Sunday, July 27, 2008

Lettau-Ludvigson vs. a Time Trend

Martin Lettau and Sydney Ludvigson’s “Consumption, Aggregate Wealth and Expected Stock Returns” finds that the ratio of consumption to wealth forecasts stock returns. In essence, consumption along with labor income form a more useful “trend” than the level of dividends or earnings. They find this factor can explain the 25 Fama-French portfolios, that is, the spread we observe when stocks are sorted by size and book/market value. Cochrane calls this a 'stunning result' in his new text on Asset Pricing.

But the Fama-French result was conspicuously absent in their ultimate Journal of Finance paper. And Brennan and Xia produced this devastating critique:

The empirical evidence that the consumption–wealth ratio, cay, has strong in-sample predictive power for future stock returns has been interpreted as evidence that consumers take account of future investment opportunities in planning their consumption expenditures. In this paper we show that the predictive power of cay arises mainly from a “look-ahead bias” introduced by estimating the parameters of the cointegrating regression between consumption, assets, and labor income in-sample. When a similar regression is run, replacing the log of consumption with an inanimate variable, calendar time, the resulting residual, which we label tay, is shown to be able to forecast stock returns as well as, or better than, cay. In addition, both cay and tay lose their out-of-sample forecasting power when they are re-estimated every period with only available data.

Lettau and Ludvigson reply is threefold. First, they say that that the forecasting power of cay for future returns cannot be spurious merely because the full sample has been used to estimate the cointegrating coefficients. Second, tay likely contains more economic content that the authors realize. Lastly, they assert that those in-sample tests are more credible than out-of-sample tests for assessing forecasting power.

I think the bottom line is that when a time-trend does better than your economic variable as an explanation of the data, you're doing it wrong.


  1. Anonymous10:53 PM

    by now it should be clear we won't see a tradable, persistent, predictive out-of-sample method in our life time. the only time tested method i know of is that applied with success by a young fellow in omaha. so let's move on.

    what do you think is the impact of recent increased information availability on the markets? ( see all the financial blogs coverage on GSE's, WaMu etc. plus the macro economic decisions/conspiracy theories sliced and diced and available to read to the last village in china etc.) do you think it makes the market more efficient or less?

    I wonder if a theory can be constructed using this analogy?

  2. I've had a google alert set up for "Martin Lettau" for a couple of years now, hoping to see some progress in this area (that's how I found this post). If you step back from the problem a bit, it seems unlikely that anything could ever predict equity returns. In what field can people make accurate long-term predictions about human affairs?

    It's too bad about cay though, I thought that was a great stat. Are there other applications for it besides market returns?

  3. Anonymous4:00 AM

    In what field can people make accurate long-term predictions about human affairs?

    I can think of a few ones. For example, water demand is commonly calculated to 25 years ahead. The use of a road. Marriages. Voting patterns. Religion. Language. People has extreemely stable habits to the point of boring predictability.