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Using Historical Returns to Predict the Future

Historical financial data can be a useful tool. It can confirm common sense ideas such as the concept that stocks should usually earn more than bonds, and that bonds should usually earn more than cash.

And it can be used to find flaws in plans — as William Bengen did in his famous 1994 study, which found that you’re setting yourself up for trouble if you spend from your retirement portfolio at a rate equal to its historical average return.

But it’s easy to get into trouble by using specific historical figures as a tool for predicting the future.

Which Figures Should We Use?

According to my 2012 edition of the Ibbotson SBBI Classic Yearbook, the annualized after-inflation return for U.S. stocks from 1926-2011 was roughly 6.6%.* And the inflation-adjusted return for U.S. Treasury bills over the same period was roughly 0.6%.

So, if we’re trying to pick a number to use for average stock returns for the future, should we use the 6.6% real return figure? Or should we expect the more stable figure to be the 6% equity risk premium (that is, the difference between stock returns and Treasury bill returns)?

If it’s the risk premium that we expect to be more stable, given how low interest rates are right now, that would give us an expected real return for stocks of just 4.1%.**

And according to a paper from the Credit Suisse Research Institute***, from 1900-2012, the global equity risk premium was just 4.1%. So going forward, should we be projecting based on the historical equity risk premium in the U.S.? Or should we be using a global average? Using that 4.1% figure would give us expected inflation-adjusted stock returns of just 2.2%.

The World Changes

In statistics, you learn about a given population by studying a sample of the population. And the larger your sample size, the more confident you can be in your conclusions about the underlying population.

With investing, the only way we can increase our sample size is to wait. For instance, if we’re concerned about annual U.S. stock returns, we have no choice but to collect that data at the glacial pace of one data point per year.

And a decent case can be made that the underlying population from which we’re drawing our sample is in fact changing over time, thereby reducing the usefulness of our older data points.

For example, in the 1930s, most U.S. households did not own stocks, placing a trade took several minutes and required talking to an actual person, trades were much more expensive, there were hardly any mutual funds (and no index funds or ETFs), nobody had up-to-the-second news, and the regulatory environment was entirely different.

So, if the purpose of our statistical analysis is to draw conclusions about what we can expect in the future, should we really be including results from the 1930s in our analysis? What about the 1940s? It’s not really clear where to draw the line.

Should We Ignore History?

My point here isn’t that history is useless. Rather, my point is that any time you encounter projections or conclusions based on historical figures, you would be well served to maintain your skepticism. In many cases you will find that there are alternative ways to interpret and apply the historical data that would lead to different conclusions.

*”Stocks” meaning the S&P 500 and the S&P 90 prior to the creation of the S&P 500.

**Calculated as 0.1% Treasury bill yield, plus 6% risk premium, minus 2% inflation (based on the market’s apparent expectation of roughly 2%, calculated as the spread between yields on short-term TIPS and nominal Treasuries).

***The study in question has since been taken offline. The 2014 version, however, can be found here.

It Pays to Start Saving Early: a Realistic Analysis

A reader writes in,

In my opinion, Social Security and Medicare are likely to be around for many years to come. Still, I think it is rational for people under 30 to acknowledge that the benefits will probably be reduced, kick in at a later age, and be means tested to the hilt — thereby making it more important than ever for young people to start saving for retirement as early as they can.

Would you consider writing an article about the benefits of starting in your 20s rather than putting it off? I know there has been a fair amount written about this subject, but there can never be enough information about the power of compounding investments — especially at an early age.

Overstating the Case

It is quite beneficial to start saving early. But I find that most articles making the case for doing so are a bit unfair to their readers because they use unrealistically rosy figures in their math.

For instance, I recently came across a blog post in which the writer calculated the wealth accumulated by age 65 for an investor who makes a $5,000 contribution to a Roth IRA every year. The author used a historical stock return figure of 9.8%, showing that if the investor starts at age 22, he accumulates more than $3.3 million. By waiting until age 35, however, that number is reduced to approximately $960,000.

The message was essentially that you can be filthy rich if you start investing as soon as you finish school.

But there are two major problems with that analysis. First, it uses nominal return figures rather than inflation-adjusted figures. Because we’re talking about a period of time that spans more than four decades, this error makes the resulting figure (the wealth built by age 65) look much larger than it really is — more than 3.5-times as large, in fact, if inflation averages 3%.

