Why volatility means you should sell stocks

By Felix Salmon
May 10, 2010

huffpofront.jpgMany thanks to the guys at HuffPo, who splashed my video from Friday all over their front page this weekend: the resulting post has now received well over 2,500 comments, and there’s even now a “Felix Salmon Investment Advice” tag over at HuffPo, which is scary.

Naturally, the video being less than 80 seconds long, there wasn’t room for a lot of background and exegesis. But the message I was trying to send is not that I think stocks are going to fall. Rather, it’s that volatility has risen, and that it makes sense to sell stocks in periods of high volatility.

I had a very interesting conversation with Barry Nalebuff today, co-author of Lifecycle Investing: he’s the guy with the idea that young people should lever up their stock-market investments, and that pretty much everybody under the age of 40 should have 100% of their retirement funds invested in stocks. I wrote about his idea a couple of years ago, and I found it intriguing; my main issue with it is that it’s very hard to implement in practice, and that someone trying to do so might well fail miserably. Basically, it’s far too complicated for a typical young investor to even try to follow.

Barry made one thing very clear to me today: if you don’t believe in the existence of the equity premium — if you don’t believe that stocks are going to outperform bonds over the long term — then you shouldn’t invest in stocks at all. Even if you’re completely agnostic on the issue — if you have no idea whether the equity premium exists — you should still have no money in stocks.

The advice in Barry’s book is entirely for people who are invested in the stock market, and who will invest even more in the stock market. They are likely to put in far too much money towards the end of their lives, when they’re at the peak of their earning power, and far too little at the beginning; Barry’s idea is to even things out a bit so that they’re less likely to get wiped out by a freak stock-market fall just before they retire. If you can follow his strategy — and that’s a very big if — then it’s actually safer than most retirement-fund strategies.

So let’s say that you’re a long-term investor, and you believe in the equity premium, and so you want to invest a chunk of your money in stocks. What percentage of your money should that be? Ayers and Nalebuff helpfully provide a downloadable “Samuelson Share Calculator” to come up with a number for that.

The Samuelson Share is named after Paul Samuelson, and basically says that the percentage of your retirement funds that you should have in stocks is found by a pretty simple formula:

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

Here, Return is the expected equity premium: the degree to which stocks will outperform bonds, on an annualized basis. Risk is the VIX, and RRA is your own Relative Risk Aversion.

On the downloadable spreadsheet, you can fill in whatever numbers you like for the different variables. Ayres and Nalebuff plug in a pretty high equity premium of 5.04%: that doesn’t mean that they expect stocks to rise by 5.04% a year, remember, that means that they think stocks will outperform Treasuries by 5.04% a year. I find that very optimistic, but fine, let’s leave it there. They also assume an RRA of 2, which means your risk appetite is greater than that of about 76% of the population. Given the expected audience for their book, maybe that’s reasonable. And finally, they plug in a value of 18% for the VIX. With all those inputs, the Samuelson Share output is 78%: you should have 78% of your investments in stocks, on average, over the course of your investing life.

But now what happens if you change the 18% value for the VIX to its actual closing level on Friday, which is 40.95%? Suddenly, the Samuelson Share plunges to just 15%.

And if you go from a portfolio with 78% stocks to a portfolio with 15% stocks, then that means you have to sell more than 80% of your stocks, pretty much overnight.

Meanwhile, if you think that the equity premium is just 1% rather than 5%, your Samuelson Share falls even further, to just 3%. And if your risk aversion is a pretty typical 4, rather than a relatively aggressive 2, then your Samuelson Share becomes a barely-visible 1.5%. At that point, you basically have to sell all your stocks.

And remember, none of these calculations are based on the expectation that stocks will fall — in fact, they’re all based on the expectation that stocks will rise!

The point here is that volatility alone is reason enough to exit the stock market. If you want your lifetime investments to have an average 78% exposure to the stock market, then it makes sense to have 100% or even 200% exposure when you’re young. But that’s no longer the case if the VIX is somewhere over 40. (And remember, it hit 80 at the height of the market chaos at the end of 2008.)

I feel I ought to have some money in the stock market. But if I take the spreadsheet and plug in an equity premium of 2.5%, a VIX of 30%, and an RRA of 2, then my Samuelson Share comes out at a decidedly modest 14%. And that’s being very generous, in my view, when it comes to the equity premium.

You don’t need to have a very long memory to remember how loss-averse people turn out to be when the stock market plunges. They hate it when that happens — even if their stock-market investments are long-term savings which they have no need to liquidate. That kind of risk aversion is — or should be, in any case — an incredibly important driver of asset-allocation decisions. And in a time of great uncertainty and stock-market volatility, the lesson to be drawn is that most of us will be able to sleep much better at night if we’re not invested in the stock market.

