Blogger Barry Ritholtz has unearthed an 80-second video I made five years ago, with the title "Why it makes sense to sell your stocks." He's placed it under the category "really, really bad calls," presumably on the grounds that stocks are higher today than they were five years ago:

Barry is intellectually honest enough to link to the accompanying column, where I explain my reasoning in a lot more detail. But he doesn't actually rebut anything in that column, so I guess it falls to me to work out where and whether I was wrong.

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I won't keep you hanging: yes, I was wrong. But I never said that stocks were going down: I wasn't wrong about that. Indeed, I explicitly assumed that stocks would go up, not down. My big mistake, rather, was a category error. I said that stocks were incredibly volatile, with the VIX (a volatility index) around 40. Then, doing the math on how much stock exposure investors should have at those levels of volatility, I got very low numbers, around 15% or below.

Let me give you a bit of context, here. Five years ago, the financial crisis, and its associated stock-market volatility, was very, very fresh in people's minds. And then, on May 6, 2010, the so-called "flash crash" happened. No one really knew why it happened; all we knew was that stocks had been obliterated in a matter of mere seconds, before suddenly bouncing back.

So here's my mistake: I looked at the flash crash, along with some other pretty volatile days in the stock market, and I thought that volatility was back. But, with hindsight, the flash crash was pretty much the end of stock-market volatility. The Fed started embarking on its quantitative easing program, which flooded the market with so much liquidity that volatility went away. And the flash crash, it turned out, wasn't symptomatic of any kind of panic by investors: rather, it was symptomatic of market-structure weaknesses which (to many people's great surprise) turn out not to have hit the stock market again over the past five years.

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My calculations were made using this formula for what percentage of stocks you should have in your portfolio:

Samuelson Share = Return / (Risk^2 x RRA)

Here's a little widget you can use to work out your own number:

[wolframalphawidget id="da6cb383f8f9e58f2c8af88a8c0eb65e" output="iframe"]

If you put in a VIX of 40, which is what it was when I wrote my column, and a risk aversion of 4, which is roughly normal for Americans, then the result is that you should have just 8% of your investment capital in stocks.

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On the other hand, if you put in a VIX of 14, which is where it's at today, then the formula spits out that you should have a much more normal 64% of your investments in stocks.

Obviously, the formula is highly sensitive to stock-market volatility — which was exactly my point. When volatility spikes, it makes sense to scale back your stocks, and when volatility is low, as it is now, then you can have a riskier asset allocation with more stocks in it. My main error was that I looked at a market-structure artifact, the flash crash, and saw volatility, rather than a one-off event.

So how much of your money should you have in stocks today? Well, the past five years have seen significant outperformance by stocks, and that can't go on forever. So probably the "equity premium" part of the formula, the amount by which stocks are going to outperform bonds and cash, should be lower than 5%. Let's call it 3%, going forwards. Let's set risk aversion at 4, and expect the VIX to be roughly 18, going forwards.

Plug those numbers into the spreadsheet and you get a stocks allocation of 23%.

To a buy-sider like Barry Ritholtz, who always tries to maximize returns, that number I'm sure seems crazily low. Just think of the opportunity cost, if stocks go up! After all, isn't that exactly what they did over the past five years?

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Well, yes. But real people aren't like Barry — and don't have Barry holding their hand telling them that everything is going to be OK when their portfolios plunge by 50%, as they did during the crisis. Real people behave in surprisingly predictable ways once they've lost 30% of their money. And real people generally hate losing money about twice as much as they like making it. Once we have a certain amount of money, we naturally start to concentrate more on preserving our money than on making it grow.

Which is another part of what I was saying five years ago. During the financial crisis, a lot of people saw a lot of their retirement money evaporate, thanks to the way in which the stock market cratered. When stocks were near their lows, those people thought to themselves things like "I should never have had so much money in such a risky asset class". But then the Fed swooped in and saved them, and stocks went back up to their pre-crisis levels. This was, essentially, a do-over. With hindsight, do you feel that you shouldn't have had so much money in stocks? Well now you get to sell those stocks, put your money into something safer, and lose no money. That's entirely rational, no matter what stocks end up doing over the next five years.

So yes, Barry, I was wrong in 2010 — but I'm not a fan of the implication that I was making a "call" and saying that stocks were going to go down, or that they were not going to go up. In fact I took great pains to make it as clear as I could that I had no idea whether stocks were going up or down, but that they were more likely to go up than down. And I still think that the optimum stock allocation is much lower than most financial advisors would recommend.