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Measuring the Performance of Accounts with Deposits and Withdrawals

The way to make those returns for different time periods comparable is through annualization. The idea is to replace the return with an equivalent annual fixed interest rate. For example, regarding the full five year period, imagine that those $10,000 had been placed in a savings account with a constant annual interest rate. Then we can ask, “What annual interest rate does that savings account have to have so that it ends up with the same $13,502.52 ending balance as the real account?” That rate is the annual rate of return, or annualized return for short, of the account for the five year period.

In our example, for the 35.0252% return over a five year period, the annualized return is 6.19%. For the 21.48% return over a two year period, the annualized return is 10.22%. These numbers are now comparable: over the two year period 2005 and 2006, the portfolio created return like a 10.22% savings account, while for the entire five year period, it created return like a 6.19% savings account. If you are mathematically inclined, you can read more about annualization and how it is calculated here.

Comparing the concept of annualization to the definition of the FREQ, we see that both employ the fixed rate account as a yardstick for measuring performance, with the annual interest rate being the scale on the yardstick. In particular, if you calculate a FREQ for a time period where there are no deposits or withdrawals, then the FREQ equals the ordinary annualized return. This connection provides additional evidence that the FREQ is an appropriate measure of performance for accounts with deposits and withdrawals.