Learning outcomes. After watching this video, you will be able to explain the importance of performance evaluation, describe the problem with using holding period returns to evaluate performance, calculate dollar and time-weighted returns and discuss which is better. Measuring portfolio or fund returns, until now, we have largely focused on the asset allocation and asset selection decisions. Say, you are making your own investment decisions. How have your investments performed? Are you doing a good job of identifying profitable investment opportunities or do you need to change your methods? Alternatively, you may have invested your wealth in a mutual or pension fund. From time to time, you would like to know how the fund manager has performed. Should your wealth continue to be invested in the same fund, or should you move your money to another fund? Even if the portfolio has performed well, the big question is if it has resulted from skill, or sheer good luck. This is why performance evaluation is an important step in the entire investment process. However, there are two basic problems with performance analysis. One, we need to obtain many observations to achieve significant results. Two, shifting portfolio parameters like risk, covariance, etc, and style could make evaluation quite difficult. So we need to be very careful with how we measure portfolio performance. If the fund or portfolio doesn't have any new inflows or outflows, then it is easy to calculate its performance. It is simply it's holding period return, which we have seen earlier. But in reality, investors are constantly investing and withdrawing money from the fund. This makes it really difficult to measure its performance. Let's look at an example to illustrate this. Say a fund's value is $200 million at the beginning of the quarter, and its value is $220 million at the end of the quarter. A simple holding period return calculation would estimate it's return to be 220 million over 200 million minus one, which is 10%. But, this ignores any fund flows during the quarter. For simplicity, let's say that the fund received inflow of $40 million at the middle of the quarter. So it appears that a part of the increase in the fund value can be attributed to this inflow of $40 million. How do we now assess the fund's performance? It appears that 10% may overstate its true performance. One way to address this issue is to use dollar-weighted returns or more generally, currency-weighted returns. Let's assume that every half a quarter is one period, and r denotes the dollar-weighted return over this period. Then we have $200 million equals negative $40 million over one plus r, plus $220 million over one plus r, the whole square. Solving for our R, we get a -4.64%. Remember, this is the return over half a quarter. Over one quarter the return would be -4.64 x 2, which is -9.28%. So once we add this for inflows during the quarter, the fund has actually earned negative returns. An alternate is to use time-weighted returns to determine the fund's performance. Here we calculate the fund's performance based on the fund value just before every flow. Continuing with that example, we need to know what the fund value was at the middle of the quarter just before it received an inflow of $40 million. Let's say that its value was $170 million. Right after the inflow of $40 million, its value goes from $170 million to $210 million. The funds performance from the beginning of the quarter to just before the inflow of $40 million is $170 million over $200 million minus one, which is negative 15%. It's performance from just after the inflow until the end of the quarter is $220 million over $210 million minus one, which is 4.76%. The time-weighted return is simply compounding these two returns, that is one minus 0.15 times one plus 0.0476 minus one, which is -10.95% over the quarter. This is slightly different from the dollar rated average return of -9.28% over a quarter that we calculated earlier. Dollar-weighted returns are usually influenced by the timing as well as the size of cash flows, whereas this is not the case for time-weighted returns. Hence, time-weighted return is generally preferred over dollar-weighted return. We have understood how to calculate the returns of a portfolio or fund, but is that return good or bad. In our example, the time-weighted return is negative 10.95% a quarter. Is it a bad return as it is negative? Not necessarily, because the rest of the market may have actually performed worse than this, so it is important to identify benchmarks that we can compare our portfolio's performance to. This is what we will look at next time.