Equally important: The article used historical U.S. stock returns for the calculations, implying that an investor today is likely to earn such returns with his/her portfolio. Of course, that assumption is flawed for two reasons:

  • By most estimates, future stock returns are unlikely to be as high as 20th century U.S. stock returns, and
  • Most investors don’t (and shouldn’t) use a 100%-stock portfolio. And with interest rates as low as they are, bond returns going forward are likely to be far lower than historical U.S. stock returns.

I appreciate the motivation behind such articles — it is important to get young people investing early. But what happens if we substitute more realistic return figures?

A More Realistic Analysis

The following table shows the inflation-adjusted wealth an investor would accumulate by age 65 if she invested $5,000 per year (starting at either age 22 or 35) and earned real returns of 3-5% per year.

Assumed Real Return Starting at Age 22 Waiting Until Age 35
3% $458,599 $257,514
4% $600,147 $308,507
5% $793,501 $371,494

So, yes, there’s still a large benefit to starting early. In fact, one could argue that low return expectations make it even more important to start early.

But these numbers don’t exactly strike the, “you could be rich!” chord, which is typically what such articles attempt to do.

If anything, with realistic return numbers, the appeal would more likely be to fear. It’s hard to retire on $300,000 unless you have a pension (or a part-time job) or are willing to rely on Social Security benefits for the majority of your income.

Financial Simulations: Should You Trust Them?

Financial simulators–broadly grouped into a) historical return calculators and b) Monte Carlo simulators–are popular tools for financial planning. But it’s important to recognize their limitations.

Historical Return Calculators

Historical return simulators (e.g. FireCalc) allow you to test a given strategy against historical returns to see how often it would have worked. For example, you can check how often a 4% starting withdrawal rate would have been successful over a 30-year retirement given various stock/bond allocations.

Such calculators are useful for showing what has not worked in the past. Showing that a strategy has worked only occasionally tells us that we should have little confidence that it will work in the future. That’s why, for example, we know that it’s unwise to plan to withdraw 7% of your portfolio every year during retirement.

Monte Carlo Simulations

Monte Carlo simulators allow you to perform similar tests. But instead of testing a proposed strategy using actual historical sequences of returns, they ask you to provide statistical descriptors of investment returns (average return, standard deviation of returns, correlation to other investments, etc.), then they test the proposed strategy against numerous return sequences generated using those descriptors.

Monte Carlo simulations are especially useful for testing how much a plan’s probability of success will change as a result of changing assumptions. (For example, if stocks end up being 10% more volatile over annual periods than they’ve been historically, will that be a major problem?)

Are Historical Returns Meaningful?

Consider this analogy: You’re trying to determine the average height of a group of people (as well as other facts such as the standard deviation of heights among the group). With every additional person from the group that you measure, your data set grows and you can be more confident in your conclusions.

We try to do the same thing with historical returns–collect an ever-growing pile of data and use it to determine things like average annual stock market return.

But there’s a problem here: As our sample size grows, our population could be changing. For example, I’d assert that the financial markets and world economies are meaningfully different from, say, 50 years ago in several ways (examples: instantaneous information on stock, bond, and commodity prices; automated trading in very large amounts by institutional investors).

What effect will those changes have on investment returns in the future? I don’t know. But I don’t think we can simply assume that such changes will have no effect.

As such, any data older than 50 years is of limited value. As we continue to collect more data, we have to keep throwing our old data out as it becomes less and less relevant. Even today’s data may not be particularly relevant if you’re concerned with returns several decades into the future.

Conclusion: The predictive value of any simulations based purely on historical data must be taken with a healthy dose of skepticism.

Vanguard Investors Outperform Fidelity Investors

Russell Kinnel, director of mutual fund research at Morningstar, recently compared investor returns at Vanguard to investor returns at Fidelity. His study is interesting because it looks at investor returns (aka “dollar-weighted returns“) rather than investment returns (aka “time-weighted returns”).

A brief example of dollar-weighted returns

If Mutual Fund ABC earned a 25% return in Year 1, then lost 20% in Year 2, its effective annual return over the two years would have been 0% (because it would be back exactly where it started).

If, however, the fund had doubled in size at the end of Year 1–due to investors chasing performance and buying the fund after a great year–its dollar-weighted return would be significantly below 0%, because the performance in Year 2 would be weighted twice as heavily in the calculation. In short, dollar-weighted returns measure how the investors performed rather than how the investments performed.

What did Morningstar’s research show?

