Stock market investors have suffered deep losses in the past 18 months, challenging the belief that stocks are the best long-term investments. Indeed, Wharton finance and economics professor Robert Stambaugh recently coauthored a paper titled, “Are Stocks Really Less Volatile in the Long Run?,” which suggests that equities are subject to bigger price swings than previously understood. The research adds a new perspective to the work of Wharton finance professor Jeremy J. Siegel, author of the book, Stocks for the Long Run, which says stock returns more than offset risks if you stay with the market through its ups and downs. In a recent interview with Knowledge at Wharton, the professors described their views about the market’s long-term behavior.

An edited transcript follows.

Knowledge at Wharton: Professor Stambaugh, your work finds that volatility in stocks — the ranges of ups and downs — can be considerably more severe than most people believe. And your paper focuses on uncertainties that cloud the future. Can you put this in laymen terms for us?

Robert Stambaugh: Generally when we think about volatility in the stock market, we think about the value of the market fluctuating, typically around some sort of trend or long-term expected rate of return. Our work makes the point that uncertainty about that trend itself adds to the uncertainty that investors face and should be perceived by them much like volatility — much like the fluctuations around the trend.That uncertainty about the trend itself becomes more important the further into the future you project investment outcomes. So our paper basically makes the point that to an investor with a long horizon, stocks actually are riskier per period.That is, the rate at which risk grows over the horizon such that it makes the investment riskier over the long run.This is basically in contrast to what we think of as more conventional wisdom that says over the long run, fluctuations in the stock market will to some degree cancel each other out and, therefore, make risk to an investor in the long run look [smaller] per period than [it would] to a short-run investor.

Knowledge at Wharton: There are a number of factors that you say contribute to this uncertainty about the future. What are the most important of those?

Stambaugh: Probably the most important is just uncertainty about the overall long run trend.The other feature of the stock market that contributes to uncertainty is the fact that at some points in time we think the expected rate of return is higher than at other points in time.In other words, over time the rate of return that you can expect to earn over the short- and intermediate-terms fluctuates.The fact that the expected return fluctuates also adds to uncertainty because we do not know — for example — if expected returns are currently high, which many of us would guess they are.We don’t really know how long they’re going to stay high.That may in part depend on how quickly the economy recovers. That additional uncertainty also contributes to higher uncertainty in the long run.

Knowledge at Wharton: What would be an example of a kind of event that could occur that people simply can’t take into account ahead of time? I saw in one story a mention of global warming, for example.

Stambaugh: Global warming is interesting. It provides an interesting analogy to this concept because … we might be very uncertain about how quickly the Earth is warming,but that uncertainty doesn’t much impact our uncertainty about crop output and economic output next year. But if we look 50 years down the road … uncertainty about the rate [at which the Earth is warming] has a much bigger impact on our overall uncertainty.

Knowledge at Wharton: Professor Siegel, your work in Stocks for the Long Run, and in the years since then, talks a lot about the long-term trends — a couple of hundred years of stock market data, and bond and cash returns — [showing] that volatility does tend to even out over time.Is that right?

Jeremy Siegel: Yes.My empirical work — which tracks stock returns since the beginning of the 19th century, so now we have a little bit more than 200 years of data — showed that stock returns display what economists call “mean reversion,” or reversion to the mean.In the short run, there seems to be a lot of volatility, uncertainty.But if you draw a trend line… it tends to fluctuate around that.And if I understand Rob’s work, he still agrees there is mean reversion.

Stambaugh: Yes, exactly.

Siegel: He’s not denying it and most researchers — actually even before me — had suggested [mean reversion]. When I did it, it got stronger. And almost everyone has confirmed it.So the mean reversion story, I think, it is still there.What Rob is bringing up is, as he calls it, trend uncertainty. That analogy to global warming is a good one in the sense that … crop yields fluctuate a lot year-to-year. But we know that over 5- or 10-year periods they tend to get back to a mean.But if there’s going to be some big change in the future — and what Rob seemed to say is even with 200 years of data — you can’t really be that certain of the long-term trend.In my first chapter in Stocks for the Long Run … I say that we could be seeing that the last 200 years are the golden age of capitalism.When we look through the centuries, there have been an awful lot of huge changes. That golden age may be over.So, even 200 years doesn’t give you confidence. We have empires that have ruled 1,000 years and more and then they fail.That sort of big picture uncertainty really could be a dominant feature looking far into the future.

Knowledge at Wharton: We’re all familiar with the warnings we get from our brokers when we invest in something, that past performance is not a guarantee of future results.So most people recognize that there are uncertainties about the future, but when we talk about volatility and uncertainty, a lot of people automatically translate that into risk. They look at the downside.But we also have surprises on the upside, don’t we? Such as technological breakthroughs that nobody could imagine earlier, things that improve productivity….So, professor Stambaugh, according to your work, it’s possible not just that results could be worse than they have been in the past, but that they could be better?

