Calculating Returns in a Portfolio
One would think that determining the return in a portfolio would be simple: divide the change in value by the beginning value. In the most simple of 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 measured. 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.
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)Â – 1 = 10.7% (which is slightly off from the 10.8% in the exhibit due to rounding).
For more information, see all articles on: Active Management, Investment Returns, Passive Management, Portfolio Management, Valuation See also:
The Intelligent Investor: The Classic Text on Value Investing
Financial Statement Analysis: A Practitioner's Guide, 3rd Edition
Managing Investment Portfolios: A Dynamic Process (CFA Institute Investment Series)
[...] Time weighted rate of return measures the compound rate of return over a given period for one unit of money. Money-weighted rate of return, by contrast, measures the compound growth rate in the value of all funds invested in the account over the evaluation period. [...]
February 6th, 2008 at 7:19 am
[...] requires portfolio returns to be calculated using time-weighted total return, adjusted for external cash flows. Portfolios must be valued for return calculations at least [...]
February 9th, 2008 at 7:32 am
[...] Time weighted rate of return measures the compound rate of return over a given period for one unit of money. Money-weighted rate of return, by contrast, measures the compound growth rate in the value of all funds invested in the account over the evaluation period. [...]
March 6th, 2008 at 7:28 am