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Measuring the Performance of Accounts with Deposits and Withdrawals

In our example, the fixed rate equivalent equals 10.07%. This is not the place to discuss the calculation of the FREQ. However, once the value of the FREQ is known, it is easy to visualize and verify it. The green line in the chart below shows the account balance over time of a fixed rate account that pays 10.07% annually and receives the same deposits as the actual account of the example.

Figure 3

We see that the green line ends at the same point as the blue one, which is the actual account's balance over time. The 10.07% fixed rate replicates the performance of the account. Therefore, it is the FREQ.

Measuring perfomance the way the FREQ does, taking into account the effect of deposits and withdrawals, is also called money-weighted performance measurement.

The FREQ is a very real measure. For example, if your FREQ comes out as 0.7% for the last five years, then you can say, “Gosh, that high-yield savings account had an annual interest rate of more than 0.7% even in the worst of times. Had I put my money there, I would have more now.” If using the fixed rate account as a yardstick for measuring performance still does not seem natural to you, you may want to take a look at the appendix on annualization. It provides some additional motivation for the use of the FREQ.

It is perhaps noteworthy that the calculation of the FREQ requires a different kind of knowledge of the account data than the calculation of the time-weighted rate of return. For the time-weighted rate of return, one needs to know the beginning date and balance, the ending date and balance, the amounts of the cash flows, and the account balances on the dates of the cash flows. (The begin and end date are needed for annualization only.) For the FREQ, what's needed is the beginning date and balance, the ending date and balance, and the dates and amounts of the cash flows. The calculation of the FREQ does not, repeat not, require the account balances on the dates of the cash flows. That is fortunate because banks and brokerage houses do not usually provide the account balances on the dates of deposits and withdrawals to an individual investor on their account statements or websites.

## Summary

The table on the following page summarizes the differences between the two ways of measuring the performance of accounts with deposits and withdrawals, depending on whether the measurement occurs in the context of a mutual fund or of an individual investor's account.