investors a higher return? Or should you invest in the fund which has a better fund manager? You might ask “Is it not that the fund which has performed better have the better manager?” Well, the answer surprisingly is “No.”

To understand that you must get to know two more “rates of return”. Let me explain them with an example

Scene 1: Mr. X, Mr. Y and Mr. Z are the chief investment officers (CIO) of three funds namely Fund X, Fund Y and Fund Z respectively. Each of these funds began on 1st Jan 2006 with a portfolio of Rs 100 crore. A year later the value of their portfolio fell by 50%. That is, on 1st Jan 2007 it stood at Rs 50 crore. This means that the performance of all three CIOs in the first year has been identical. Now suppose in the second year the portfolio appreciated by 100%. That is, on 1st Jan 2008 it stood at Rs 100 crore. This means that the performance of all three CIOs the second year has been identical. Hence, across two years, all three of them have performed alike.

Scene 2: Let’s tweak the scene a bit. Suppose at the end of year 1 when the market had fallen, investors of Fund X thought that this was the right time to invest further and that they poured an additional Rs 50 crore into Fund X. So on 1st Jan 2007 the Fund holds the initial Rs 50 crore plus the additional Rs 50 crore, adding to Rs 100 crore. This Rs 100 crore doubles in the second year to touch Rs 200 crore. In essence a total investment of Rs 150 crore has grown to Rs 200 crore generating a positive IRR.

Now turn to Fund Y. Suppose at the end of year 1 the investors of Fund Y decided to adopt a wait and watch attitude. Hence they decided to keep off the market. So on 1st Jan 2007 the Fund holds the initial Rs 50 crore only. This doubles in value in the second year to touch Rs 100 crore. In essence, across two years, a total investment of Rs 100 crore has stagnated at Rs 100 crore giving a zero IRR

Finally, let’s look at Fund Z. Suppose at the end of Year 1 the investors of Fund Z felt that it was time to partially exit the market and hence withdrew Rs 25 crore. So on 1st Jan 2007, the fund whose value had like others depleted to Rs 50 crore paid Rs 25 crore and has Rs 25 crore only for investment. This Rs 25 crore doubles in value in the second year to touch Rs 50 crore. In essence a total investment of Rs 75 crore has fallen to Rs 50 crore generating a negative IRR.

The bottom line: Fund X has given the best return, Fund Y the second best return and Fund Z the least return. This however does not mean that CIO Mr. X is more skilled than CIO Mr. Y and that CIO Mr. Y is more skilled than CIO Mr. Z. Remember the performance of the three CIOs is identical because in the first year their value went down by 50% and in the second year it rose by 100%.

Yet their IRRs are different; the first was positive, the second zero and the third turned out to be negative. This had to do with the intervening inflows and outflows of cash. Additional moneys came to Fund X at the right time and additional moneys went out of Fund Z at the wrong time affecting the overall return. The moral: Fund returns are a function of fund manager’s skills and the time when investors pour money.

So what does this mean?

This brings us to a crucial point. That we must make a distinction between the skills of the manager and the returns earned. The return relevant to measure skill is called time-weighted rate of return. In this case we ignore the intervening inflows and outflows of cash. We merely look at how Rs 1 has progressed over a period of time. In our example, in the case of each of the funds, the Rs 1 invested in time zero became Rs 0.50 in time 1 and ended as Rs 1 at end of second year, leading to nil over-all return.

The return relevant to measuring returns earned is called rupee-weighted rate of return. It considers the intervening inflows and outflows of cash and is the same as IRR. This in our example was highest in the case of X, second highest in the case of Y and least in the case of Z