E-piphany

Point forecasts are evil.

Economists are asked to make point forecasts, and they oblige. But it’s a dumb thing to do, and they know it. Practitioners, who should know better, rely on these point forecasts far more than they should. Because, in economics and especially in markets, there are enormous error bars around any reasonable point forecast, and those error bars are larger the shorter-term the forecast is (if there is any mean-reversion at all). I can no more forecast tomorrow’s change in stock market prices than I can forecast whether I will draw a red card from a deck of cards that you hand me. I can make a reasonable 5-year or 10-year forecast, at least on a compounded annualized basis, but in the short term the noise simply swamps the signal.[1]

Point forecasts are especially humorous when it comes to the various year-end navel-gazing forecasts of stock market returns that we see. These forecasts almost never have fair error bars around the estimate…because, if they did, there would be no real point in publishing them. I will illustrate that – and in the meantime, please realize that this implies the forecast pieces are, for the most part, designed to be marketing pieces and not really science or research. So every sell-side firm will forecast stock market rallies every year without fail. Some buy side firms (Hoisington springs to mind) will predict poor returns, and that usually means they are specializing in something other than stocks. A few respectable firms (GMO, e.g.) will be careful to make only long-term forecasts, over periods of time in which their analysis actually has some reasonable predictive power, and even then they’ll tend to couch their analysis in terms of risks. These are good firms.

So let’s look at why point forecasts of equity returns are useless. The table below shows Enduring’s year-end 10-year forecast for the compounded real return on the S&P 500, based on a model that is similar to what GMO and others use (incorporating current valuation levels and an assumption about how those valuations mean-revert).[2] That’s in the green column labeled “10y model point forecast.” To that forecast, I subtract (to the left) and add (to the right) one standard deviation, based on the year-end spot VIX index for the forecast date.[3] Those columns are pink. Then, to the right of those columns, I present the actual subsequent real total return of the S&P 500 that year, using core CPI to deflate the nominal return; the column the farthest to the right is the “Z-score” and tells how many a priori standard deviations the actual return differed from the “point forecast.” If the volatility estimate is a good one, then roughly 68% of all of the observations should be between -1 and +1 in Z score. And hello, how about that? 14 of the 20 observations fall in the [-1,1] range.

Clearly, 2017 was remarkable in that we were 1.4 standard deviations above the 12/31/2016 forecast of +1.0% real. Sure, that “forecast” is really a forecast of the long-term average real return, but that’s not a bad place to start for a guess about next year’s return, if we must make a point forecast.

This is all preliminary, of course, to the forecast implied by the year-end figures in 2017. The forecast we would make would be that real S&P returns in 2018 have a 2/3 chance of being between -10.9% and +11.1%, with a point forecast (for what that’s worth) of +0.10%. In other words, a rally this year by more than CPI rises is still as likely as heads on a coin flip, even though a forecast of 0.10% real is a truly weak forecast and the weakest implied by this model in a long time.

It is clearly the worst time to be invested in equities since the early 2000s. Even so, there’s a 50-50 chance we see a rally in 2018. That’s not a very good marketing pitch. But it’s better science.[4]

[1] Obligatory Robert Shiller reference: his 1981 paper “Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends” formulated the “excess volatility puzzle,” which essentially says that there’s a lot more noise than signal in the short run.

[2] Forecasts prior to 2009 predate this firm and are arrived at by applying the same methodology to historical data. None of these are discretionary forecasts and none should be taken as implying any sort of recommendation. They may differ from our own discretionary forecasts. They are for illustration only. Buyer beware. Etc.

[3] The spot VIX is an annualized volatility but incorporating much nearer-term option expiries than the 1-year horizon we want. However, since the VIX futures curve generally slopes upward this is biased narrow.

[4] And, I should hasten point out: it does have implications for portfolio allocations. With Jan-2019 TIPS yielding 0.10% real – identical to the equity point forecast but with essentially zero risk around that point – any decent portfolio allocation algorithm will favor low-risk real bonds over stocks more than usual (even though TIPS pay on headline CPI, and not the core CPI I am using in the table).