Stambaugh: Exactly.We’re not making any sort of bullish or bearish statement.We’re just saying that whatever projection one makes about the trend or what’s likely to happen, you can have big surprises on the upside or downside. And part of what contributes to the overall uncertainty in the long run is just uncertainty about things like the trend.Indeed, we were somewhat unsure when we began this whether 200 years of data that Jeremy has very carefully assembled — and we’re very grateful to have available — would indeed leave one with a lot of uncertainty about this trend, or whether it would resolve a lot of that uncertainty.This is where we bring statistics to bear on the problem, which allows us to quantify how much uncertainty will be left over….  And, indeed, we found out that even… two centuries of data leaves one with enough uncertainty that as you look at the implied variance of stock returns over the longer horizons, the risk actually does rise significantly with [the time] horizon.

Knowledge at Wharton: Professor Siegel, as I recall from your book, you don’t just say this is what the numbers average out to over time — when you talk, for example, about the greater returns of stocks vs. bonds and cash. But you have some reasons why you think that has been the case, right? What are they?

Siegel: Our general models take individuals as what we call risk averse.People have to be paid to take on risks.Since stocks are the residual after bonds and other claimants have their first say, it’s natural that stocks would have a higher return.What has tended to surprise economists — there are a ton of papers that have been written — is that extra return seems to be very generous over long periods of time.There has been a lot of literature about what’s called the equity premium puzzle, written in the mid 1980s by a few economists.Given the macro fluctuations, it seems that equity holders actually get a very rich premium.There have been some modifications and there’s been a lot of reworking on that.The premium I find over the long run on stocks over bonds is about 3% a year. And that’s a compound annual premium.That premium — although in the short run it can certainly be up and down over periods of decades and generations and even centuries — has been relatively constant and, therefore, for someone planning 30, 40 years into the future for their retirement, that difference could obviously accumulate to a very large sum in favor of stocks.

Knowledge at Wharton: Professor Stambaugh, when you look at your findings, regardless of whether volatility may be higher in the future than people expect, what about the relative returns of stocks vs. bonds vs. cash.Do you draw any conclusions that an investor could put to some practical use?

Stambaugh: We’ve not yet looked at this same issue with regard to nominal bonds where you have things like inflation risk present.So I’m afraid I can’t yet tell you what our conclusions would be there. But certainly the issue with regard to asset choice — if you [want to] make a simple stock versus cash kind of choice or stocks versus a TIPS [Treasury Inflation Protected Securities] or index bond — our … best estimate of what the spread would be is what it’s been historically.

Knowledge at Wharton: Between stocks and bonds?

Stambaugh: Between stocks and bonds or stocks and cash.All we’re saying is that there is uncertainty about whether that average spread will in fact be realized by investors over time.And the uncertainty — when you take into account all its components — is indeed higher for longer-term investors.

Siegel: What Robert is saying is very important. These trend uncertainties apply to other assets, too.

Stambaugh: Absolutely.

Siegel: One could say that … nominal bonds were an inflation trend. We’ve had inflation –we went up to 13% — but we know countries that have gone into hyperinflation. The risk of that may be considered a trend uncertainty — suddenly that breaks down. Rob mentioned TIPS, which are generally more protective because the government promises to pay according to the consumer price index if it isn’t manipulated, if there are not price controls — and if the government can get enough revenue to pay it.There are certainly uncertainties there in the long run.So in some sense, the trend uncertainties that Rob’s work shows apply to all other assets.I don’t know whether that would lead you — and I would want to ask Rob about that — to recommend to people that they reduce their stock allocations as a result of this uncertainty, given that it can, in fact, affect other asset classes, too.

Stambaugh: As I said, we haven’t looked at a wide variety of asset classes here.But if one were making an allocation between stocks and cash, and you had a desired allocation … and then you became aware of this additional uncertainty, you would reduce your stock allocation.Again, we’re not making a prescription about what that stock allocation should be.Our point is simply that for a long-run investor this consideration has a bigger effect.

Siegel: But, Rob, have you found the same trend uncertainties affect bonds? Let’s say the nominal bonds.Could you make a claim that you would reduce stocks versus bonds under those conditions?

Stambaugh: No.It’s quite possible that if we were to look at nominal bonds — and that would be an extension because there you do have substantial trend uncertainty, particularly with regard to inflation.It’s quite possible that this same kind of uncertainty in nominal bonds could well make them less attractive.So that’s an extension to our work that we hope to pursue but I just can’t give you an answer right now.

Knowledge at Wharton: And I can hear a lot of listeners out there gnashing their teeth and saying — well, look, I live in the real world here and I’m worried about my retirement.Are you telling me that if my asset allocation model used up to this point said I’m a 30-year-old and I should have 70% in stocks, that I should have 40% in stocks?What decisions should people make?

Stambaugh: Sorry, I can’t help you there.

Knowledge at Wharton: Jeremy, what do you think?

