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Paper: "Financial Variables and the Predictability of Stock and Bond Returns: An Out-of-Sample Analysis"

Most studies of the predictability of stock and bond returns rely on in-sample tests. In this paper, we test the ability of ten financial variables that have appeared in the extant literature to predict S&P 500 and CRSP equal-weighted stock returns out-of-sample over horizons of 1-10 years. We also test the ability of two financial variables, the term and default spreads, to predict long-term corporate bond real returns out-of- sample. For S&P 500 returns, we identify three variables with out-of-sample predictive ability: the equity share in total new debt and equity issues, term spread, and market value-to-net worth ratio ( Fed q ). For CRSP equal-weighed returns, we find that the dividend yield, price-earnings ratio, Fed q, and equity share all exhibit significant out-of-sample predictive power. In addition, the default spread exhibits significant out-of-sample predictive power for long-term corporate bond returns. As out-of-sample tests of predictive ability raise the bar relative to in-sample tests, our results strengthen the case for stock and bond return predictability.


Review by Alex Castaldo, PhD:
This paper is interesting methodologically for two reasons.  First, the regressions are estimated during one period (1927-1963) and then tested during another period (1964-1999).  This is helpful.  However, it is not the way an investor would actually operate, they would probably re-estimate the regressions each year, a more laborious procedure than the professors'.

The second interesting point is the use of recently developed statistical tests for forecast assessment and references to the literature thereon that the scholarly might be well advised to read.

The main conclusion for S&P prediction is:

In predicting one year returns only the Equity Share in New Issues of Equity and Debt of Baker and Wurgler (recently featured on the DailySpeculations Web site) was found to work.  Three other variables, the Dividend Yield, the Price Earnings Ratio, and the Q ratio computed by the Fed only worked at horizon of 8 years or more.  (As will be familiar to readers of PracSpec, such long-horizon-only predictability is of limited speculative value and is suspect due to overlap; it also raises the question of why it would take 8 years for the market to adjust to such information).

When applied to the CRSP EW index, which includes smaller stocks than the S&P500, additional variables are found to have predictive value.  However this finding may have limited practical import because the CRSP EW is not really an investable index.

Stopping the study at the end of 1999, when 4 full years have already elapsed, is annoying to the practically minded, but is fairly standard for academic work.

Overall an interesting paper. (March 2004)

Comment from Vic:
I don't believe any forecasts of 25 yearly returns with 8 and 10 years overlap could possibly be significant. And whatever tests have been developed for same are totally flawed. The stopping point is arbitrary, the methods have been selected retrospectively, they're all deflated by some crazy CPI adjustment (retrospective or prospective) that introduces biases, and all the results would have led to randomness on top of randomness, a hodgepodge, like a consensus of mutual back slapping of each other's Web site and professorial affiliation.

Let us hope that one of the big fund-of-fundists backs this method as an augmentation to the long wait that may be forthcoming to profit from the derivative expert's work during this environment of asset diminution and seminar speaking and fee income for all.

Comment from Dr. L:
Nice response. Here's a somewhat shorter reply:

Q: How many out-of-sample backtests does it take before they become in-sample?
A: Two.

Comment from Alix Martin:
I agree with Dr Lo's comment. The very process of academic publication actually makes the data not so out of sample, as we wouldn't have heard about it if it didn't concur with the in-sample hypothesis.

The issue is stability of certain predictive relationships. I don't think using only two time-periods is likely to tackle this issue the most conclusively.

To try to get a picture of such stability, I graphed a trailing 10-year correlation between PER and next year real SP return. The correlation happily swings from -60% to +60%, with a sobering effect on any thought of using it as a market timing indicator. I would like to try that with the supposedly more predictive variables if I can find the data.

Besides, Rapar and Wohar's point doesn't seem to be that they can predict the market, but rather that they used the right statistics. I certainly can't reject this hypothesis.


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