The confusing part is that, even if you had stayed within a particular fund for the entire year, the return shown on the statement will likely be different than the return of the fund. This happens because people add money to their retirement accounts throughout the year. Every time you add money, you buy a little bit more of the fund at the then current price. This is known as dollar cost averaging or DCA.

What’s more, even if two people were in the exact same fund for the whole year, the returns shown on their statements will likely be different from each other. This is because the return depends on several factors, such as:

• the amount of money in the account at the beginning of the year;
• the amount of regular contributions; and
• the timing of the regular contributions.

Since these three factors are likely to be different for different people, the returns they see on their statements will also be different. Because of this, the return is often called the personal rate of return (PRR) or the personal investment performance (PIP).

Below, I discuss two formulas for calculating this personal return. The first formula, which I call the personal rate of return, is relatively easy to use and to interpret, though it is an approximation. The second formula is the one used by the TSP and other retirement plans. The formula is commonly called the modified Dietz method, while the TSP simply calls it the personal investment performance. Though the formula is exact, I think it is more difficult to use and interpret.

Personal rate of return. The personal rate of return (PRR) is calculated as the weighted average of two other returns, the lump sum total return (LSTR) and the dollar cost averaging total return (DCATR). These are explained below.

Let

• MB be the money in the account at the beginning of the year; and
• let MC be the total amount of money contributed throughout the year (that is, it’s the amount contributed per pay period multiplied by the number of pay periods).

Then,

PRR = (MB x LSTR + MC x DCATR) / (MB + MC) – 1

For example, suppose that,

• at the beginning of the year, you had $50,000 in your retirement account;
• you contributed $500 per pay periods for 26 pay periods (1 pay period every two weeks);
• the lump sum total return (discussed below) was 1.2; and
• the dollar cost averaging total return (discussed below) was 1.1.

Then, the calculation is as follows:

• MB = $50,000
• MC = $500 x 26 = $13,000
• PRR = ($50,000 x 1.2 + $13,000 x 1.1) / ($50,000 + $13,000) – 1 = 17.94%

Now, let’s discuss LSTR and DCATR.

Lump sum total return. “Total return” means 1 plus the return. For example, a return of 20% corresponds to a total return of 1.20. “Lump sum” means the total return on the money that you had in your account at the beginning of the year. For a fund, LSTR is equal to the price on the last day of the year divided by the price on the last day of the previous year.

Dollar cost averaging total return. This is the total return on the money contributed throughout the year. The formula is similar to that for LSTR. It is the price on the last day of the year divided by the effective purchase price. The effective purchase price is the harmonic mean of all the fund prices throughout the year. For details, see a more thorough explanation with graphs and examples.

Personal investment performance. We now come to the formula used by the TSP, called either the modified Dietz method or the personal investment performance (PIP).

Let

• EMV be the market value of your account at the end of the year;
• BMV be the market value at the beginning of the year (this is the same as MB above);
• CF be the total cash flow or contribution into the account (this is the same as MC above);
• i be the index on specific contributions to the account;
• CFi be the amount of the i-th contribution (in other words, CF = sum CFi); and
• Wi be the number of calendar days from the i-th contribution until the end of the year divided by the number of calendar days in the year.

Then,

PIP = (EMV – BMV – CF) / (BMV + sum (Wi x CFi) )

… And that’s how the personal returns are calculated and why they are different for each person.

Related posts:

1. Reported returns do not account for new investments
2. Dollar cost averaging does not turn bad investments into profitable ones
3. Buy and hold stocks for the long term

Ideally, the tracker would allow me to compare returns from Date x to Date y, and it would incorporate some investment amount per period z, starting with 0 at Date x (otherwise you can always rig the results with a bigger or smaller starting value at Date x).  And it would allow comparisons to indices (such as the S&P 500) using the same mechanism.  I suppose you could make the starting value a variable to be entered by the user, but leaving it unvariable and fixed at some amount determined by you (even if seemingly reasonable, like $10k) just opens you up to the criticism of manipulation.

Response: A lot of people think that each strategy has a particular return, but, as you point out, things are not that simple.