Siegel: It is easy to jump to the conclusion that: “Oh my goodness, stocks are riskier.Let me get into these other asset classes.” Global warming really happens. These are big trend-changing events that really could affect all assets.

Knowledge at Wharton: And just to go back for a second, Rob did say that these uncertainties could be uncertainties on the good side.Good things can happen as well.

Stambaugh: Yes, except that uncertainty is never viewed as a good thing for an investor. In general, we think of — as Jeremy said earlier — investors being risk averse.So as you crank up uncertainty, you need to provide some reward.The fact that you can be surprised on the good side, generally, to a risk averse investor, doesn’t offset totally the fact that you could be surprised on the downside.

Siegel: In my book, Future for Investors, I speculate a bit about trends of technology and the fact that the communications revolution suddenly opening up — connecting people and research centers in a way that hasn’t been done before — could … increase growth.There are potentials for very favorable surprises in terms of inventions, discoveries, innovation, etc. … so, in a way, Rob is right.You don’t generally like uncertainty because the downside is more hurtful than the upside is helpful. But there can very well be that upside, too.

Knowledge at Wharton: But an investor would not be irrational to sit there and say, “Well I realize there are uncertainties of global warming and these other kinds of things we’ve mentioned, but at the same time maybe somebody will invent a breakthrough battery for electric cars, or nuclear fusion will suddenly become practical,” or something like that.

Siegel: It’s not too late for that.Some people say there’s already too much carbon dioxide in the atmosphere, but I understand what you’re saying.

Knowledge at Wharton: I just want to turn finally for a minute or two to the market of the past couple of years, which has been just terrible for people.The S&P 500 is still down about 45% from its peak.Are these events that we have seen in the last couple of years anomalies or are they things that people should expect to happen every once in a while?Where do they fit into your view of the trends over the years?

Siegel: We had a 20-year period of very low volatility of real economic variables.We had two very mild recessions.If you look at quarterly changes in real GDP or any of the real economic factors, their variability went down. That lulled a lot of people into thinking, “Hey, we’re in a more stable world.”That led to a lot more leverage and, therefore, a ripple — which I interpreted as not being something disastrous — turned into a tidal wave because of the leverage firms took.It pushed us back into a recession which I now look at as about as severe as I remember in the 1970s and 1980s….  Obviously there are people out there talking about the 1930s.We are miles away from that at the present time.But it looks like we have moved back at least on this recession to the severity of the ’70s and ’80s.And that period of low volatility — which economists called “the great moderation” — seems to be over and could have been an anomaly.

Knowledge at Wharton: And your view?

Stambaugh: I guess I should take the opportunity at this point, since you raised the issue of the current economic environment, to point out that I would not want to claim as we sit here currently that stock volatility in the long run is going to be higher than current short-run volatility.We were at very historic highs in terms of short-run volatility.The VIX, Volatility Index, has hit all-time highs recently.So certainly we expect that sort of short-run volatility to moderate. I wouldn’t want readers and listeners to misinterpret our work as claiming that we’re making a statement about the current environment where we think long-run volatility is going to be even higher than it is today.Our paper is more about what a more typical environment — or more average environment — for volatility would offer an investor in terms of short-run versus long-run.That is, in a more typical environment we would argue that stocks look riskier in the long run, but certainly today stock’s volatilities are at all-time highs — at least over relatively short horizons such as those measured by things like the VIX.

Knowledge at Wharton: So you would not expect this kind of volatility to continue for long periods?

Stambaugh: I would certainly hope not.I don’t expect it — I don’t think anyone does — and we’d all be very surprised if it were to continue.

Knowledge at Wharton: That gets us to the last question.It is customary to ask professor Siegel for his thoughts about what the markets and the economy are likely to do over the next year or two.

Stambaugh: I will defer to Jeremy on that question.

Siegel: I put my head on the chopping block each time I’m here.I was giving a talk this morning and I said, “I can finally take off my bullet-proof vest.”I talk about stocks and there are a few people who say, “Maybe that is better.”What the rally reflects is that people are now saying, “You know what? The world isn’t coming to an end.”Obviously I’m saying that people were really discounting [the market] because we had a financial shock almost as bad as the 1930s, but certainly not an economic shock with the same tremendous response.So, again, it’s going to be a recession just like we had in the ’70s and ’80s, and those periods have always been very good buying opportunities for stock investors.So you missed a part of this rally, but it is still a very reasonably priced market and you will be very amply rewarded in the long run.

Knowledge at Wharton: So you still believe in stocks for the long run?

Siegel: Oh, yes, I definitely do.Let me just say that …  once you’re down 50% from the high — and we’re actually down a little bit more but we’ve come back — the returns from those levels are even greater than the long-run mean.We can’t be certain of that, but you face historically even better prospects.

Knowledge at Wharton: Thank you.And professor Stambaugh, thank you very much for your paper as well. It reminds us that we can’t always count on the past being prologue.