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Quick Introduction to ANP and FREQ

The ANP (Absolute Net Performance)

The ANP (Absolute Net Performance) is a first, simple way to get a grip on the performance of an account that underwent deposits and withdrawals. In fact, the ANP is so simple that it can be called crude and primitive. Yet, it has value as an eye-opener and, to some extent, for your financial planning.

For the ANP, you start with your account's beginning balance, add to that the grand total of all deposits, and subtract the sum of all withdrawals. That's how much you would have had you kept your money under the mattress. It is your mattress equivalent. Then you compare that to what you really have, that is, to your account's ending balance. The difference between the two is your absolute net performance, or ANP for short. It is the absolute amount of money that you made or lost with your investments.

ANP (Absolute Net Performance) = ending balance − mattress equivalent
= absolute amount of money made or lost

In the example that we looked at earlier, we have:

mattress equivalent = $100,000 + $1,000,000
= $1,100,000
ending balance = $2,100,000
ANP = $2,100,000 − $1,100,000
= $1,000,000

It is interesting how few people know if their ANP is positive or negative, let alone what exactly it is. Think about the money that you put in your brokerage account, or 401k account, minus the money that you withdrew, if any. That's your mattress equivalent, the amount you'd have had you kept your money under the mattress. May we suggest that you ask yourself: do I have more, or do I have less? How much more or less?

The FREQ (Fixed Rate Equivalent)

Knowing how much money you made or lost is a good thing. So what's so primitive about the ANP? One obvious shortcoming is that the ANP states gains and losses in absolute terms, rather than as a percentage of principal. This issue looks like a tough one to resolve, because in the presence of deposits and withdrawals, the account's principal is an “elusive” one: it changes with every deposit and withdrawal. The other thing—and this will show us the path to the solution—is the fact that the ANP does not account for time. It treats all deposits equally, regardless of when they were made. But nobody should keep their money under the mattress, where it just sits and does nothing. The simplest form of investment is a savings account, where money accumulates interest over time. Therefore, the proper measurement of performance is not the comparison to the mattress. It is the comparison to an account with a fixed interest rate. To make that comparison, imagine that instead of investing your money the way you did, you would have made the exact same deposits and withdrawals to a hypothetical account with a fixed annual interest rate, like a (somewhat idealized) savings account. Now you can ask, “For which annual interest rate would the ending balance of the imaginary account be the same as my real ending balance?” That rate is your fixed rate equivalent, or FREQ for short.

The FREQ is the fixed interest rate that replicates your account's performance. It is the annual interest rate of the savings account which, when subjected to the same deposits and withdrawals as your actual account, has the same ending balance as your real account.