Even if two people follow the exact same strategy, their return might be different. This is because each person has some initial amount and some amount they are contributing throughout the investment period. We can think of there being two returns: a return on the initial amount (the lump sum return) and a return on the money contributed throughout (the dollar cost averaging return). The personal return is a linear combination of the two, with weights being proportional to the two sums of money (initial sum and the sum being contributed throughout). Since these sums differ between different people, so do returns, even if following the same strategy.

My methodology does not seek to simply maximize return — it seeks to maximize performance, of which return is an important part, but which has other components as well. Ideally, the goal is for the profit curve to go up more or less smoothly. This behavior achieves good returns, both lump sum and dollar cost averaging.

I haven’t seen a lot of discussion of this fact that each strategy has two returns. Whenever I see returns discussed, it is only the lump sum return that are being discussed. The ridiculous statement that “stocks go up in the long term” becomes even more ridiculous when we take dollar cost averaging into account. For example, stocks have lost money over the past 10 years, both on a lump sum and dollar cost averaging basis.

I think one reason why everyone just focuses on lump sum returns might be that this assigns just one easy number to each strategy. If you do things properly then strategy rankings would depend on each investor, which might be too confusing for some people.

Now, to answer your question. The third party tracker that I use reports only the lump sum return. I realize that that’s not how retirement savings works, but that’s what they report. I do not know of any service that accounts for DCA. If you do, please let me know. Also, you might want to email TimerTrac about this.

However, even though they only report the lump sum return, they also show you the full profit curve. They also allow you to see some “statistics” (if you click on “Graph with Statistics”). However, besides the maximum drawdown, I see those as being largely meaningless.

Related posts:

1. Dollar cost averaging does not turn bad investments into profitable ones
2. Personal Investment Performance (PIP) calculation
3. Buy and hold stocks for the long term

My TSP allocation has been 50% C, 25% S and 25%G and the performance shows YTD -10%.

Response: I am not sure I understand your question completely. If you switch from funds that are doing poorly to funds that are doing well, or the other way around, then that’s certainly going to change your return.

A lot of people are confused about dollar cost averaging (DCA). There is nothing magical about DCA. DCA does not turn bad investments into profitable ones.

When calculating return from investing a lump sum, all that matters is the initial price and the final price. With DCA, what matters is the final price as well as the path that the price took from the initial price to the final price. Because of this, knowing the return from investing a lump sum does not tell you anything about the return from dollar cost averaging. Either return could be higher than the other. It depends.

Just as a note, my newsletter’s YTD return is about +2%. Also see our verified returns.

Related posts:

1. Reported returns do not account for new investments
2. Personal Investment Performance (PIP) calculation
3. Focus on return and risk, not price; losses are locked in as they occur

Response: Here is the short answer, in two parts:

• First, what matters is the return, not the price. The principle behind my method is that one should pick the investment strategy with the highest possible return, given that it is within one’s risk tolerance.
• Second, both gains and losses are incurred at the time that they occur. There is no distinction between “paper” losses and “real” losses. All losses are real. There is no such thing as “locking in” one’s losses. Losses (and gains) are locked in as soon as they occur.

Now, let’s look at an example similar to the one that you give. For simplicity, let’s assume that you are not putting money in or taking money out of your account.

Let’s say a year ago, you had $13,000 in your account. You were following a certain investment strategy, let’s call in Strategy “A”. It does not matter what that strategy was. The strategy could have been to buy and hold the C Fund, or it could have been something else. Now, after a year, you have $10,000 left in your account. Strategy “A” has lost 23% ($3,000 / $13,000).

To recover this loss, you need to make 30% ($3,000 / $10,000). The problem is to find an investment strategy within your risk tolerance that is likely to recover this 30% the quickest. Another way of putting it is that you want to find the investment strategy within your risk tolerance with the highest return.

Say you estimate that Strategy “A” might return 10% per year. Then you find another strategy, Strategy “B”, that you think might return 15% per year. Given that the risk is acceptable, “B” is better than “A”.

Notice two things. First, price does not enter into the reasoning, just the projected return. Second, what the strategies themselves are does not matter. All that matters is their return and risk. The strategies could call for buying and holding, they could involve frequent trading, they could involve occasional rebalancing, or anything else. It doesn’t matter. Your decision is based only on the return and risk of the strategies.

