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Measuring the Performance of Accounts with Deposits and Withdrawals

The Individual Investor's Point of View

Now let us go back to the point of view where the account is your personal brokerage account, and the two investments of $5,000 each are both yours (see Figure 2). The time-weighted rate of return as described in the previous section is not entirely irrelevant to you. For example, if you wanted to compare your stock-picking skills to that of the manager of a particular mutual fund, then—perhaps among other things—you'd have to compare your TWR to that of the mutual fund.

Also, remember that first and foremost, the TWR is the return on the initial investment, that is, the first $5,000 that you started with. That particular sum of money may be special to you. Perhaps it was an inheritance, or the proceeds of exercising stock options. You may want to know what became of those particular $5,000 in your account. We have heard behavioral psychologists advise both for and against such an attitude, where different parts of one's money are considered separately depending on when and how they were obtained.

Be that is it may, the important point is that these things must be considered "musings" on your money rather than performance measurement. As far as dollars and cents are concerned, you turned $10,000 into $15,417.89. The time-weighted return of 35.0252% does not capture that. As a matter of fact, it was specifically engineered not to capture it: the whole point of the calculation was to remove any trace of the second $5,000.

The Absolute Net Performance (ANP)

A simple (some would say primitive), yet somewhat useful attempt at measuring the performance of your account in the presence of deposits and withdrawals is the absolute net performance, or ANP for short. For the ANP, you start with your beginning balance, then add to that the sum total of all deposits, then subtract from that the sum total of all withdrawals. The result is the amount of money that you would have had you kept your money under the mattress. It is your mattress equivalent. The ANP is the difference between the ending balance of your account and the mattress equivalent. It is the absolute amount of money that you made or lost in your account. In our example, the ANP equals $5,417.89.

Simple as it is, the ANP has its uses in a person's financial planning. Suppose, for example, that you are considering quitting your job and living off of your savings for a while to work on your startup idea. Last year's ANP tells you how much money you could have taken out at the end of the year without dipping into your principal. Needless to say, that number cannot predict the future. But it is one useful datapoint among others.

The Fixed Rate Equivalent (FREQ)

The ANP qualifies as a measure of performance because it measures “by alternative”: had I kept my money under the mattress, how much more or less would I have? However, it has a severe shortcoming: it accounts for neither time nor principal. The bigger a chunk of money is, and the more time it spends in your account, the more return you may expect from it. The ANP is oblivious to all that. To overcome that limitation, we must measure the account's performance by an alternative that produces more return in more time and on a greater principal. That alternative is the fixed rate account, that is, a somewhat idealized savings account paying a fixed annual interest rate.

Imagine that instead of investing in your actual account, you would have made all deposits and withdrawals to an imaginary account that pays a fixed annual interest rate. Then you can ask, “What annual interest rate does the imaginary account have to pay so that its ending balance is the same as the ending balance of my real account?” In other words, “Which fixed annual rate replicates the performance of my account?” That rate is your fixed rate equivalent, or FREQ for short.