# Fear of a crash

We know that people dramatically — dramatically — overstate the probability of a large market crash. I mentioned one study before — “Crash Beliefs From Investor Surveys”, by Goetzmann, Kim, and Shiller — which found that the actual probability of a crash in the next 6 months is 1.7% but investors think the probability is 19%.

The average reported crash probability from the Shiller surveys is thus more than 10 times the conservative estimate.

Even if we overstate the probability, we know that market crashes do happen and some people do get unlucky and retire right before a crash. It is understandable why people would worry about — and try to plan for — such a tail risk.

In “The Glidepath Illusion” (Estrada 2014) the author suggests that

An investor following the alternative strategies discussed here may be knocked down more than another following a lifecycle strategy, but will fall from a higher place, thus ultimately being better off. (emphasis added)

What Estrada is suggesting here is that you will make so much money from a heavy equity strategy that, even if you lose 50% of it in a crash, you’ll still have more money.

This got me to wonder. Is there any way to quantify this dynamic of “falling from a higher place” and see what it looks like in practice?

Here’s my first cut at trying.

What is this chart? Well, thanks to Shiller we have monthly data on the S&P 500. He provides nominal prices and monthly dividends but we can convert that into a monthly total return. For instance, including dividends, the monthly total return in November, 1954, was 4.2%. Not bad!

Once we have monthly returns, we can calculate the rolling returns over various periods: 3-, 6-, 12-, 24-, and 36-months. This let’s us figure out that, say, the worst 3-month period started in March, 1932 (-40%); the worst 6-month period started in November 1931 (-43.8%); and so on.

This let’s us see when some of these crashes we are worried about actually happened.

Granted, those are nominal returns (not adjusted for inflation/deflation) but you can see, with numbers like that, why people are afraid of crashes. Having -78% returns over a 3-year period would definitely suck for a retiree.

We already knew that historical crashes weren’t much fun. But Estrada’s contention is that instead of just focusing on how much in the crash, we also need to count how much we earned before the crash.

(While this makes complete sense, I admit it hand waves away a lot of human irrationality.)

One thing we could look at is how much of our previous gains are wiped out by a crash. And that’s what the chart above shows.

What is it actually calculating? Let’s take June 1902 as our starting point. Over the next 6 months the total returns were -2.39%. So let’s pretend that we invested all of our money in June 1902 and pull it all out 6 months later. We lost -2.39%. Not exactly a crash but this is just an example to show you how the calculation works.

What if we had invested earlier? What if we invested in May 1902? Well, May was almost totally flat, with no real gains. So our total loss is still -2.31%.

So let’s go back another month to April 1902. April posted decent gains (3.72%) which is enough enough wipeout the losses in June 1902.

In other words, if we treat June 1902 (and the six months following it) as a “crash” then it wiped out two months of gains.

Another way of stating that is, if had invested in April of 1902 then the “crash” of June 1902 didn’t actually lose you any money. You had made enough in April and May to offset the loses in June through October.

Of course, June 1902 wasn’t a real crash. But now you see how the calculation works. And we can let a computer apply it to every single month from January 1900 to the present.

Let’s look at the chart again.

We can see that most crashes wipe out fewer than 40 months of gains. In other words, as long as had been invested for more than about 3 years before the crash happened, you came out ahead.

And, remember, this all assuming that you panic and sell everything after six months. So you even if you never participate in the recovery you come out ahead so long as you were invested for around three years before the crash.

I said “most” crashes…there are obviously the four big outliers. And honestly, that’s probably what most people are worried about. The 2008 crash wiped out 64 months of gains. The 2002 crash wiped out 61 months of gains. The 1974 crash wiped out 86 months of gains. The worst part of the Great Depression wiped out 125 months of gains.

Even there, though, I think there is reason for a lot of optimism. The data is telling us that if we used our life savings and bought 100% stocks 5 years before the 2002 crash and then sell out everything after six months…we would still break even.

Is using “returns over the next 6 months” the best definition, here? I don’t really know. I think that captures the “sudden sharp drop” that is the crash of the popular imagination. It also minimises the chance that we include any of the ensuing recovery. But let’s look at other lengths of time as well.

It does look like extending beyond the 6-month window starts to include lots of the recovery. Just as an example, going from 6-months to 12-months gets rid of the 1974 crash to a large extent.

So I feel better about choosing the 6-month window in the original chart.

Does this support Estrada’s claim, that we will fall from a further height? To some extent. Investing five years before the crash seems like a lot but isn’t when we’re talking about a lifetime of investing. Even in the absolute worst case, the Great Depression, we’re “only” talking about losing 10 years of gains. If you’ve been saving and investing for 40 years that’s only a fraction of your total gains.

But there are still some reasons for caution. First, the analysis above is, essentially, comparing 100% stocks to 100% cash. For most people that’s not a very realistic comparison. A better comparison would be 100% stocks to 60/40. Or 60/40 to 30/70. Figuring that out would require monthly bond returns, which I don’t (yet) have available.

It also seems clear that if you retire the exact moment you hit your number, you are taking some risk. Estrada’s point of view is “time based” rather than “goal based”. In other words, he assumes that everyone works to age 65, no matter what. Even if they have a \$5 million portfolio at age 50 and hate their jobs.

Admittedly, I am not an ultra-conservative investor, so this may just be confirmation bias. But when I see the above charts I read it as further evidence that a heavy-equity strategy has less risk that one might think, as long as you can remember that your portfolio got to where it is thanks to the previous years of equity returns.

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