The study showed that Vanguard investors earned greater returns than Fidelity investors over the last 10 years. But that doesn’t really mean a great deal to me. It could simply be the result of Vanguard’s larger funds being in more successful asset classes than Fidelity’s.

What does interest me, however, are the two following facts:

  • As usual, mutual fund investors underperformed their own investments across the board.
  • Vanguard’s investors underperformed their investments by a smaller margin than Fidelity’s investors.

Why do we underperform?

We underperform because we try to time the market, and we (usually) fail. We chase performance–both in terms of hot asset classes and in terms of hot funds–and it destroys our returns.

Why do Vanguard investors perform better?

My hypothesis is that it has to do with the core philosophies of the two companies. As a company whose success has been based on index funds, Vanguard’s core tenets are minimizing costs, diversifying, and buying and holding.

In contrast, Fidelity, at its core, is about active investment. Many of their own fund managers turn over their portfolios more than once per year. It wouldn’t be terribly surprising to learn that their investors do something similar.

Kinnel has a similar opinion:

“It’s possible that the performance gap also has something to do with each firm’s message to investors. Vanguard preaches long-term investing and goes so far as to warn investors away from hot-performing funds…Fidelity also preaches long-term investing, but it sometimes nudges people to invest based on short-term results.”

What can we learn here?

Surely, some people will look at this study and see it as evidence of an opportunity to outperform the market. They’ll draw the conclusion that we must learn to “be fearful when others are greedy and greedy when others are fearful,” as Warren Buffett would say.

To me, the lesson is slightly different. I see it as another piece of evidence that our predictive abilities are decidedly lacking. After all, nearly every single one of those people who underperformed sincerely believed that he was going to outperform.

“I am above average!” is the battle cry of underperformance.

Historical Stock Market Returns

A bit of a different post today: I wanted to share a spreadsheet that I maintain, which includes a good deal of data regarding historical stock and bond returns (in the U.S.).

Click here to download the spreadsheet.

Historical Return Data Included:

If, for example, you wanted to know any of the following, you could find it in the spreadsheet:

  1. The return of the U.S. stock market for each calendar year from 1928-2008.
  2. The nominal return for stocks or 10-year T-Bonds for any 3-year, 5-year, 10-year, 25-year, or 30-year period between 1928 and 2008.
  3. The inflation-adjusted version of #2 above.
  4. How you would have fared if you’d been dollar-cost-averaging into the market across any 10-year period from 1928-2008.
  5. The standard deviation of stock or bond market returns over 1-year, 3-year, 5-year, 10-year, 20-year, and 30-year periods from 1928-2008.
  6. Changes in gold prices each year from 1900-2008.


My thanks go to the following people/organizations for the underlying data:

Other Notes

I’m not perfect, and the data might not be either. If, after downloading the spreadsheet, you have any questions or see any errors in any of my calculations, please let me know.

Lastly, please remember that past performance is exactly that: past performance, not to be confused with future performance.

Enjoy. 🙂

Results of a Balanced Portfolio

For whatever reason, anytime somebody brings up index funds one of the bigger personal finance blogs (like The Simple Dollar or Get Rich Slowly), there tends to be somebody in the comments who says something to the effect of “Index funds failed investors over the last decade.”

I can’t tell you how much this frustrates me given that:

For those who are not aware: “Index Fund” is not synonymous with “S&P 500 Index Fund.” There are index funds that track a whole host of other things, including bonds, commodities, and REITs.

How did a (re)balanced portfolio perform?

Just to set the record straight, I thought I’d take a minute to share the results internationally diversified portfolios, constructed from real index funds over the last decade.

The following portfolios are assumed to have been rebalanced annually on January 1 of each year. The stock portion is assumed to be 30% international (Vanguard’s Total International Stock Index Fund) and 70% U.S. (Vanguard’s Total Stock Market Index Fund). The bond portion is assumed to be Vanguard’s Total Bond Market Index Fund.

From 1999-2008, the following are the annualized rates of return for various asset allocations:

  • 70% bonds, 30% stocks: 4.44%
  • 60% bonds, 40% stocks: 4.02%
  • 50% bonds, 50% stocks: 3.54%
  • 40% bonds, 60% stocks: 3.00%
  • 30% bonds, 70% stocks: 2.39%

[You can see a screen shot of the spreadsheet with all the results here.]

Now, I’ll be the first to admit, those returns are hardly spectacular, and they were almost certainly below investor expectations. But they’re hardly the catastrophic declines in value that some people seem to think occurred.

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