Past market variance and asset prices

Over the long run, past market variance is better at predicting excess market returns than other accepted predictors, including the ratio of consumption to wealth, said Federico Bandi, associate professor of econometrics and statistics. “Past market variance has predictive ability for future long-run market risk premia” Bandi said during a presentation hosted by the Initiative on Global Markets at Gleacher Center on May 17.

If consumption is high with respect to wealth, people expect high returns on wealth or low consumption growth, he said. “When you look at the relationship between excess market returns and the consumption-to-wealth ratio, you see quite a bit of predictability in the sense that the consumption-to-wealth ratio highly correlates with future excess market returns,” Bandi said. “But it does so less than past market variance when you look at long horizons.”

The longer the horizon, the more reliable past market variance becomes as a predictor, he said. “As you go from one month to 10 years, say, the relationship between excess returns on the market, where the market may be measured by any accepted index, and past market variance increases with aggregation” Bandi said.

Furthermore, the betas, which are measures of the relation between asset returns and factors driving prices, appear to be economically meaningful when computed conditional on past market variance, he said. This finding occurs both over the long term and over business cycle frequencies, two to five years, Bandi said.

“Normally, betas are computed unconditionally,” he said. “When you price a cross-section of assets, if you compute betas conditional on past market variance rather than unconditionally, you obtain pricing errors that are drastically smaller than the pricing errors that you would obtain if you didn’t condition on past market variance.”

Intuitively, past market variance works because it implies higher risk, i.e., higher conditional betas, for portfolios of small and value firms (which have relatively higher average excess returns) in bad states of the economy, Bandi said. “If you compute unconditional betas with respect to consumption growth, for example, the betas do not appear to be higher for portfolios of firms with higher average excess returns and do not align properly with those average excess returns,” he said. “As is well known, this is why the Consumption CAPM model, arguably the purest pricing paradigm, fails.”

One way to correct this problem is to allow for time-variation in the betas, Bandi said. “Existing work has suggested that allowing for notions of conditional (on the state of the economy) risk, as implied by conditional betas, might improve on the fit of conventional pricing models. This (still very preliminary) work with Benoit Perron (University of Montreal) is showing that past market variance can serve as a useful conditioning variable performing as well as, or better than, existing, successful variables, such as the consumption-to-wealth ratio. “

The key takeaway of Bandi’s presentation was his analysis of asset prices as conditional to different states of the market and the economy, said Zsolt Bendel, ’08, who analyzes investment risk for Northern Trust, which sponsored the talk. “I was especially interested in his final conclusion that different assets behave differently based on whether the markets are in bad times or in more usual or normal times,” Bendel said. “For me, more important than the number-crunching was the big picture. And to understand it better, I actually have to review his research.”

--Phil Rockrohr