# Thrift Savings Plans: The Truth About "PIP"

Updated: Jun 30, 2020

When we think of our personal performance it likely isn't the PIP that the TSP uses

**The Personal Investment Performance Metric**

A Thrift Savings Plan (TSP) is a retirement plan structured like a 401(k) available for government employees. One of the metrics that the TSP displays is what they call a "Personal Investment Performance (PIP)." Many people across the U.S. rely on this metric to see how well they performed in a year and may extrapolate that figure out to see what they expect to return. They may use this figure for retirement plans or deciding on plans to choose...but how accurate is it?

If you had a PIP of 10% year after year after year and you planned on putting in $100. What would you expect to see at the end of one year invested? $110? Unfortunately, that might not be the case.

**Rate of Return **≠ **Rate of Return**

Above is the definition of the "Personal Investment Performance (PIP)" metric TSP uses. As you can see, the formula they choose churns out an *estimate* of your rate of return. This formula is called the *Modified Dietz Method* and it looks like nothing short of a scary college math formula that we try to forget.

**The Modified Dietz Method**

For simplicity it looks like this:

Where the variables are:

A = Ending Amount

P = Beginning Amount

C = Contribution/Withdrawal totals; i.e. the sum of cash flows

W = Time weighting; Found with the formula (Total Periods - Number of Periods Passed)/Total Periods

**Our Favorite Way to Measure Portfolio Performance**

The problem is that if we take the rate of return that the *Modified Dietz Method* yields and plug it back into the history we don't get the same ending balance. We want the numbers to be as authentic as possible. In the best case scenario we would have the exact day-by-day change, dividends, contributions, withdrawals, etc. line item by line item and you can see how changes where reflected in that moment but we've never seen that. The next best case, which is equally effective, is using the *Annualized Rate of Return*. Annualized being a fancy finance term for extrapolated or drawn out. The simplest way to describe it is like applying a smoothing effect to the performances. The *Annualized Rate of Return *will give you the same ending balance, unlike the *Modified Dietz Method*.

**Our Example**

Here we created a portfolio with a random starting balance, random contributions, and a random ending balance (the days in between are hidden for sake of the picture being too large). Using the *Modified Dietz Method* and the *Annualized Method* we receive these values for *Annual Percent Yield (APY)*:

Immediately you can tell they're not off by a significant amount (slightly shy of 1% margin of error) but there is a difference and it enlarges or shrinks depending on how the contributions/withdrawals are made (beginning of the year heavy vs end of year vs equal spread throughout vs random vs lots of zero changes vs lots of changes etc.). To verify which one was correct we simply plugged the rate of return back into the original data to see which Rate of Return was closest.

**The Results**

As you can see the *Annualized Method* is the rate that we'd expect and although the Dietz gets us close in this scenario it might not necessarily always be close and it might be over or under what we actually returned. But why might the TSP use the inferior method instead? Well as far as we can tell (and feel free to comment below if we're wrong) we can't find a formula for the *Annualized Method* that solves for the rate. We had to use a function in excel called "Goal Seek" which essentially solves the rate for us by testing a bunch of values. That doesn't mean we should settle for less however because if we can make an easy solution in excel it should be possible for the TSP to do as well. Until then we find that using the *Annualized Rate of Return *ourselves is the more accurate way to go.

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