Just ask Barry Nalebuff. His net worth isn’t in stocks: it’s tied up in a company he co-founded, Honest Tea. Which has surely provided a much better return than any index fund, no matter how leveraged: ten years after he founded it, Coca-Cola bought a 40% stake for $43 million.


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“Just ask Barry Nalebuff. His net worth isn’t in stocks: it’s tied up in a company he co-founded, Honest Tea. Which has surely provided a much better return than any index fund, no matter how leveraged: ten years after he founded it, Coca-Cola bought a 40% stake for $43 million.”

Technically, he is even more exposed to economic (if not market) volatility. His net worth as well as his income are tied up in one illiquid equity investment in his own business. A positive outcome ten years on does not invalidate the point that an nondiversified investment in one illiquid equity is likely more, not less, risky than investing in a diversified, liquid portfolio of stocks (and bonds).

Posted by blakegoud | Report as abusive

Clearly, Felix, you should join CNBC and take over Cramer’s job.

Posted by MarshalN | Report as abusive

May I humbly submit an offering to the “Felix Salmon Smackdown Watch”:

http://mbablogreader.blogspot.com/2010/0 5/5092010-on-peculiar-advice-of-mr-salmo n.html


p.s. nice link to your blog in this weekends NYTimes magazine….

Posted by bkmacd | Report as abusive


1) Risk is not volatility.

2) Even if vol were risk you mismatched the term structure of volatility to the term of the equity returns. The vix measures 30 day vol not 40 year vol.

Posted by Kurt_Osis | Report as abusive

Real-life return distributions are not stationary and probably not even ergodic, but it does seem that vols possess a mean-reverting property. At any rate, AR-type models provide the best fits. It follows that vol is not timescale-invariant and unless you think Samuelson wanted you to rebalance your retirement portfolio daily, you cannot just plug the latest VIX quote into his formula and hope to get a sensible result. So the smack-down is correct.

Secondly, the stability of bond returns is in part illusory because of the long downside tail risk that does not appear in daily or monthly bond returns even on an mtm basis. Many retail investors view their bond portfolios in accrual terms which further exaggerates this illusion. Even worse, their accounting is done in nominal terms when what they really care about is real dollars.

Finally, your last paragraph is completely nutty – any lottery winner could say the same. It just detracts from your argument, so why did you include it?

Posted by Greycap | Report as abusive


Using volatility as a way to decide whether stocks are a good buy is the living embodiment of all that is laughable about Efficient Market Theory.

Needless to say, your timing has been impeccable.

Posted by DanHess | Report as abusive

Hmm, an arbitrary formula offered with no justification whatever, which depends on one unknowable statistic and one entirely arbitrary fudge factor. Yes, I certainly get the urge to entrust my financial security to that….

Posted by Ian_Kemmish | Report as abusive

Risk, as Buffett says, comes from not knowing what you’re doing.

If you’re an efficient markets guy, you’ll say the market is more volatile and risky so I should reduce my positions (as if someone fat-fingering an order is a fine example of the market reflecting all available information).

If you’re Buffett, you’ll say, there are a bunch of donkeys with fat fingers out there that I can take advantage of, so I can increase my position size.

Posted by TwasBrillig | Report as abusive

Previous comments are sort of correct; volatility is not risk, though in the Samuelson model forward volatility is a full measure of risk. It requires not daily rebalancing, but a monthly horizon, due to the term issue. Long-term volatility is less volatile than the VIX.

The Samuelson share also assumes that the rest of your portfolio is in cash. If you’re mixing in long-duration bonds, so long as the correlation between stock and bonds (over the relevant term) is less than 1, you’re generally going to benefit from an increased proportion of stocks so long as they have an expected return higher than bonds.

Posted by dWj | Report as abusive

As an investor with substantial assets and 20 years until retirement (as well as hopefully another 30+ years beyond that), I remain entirely unconvinced that jumping in and out of the market is a sensible strategy.

Remember that you are investing in COMPANIES, not markets. If the company is sound, and you don’t need the money soon, you can afford to ride out the bumps. Better yet, treat a 50% plunge with the same excitement you would a store-wide discount day at Macy’s.

If you insist that people selling you quality companies at bargain prices is a BAD thing, then you probably ought not invest in stocks. Or bonds. Or real estate. Why fear volatility when you have a 20-year time frame?

Posted by TFF | Report as abusive

ha, a value of vol of 41%? if you use this number, you mean you expect stocks to go up or down an average of 41% per year between now and when you retire. how in the world would you justify this assumption?

Posted by q_is_too_short | Report as abusive