Probability of A Stock Market Correction

The Wall Street Journal has a good article on investor sentiment, relying heavily on the work by Robert Shiller.  He argues that investor sentiment looks much more like a hindcast than a forecast.  In other words, investors tend to be optimistic after the market just rose, and pessimistic after the market just fell.

The more stocks go up and the faster they rise, the more likely you become to expect more of the same. And when they go down, your expectations fall with them. Investors are often told not to get caught up in other people’s emotions — but it’s at least as important not to get swept away by your own.

New research hammers that point home. Finance professors William Goetzmann and Robert Shiller of Yale, along with Dasol Kim of Case Western Reserve University, have analyzed the Yale surveys and found that investors’ forecasts regularly look more like aftercasts — simple projections of the recent past into the future.

I have no reason not to believe this to be true.

But I think there is something a little wrong with this logic:

You can ask yourself one of the key questions: What are the odds of a one-day crash of at least 12% in the U.S. stock market over the next six months?

You probably answered at least 10% — even though that is roughly 10 times the likely chance of a disastrous daily crash in the coming six months, based on the historical record. (The 87 years from 1929 through 2015 consisted of 174 six-month periods. But, with only two single-day crashes of at least 12% over that span, such declines occurred in just over 1% of the half-year periods.)

Remarkably, professional investors exaggerate the odds almost as badly as individual investors do. Over time, both groups overall have tended to put the odds of a crash at around 20%, with the institutional investors’ estimates ranging only about one to three percentage points below that.

Again, I have no problem with the statement that most people, in a given year, overestimate the chance of a stock market crash.  20%, for any random year, is likely a high estimate.   But that is not the same as saying it is a high estimate for this year.  One could argue that we know more about our current year than to treat it simply as a random year.  For example:

  • We are in the midst of what is soon to be the 2nd longest bull market in the market's history.  Are the odds of a significant correction higher on a particular day 2500 days into a bull market than on a random day in history?
  • Stock prices have risen faster than earning for 5 years.  Is a market correction more likely in that environment than on a random day?
  • Shiller's CAPE is close to the third highest it has ever been, and at a level that has nearly always been followed by a large correction.  Should I treat today's risk of correction as just the last century's average or is it realistically higher?

I don't think 10-20% is a bad estimate given where we are.


  1. morganovich:

    "Stock prices have risen faster than earning for 5 years. Is a market
    correction more likely in that environment than on a random day?"

    this is not the right way to frame the question. you cannot answer this without reference to the starting state and the absolute value relative to growth rates and other exogenous factors.

    to take an extreme example, let's say the historical S+P earning multiple is 15.

    let's say 5 years ago SPX EPS was $100.

    it rises to $125. that's a 25% rise.

    stocks rise 150% in that period. are they now unusually risky?

    well, that depends on where they started. if they had a 5 p/e 5 years ago, they are still only a 10 and very cheap historically.

    that effect would be greatly compounded by the far lower than average risk free rate which, all else equal, should lead to a higher than typical P/E for the market.

    it's always tempting to try to simplify these things to a couple variables, but to do so generally gets you gibberish or confirmation bias.

    CAPE is not a useful tool. it's a 10 year trailing average. in real time, it tells you damn near nothing useful.

    pull it up for the 90's.

    it was already giving warning signals in 1995. sell then and you missed the greatest stock run in living memory. you sold 5 years early.

    it's WAY too slow a MA to be at all useful. it tends to be a trailing, not a leading indicator.

    in terms of "this is a long bull market" that's not really meaningful.

    2008-9 was the sharpest selloff in living memory. the recovery from it has actually been quite slow.

    the SPX is only about 32% above the 2007 highs.

    inflation adjusted, that's barely double digit returns in 8 years.

    i'm not trying to make any statement about the current market being cheap or dear or particularly risky or not by saying this.

    fwiw, my 2c is this: the market is somewhat bifurcated just now. there is some very cheap stuff (smallcaps, energy, some biotech) and some very expensive stuff (consumer facing internet, etc).

    it's kind of a mixed bag.

    bank leverage is WAY lower than in most of recent history.

    but macro issues are pretty dire and recession risk is very real.

    i would really hesitate to try and assign a % risk to the market.

    that's really a game for mugs and talking heads.

  2. A. Ames:

    Coyote: Thanks for all the neat essays.

    Greenspan noted that the 10y Treasury corresponds with the stock market P/E or about 50 today. The DIA is paying 2.5%, which looks pretty good compared to zero or even negative for some currencies. The current CAPE is at the 87% of its cumulative distribution, which is not a looming disaster so long as the banks control interest rates. Given that prices are being driven more by P/E, not E, we can expect higher than average volatility. I will hold at least 50% stocks with my seat belt fastened until the landing.

  3. mlhouse:

    Bubble markets have always demonstrated that p(t) is a function, amongst other things of p(t-1) and that the relationship is positive.

  4. mesaeconoguy:

    Plus, let’s not forget the worldwide proclivity for mass interventionism by central banks.

    The amount of liquidity injected and actions taken have so distorted relative asset prices that traditional price signals are no longer meaningful, rendering them ineffective at predicting or signaling trouble.