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, you will largely focus on the asset allocation and the asset selection decisions. Say, you are making your own investment decisions. How are your investments perform? Are 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 it's performance. It is simply it's holding period of time 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 our funds value is two $200 million at the beginning of the quarter, and its value is two $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 1 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 the part of increasing 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 1 plus r plus 220 million over 1 plus r the whole squared. Solving for r, we get a negative 4.64%. Remember, this is the return over half a quarter. Over one quarter, the return would be negative 4.64 x 2, which is negative 9.28%. So once we are just for in flows during the quarter the fund has actually earned negative returns. And alternate is to use time weighted returns to determine the funds performance. Here we calculate the funds performance based on the fund value just before every flow. Continuing with our 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 it's value was $170 million. Right, after the inflow of $40 million, it's value goes from $170 million to $210 million. The fund's performance from the beginning of the quarter to just before the inflow of $40 million is 170 million over 200 million minus 1 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 1, which is 4.76%. The time-weighted return is simply compounding these two returns. That is 1 minus 0.15 times 1 plus 0.0476 minus 1, which is negative 10.95% over a quarter. This is likely different from the dollar weighted average in return of negative 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 off a portfolio or fund. But is that we've done good or bad? In our example the time rated return is negative 10.95% a quarter. Is it a bad return or it is negative? Not necessarily because the rest of the market may have actually performed worse than this. So it's important to identify benchmarks that you can compare portfolio performance too. This is what we will look at next time.