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# Measuring the Performance of Accounts with Deposits and Withdrawals

A GreaterThanZero White Paper

Discusses the issues that arise when measuring the performance of accounts that undergo deposits and withdrawals. Explains the meaning and purpose of the time-weighted rate of return (TWR), the absolute net performance (ANP), and the fixed rate equivalent (FREQ). No math or other special expertise other than an understanding of percentages is required.

## An Account Without Deposits and Withdrawals

Suppose that on Jan 1, 2002, you opened a brokerage account with an initial investment of \$10,000. For the next five years, you did not deposit or withdraw any money. Your monthly account balance over time looked like this:

Figure 1

At the end of the 5 year period, the account balance stood at \$13,502.52. This means that the initial \$10,000 investment grew by 35.0252%. In financial terminology, this is expressed by saying that your return for that five year period was 35.0252%.

If there is just one mutual fund in your brokerage account, then the chart above is identical to the "Growth of \$10,000" chart of that mutual fund. The 35.0252% is the return that the mutual fund would report for the 5-year period in question. Investors who bought shares of the fund at the beginning of the reporting period base their claims at the end of the period on that return: someone who bought \$10,000 worth of shares, as you did, may demand to be paid \$13,502.52. (In the real world, the mutual fund would probably report an annualized return, but that's a separate issue. We'll talk about it in the appendix.)

If, instead of holding one or more mutual funds, you did your own trading, buying and selling stocks and bonds, then you were essentially your own mutual fund manager. In that case, you may also use that 35.0252% return to compare yourself to mutual funds that traded in similar stocks and bonds as you did, that is, to mutual funds that were fishing in the same pond as you.

In summary, we see that in the absence of deposits and withdrawals inside the reporting period, measuring the performance of a financial account is dead simple. You look at the percentage change of the account balance over the reporting period. That tells you how much money you have made or lost. It may also be viewed as a measure of the portfolio manager's skill, be it you, or your financial advisor, or a manager at a mutual fund company. That's pretty much it, except for the issue of annualization, which we'll discuss briefly in the appendix.