Monday, May 13, 2013

Calculating Returns in a Portfolio

One would assume that determining the return in a portfolio would be simple and easy: Just divide the change in value by the beginning value. In the most simple of the cases, this can be true. But external cash flows (cash flows in and out of a portfolio, rather than those generated by the investments themselves) can make things more difficult.

Whenever there is an external cash flow such as a deposit to or withdrawal from the portfolio, the return should be calculated. Then, each period between cash flows (or ending at specified dates such as year-end) can be linked together in a process called chain-linking. This process is used to determine the time weighted rate of return (TWR).

Consider the following exhibit, which shows the change in portfolio value before and after cash flows.

Calculate Returns of a Portfolio


The portfolio starts the year at $100,000 and ends at $118,000 – so its return is 18%, right? Not so fast! All during the year (for simplicity it is assumed to be on the last day of the month after the ending value is calculated) there are deposits and withdrawals. The 118,000 reflects not only the investment return, but these external cash flows as well.

The proper way to calculate return in this case is to take the change in value from the beginning to the end of each month (before the cash flow). So, in the first month the return is (110,000 – 100,000)/100,000 = 10%.

Next, the cash flow is added or subtracted from the ending value to arrive at the following month’s beginning value, and that month’s return is calculated the same way.
Returns can be linked geometrically. To do this, 1 is added to each return and they are multiplied together. At the end, 1 is subtracted from the final product. So the linked return for the three months ending in March are (1.10 X 1.043 X 0.965)  – 1 = 10.7% (which is slightly off from the 10.8% in the exhibit due to rounding).