To paraphrase a Greek philosopher: “Investor, know thyself”

Sticking with the Rolling Stones, the song “Start Me Up” begins with the lines “If you start me up. If you start me up, I'll never stop.” So, with investing the first question is: when to start? One thing is sure: once you start you’ll probably never stop.

Here looking backward can help. There is a technique called back-casting that statistical modelers use. I want to introduce an analogous tool. Back-casting, as one might suspect, is forecasting backward. One might ask: “Why would anyone do that?” For some purposes it is useful because it abstracts from what really happened.

For example, back-casting is one technique used regularly to validate models. Some portion of the historical set is withheld from the model. The model is then run and the withheld portion of what actually happened is estimated or “forecast” using the model. The “forecast” of history is then compared to actual history. If the “forecast” of history is markedly different from actual events, the model is usually discarded. There are all sorts of variations, but that’s the essence of at least one use of back-casting.

Another use of back-casting is to estimate history for period where no history exists. For example, the broader measure of unemployment, U6, doesn’t have a long history. So, to compare this “total” measure of unemployment and underemployment to a like measure for other cycles, people back-cast U6. Both uses have their limitations, but are useful once the limitations are understood.

This posting discusses an approach that is analogous. In this case the purpose is to take current period data and imply something about history. It is analogous to the second use described above except in this case, the implications are about a variable not in the model, specifically ones’ personal behavior. It’s a way to check ones’ self-perception.

If you think such self-analysis is irrelevant, good luck; you can skip this posting. But, before you dismiss self-analysis consider whether the volatility in asset prices over the last few years caused you to reconsider your asset allocation. If that doesn’t convince you, consider which is more important to retirement planning: when you start or your rate of return? If you’re short of your retirement goals, is it just a bad patch for your investments or is it the amount you’re saving?

Since this posting deals with self-analysis, each reader is uniquely qualified to judge whether what is implied is valid and useful. It’s totally self-analytical. Even if a reader thinks he or she knows himself or herself, the exercise is a way to validate that assumption. Besides, it yields some data an investor should know.

Let’s start with what’s known. Most people know, or can calculate, how much money they contributed to their IRA each year. (If not the attached spreadsheet may make it easier). If they’ve mixed rollover and contributory IRAs, the analysis gets a little harder, but the approach still works. (And, the spreadsheet is still useful). Further, they know what their IRA is worth. Many know what their return has been recently. But fewer know what their compound average rate of return has been over the life of their IRA. It is this last issue that is the focus of the attached spreadsheet.

There are numerous ways to calculate an average annual compound rate of return. Many are more sophisticated (i.e., more accurate at the decimals of a percent) and many would require more data (e.g., exactly when contributions were made). But, remember the purpose of this exercise is self-analysis. A blunt instrument is all that required.

So, let’s look at the spreadsheet. It is fairly self-explanatory. The columns are the year, contributions (basic and, for older readers, catch-up), and various rates of return. Down the rates of return columns the balance at each compounded rate is calculated. I used 4, 6, 8, & 10% returns. Back when I put this together, I figured at one end, a person could average 4% in a bank. Nowadays the Fed has made sure you have to look elsewhere for an assured 4%. At the other end, if you did better than 10% over a long time (e.g., 15-20 years) you’d be sufficiently confident and competent not to need the analysis. It wouldn’t be easy since initially the investment options in IRAs were very limited (e.g., in the initial years only bank deposits were relevant to most investors).

For each year there is a cell for your contribution. The maximum allowed is shown. There were quite a few years where some people with pensions, 401(k)s, or high incomes couldn’t make the maximum contribution. Depending on your age, 1975 may be interesting history, but irrelevant. Similarly, catch-up contributions may be irrelevant. So, the actual entries and calculated balances are of passing interest; the spreadsheet is a tool (or toy) not an answer. For convenience, a spousal spreadsheet is also shown. So, working spouse or not, a tool is available.

How it works is fairly simple. You enter your contributions in place of the contribution data shown. The spreadsheet then calculates a balance as of 2009. If you’d like, add a year 2010 by copying the last row for an additional year. Either way, the result then can be compared to your balance to see which average annual rate of return fits. You now have your average annual rate of return. You also have alternative rates of return to use if you’re figuring you might try some new investment approach being promoted by some tout. It is an interesting little toy. (See, I’m easily amused). Over simplification? Yes. Yet, if you play with it for a while, you’ll see ways to illustrate some facts about investing. It’s easy to project YOUR results forward, backward, or for different levels of contributions.

Showing the full history facilitates the “what if” scenarios that allow you the flexibility to see the importance of when you start. You can calculate a dollar value associated with changes in the start date. For example, take out the first five or ten years and compare the result to the differences in results associated with different rates of return. (For example, taking out the $7,500 allowed during the first five years when contribution limits were lowest has an impact roughly comparable to a couple percentage points in average return, just slightly less). It’s very naive to assume you can overcome a late start with investment genius. Better to accept reality and figure you’ll need to pump up the savings rate.

Put differently, it sure looks better to just dive in, start investing even if it means accepting a slightly lower return: it’s better than to wait until you feel sure you can beat the averages. As the commercial says in a different context: “Just do it!” The initial $7,500, less than 9.5% of all contributions, at the sample rates accounts for from almost a fifth to almost half the balance in 2009. Such is the impact of compounding.

Alternatively, take the current contribution limits and paste them into the earlier years. You can compare your portfolio to a hypothetical portfolio earning the same return, but started at a different date. Years ago, I also used this as a forecast tool when planning -- kind of silly today given that now many web sites offer sophisticated Monte Carlo simulators.

Why did I stop at 2009? I wanted a way to show how a one year drop in value changed the lifetime average rate of return – at most a couple of percent depending on when it happens. Remember, at the end of 2008 the market had dropped almost 40%. I listened to more than one person try to argue that 2008 wiped out years of investment gains. You’d have to really fiddle the numbers to get that result.

Don’t get me wrong. A couple percentage points of return is important when compounded. For example, the discussion of cash holdings identified approaches which might increase returns by a percent or two. What would be the impact over a lifetime? Since we are talking up to a year or two’s cash needs held over most of a lifetime (exceptions being when you chose to tap the funds), it’s substantial. While designed with other purposes in mind, the spreadsheet shown below can be used to calculate a dollar value. However, that shouldn’t be necessary. It’s obvious: a few percent is important.

Similarly, avoiding declines in the value of assets can add substantially to returns. The first, second, and third rules of investing are: first, don’t lose the capital, second, don’t forget rule one, and third, never forget rules one and two. Also, rebalancing to avoid asset price declines is, after all, the reason we turned the music on in the first place. However, rules one, two, and three don’t matter if you don’t start. So, “Start me up.”

An interesting toy for the holiday. Please download it rather than using it where it is. https://spreadsheets.google.com/ccc?key=0AnZfhzwt5JapdENjcGVZcTFoS1lIZWtHTGxLemo4YkE&hl=en&authkey=CMbqjukO

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