My approach gets out of funds when they are losing money and gets into them when they are making money. You ask what will happen if you get out of C at $10 and then have to get back in at a higher price, say $11. It is true, if that happens, you will have missed the 10% up move in C. However, while you missed that return, you might have made an even higher return in whatever other funds that you were in.

If you know for a fact that C will go up by 10% and that no other fund or trading method will make 10% as quickly, then you should stay in C. But no one knows the future. There is also the possibility that, instead of making 10%, C actually loses money. My approach calculates the probabilities of various moves in all the investments and picks what it considers the optimal mix of investments.

Related posts:

1. Accumulating shares and paper losses
2. Locking in losses
3. Selling off stocks when they’re down

Long-term stock returns. Is this really true? Whenever someone makes claims about returns, always ask them to see the actual numbers that they are referring to. To evaluate the claims about stocks, lets consider the annual returns from 1998 to 2008. Why are we starting in 1998? Simply because that’s the first year for which data on all three TSP stock funds is available. From 1998 to 2008 is 11 years. Since people typically work and save for their retirements for about 30 years, performance over 11 years is a good indicator of how useful a strategy might be for one’s long-term retirement savings.

So, how well have the stock funds performed during this time? The C Fund, which invests in large-cap stocks and tracks the famous S&P 500 stock index, has had a compound annual return of 1.00%. That is correct — one percent. That’s not a typo. An annual return of just one percent every single year for a total of 12% over the 11 years. The other two stock funds have performed slightly better, returning 2.34% and 2.46% annually. Of course, one would have had a much better return by simply putting all of one’s money in the G Fund, the money market, which has returned 5.00% per year.

Returns with dollar cost averaging. But these numbers, though they are so miserable, still do not reflect the true extent of the problem. You see, this return of 1% per year assumes a lump sum investment. In other words, you would have gotten the 1% per year if you had invested in the C Fund at the beginning of 1998 and made no further deposits to or withdrawals from your account.

But that’s not how people save for their retirements. When people save for retirement, they typically put a little bit of money into their retirement plan throughout the years. This is called dollar cost averaging (DCA). Some people like to pretend that DCA somehow magically turns bad returns into good ones. Again, when you hear these claims, ask the people who are making them to see the numbers. The reality is simply that DCA returns are different from lump sum returns. They could be higher or lower – it depends. There is no one-to-one correspondence between the two types of returns.

When we account for dollar cost averaging, over the past 11 years, the C Fund has actually lost a total of 15%! Again, these are not the “short-term” ups and downs. This is a real long-term loss. For example, suppose that since 1998, a TSP participant had contributed $10,000 per year into the C Fund. This means that they contributed a total of $110,000 into the fund. However, by the end of 2008, they would have had only about $93,000 in the fund. That’s a real long-term loss of $17,000 over the 11 years.

Unfortunately, TSP only reports gains and losses on a lump sum basis. Because of this, many TSP participants do not even realize that they have lost money. Or, if they suspect that they have lost money, do not realize how much money they have lost.

If not stocks, then what? Many people feel that stocks are their only option. If not stocks, where else would you invest? Money market and bond funds are safer, but they do not generate high enough returns. What else is an investor to do?

We have a solution that is conceptually very simple. We pick the mix of TSP funds that maximizes the expected returns while not exceeding a fixed maximum risk. This means that instead of staying in a fund, we shift in and out of it based on its performance. There is nothing wrong with stocks per se. There are times when stock funds perform very well. And during those times, we are holding stocks. But when stocks are performing poorly, we get out of them. That’s our simple secret to outperforming every single TSP fund over the long-term.

Consider the numbers. During the same 11 years that the C Fund returned 1% annually, our Conservative allocation returned 6.59%, while our Balanced allocation returned 9.98%, almost ten times as much as the stock fund!

When we account for dollar cost averaging, the difference is even more stark. Over the 11 years from 1998 to 2008, on a dollar cost averaging basis, our Conservative allocation returned 41% while our Balanced allocation returned 71%. Consider the same example of a TSP participant who contributed $10,000 per year for 11 years, for a total contribution of $110,000. If this participant had followed our Balanced allocation, they would have made $78,000. By the end of 2008, they would have had $188,000 in their TSP account.

Related posts:

1. Bonds strengthen, stock “rally” not proven
2. Personal Investment Performance (PIP) calculation
3. Reported returns do not account for new investments