Choosing Temperature Variables as Asset Pricing Factors
Summary
The document discusses how to represent a proposed temperature effect when testing an asset pricing model. It distinguishes a time series of temperature levels from changes in temperature, such as a day-to-day difference or percentage change, and from an indicator for extreme conditions. The choice depends on the hypothesis: levels can represent conditions associated with returns, changes can represent a response to temperature movement, and a binary variable can isolate unusually hot or cold days.
It also considers a Hot-minus-Cold portfolio formed by sorting stocks on headquarters temperature and subtracting the cold-stock portfolio return from the hot-stock portfolio return. That spread is a return factor, though the answer questions what it adds to the analysis. The discussion says cross-sectional tests can use non-return explanatory variables, while time-series factor regressions call for return factors. It does not develop the excess-return requirement or give empirical evidence, so those issues remain unresolved.
Key ideas
- A temperature level, its change, and an extreme-temperature indicator encode different hypotheses.
- Cross-sectional asset pricing tests can use explanatory variables that are not returns.
- A time-series factor used in the described framework must be expressed as a return.
- A long-hot, short-cold portfolio produces a return spread, but its incremental value is uncertain.
- The document does not settle when excess returns are necessary.
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Full text
# When are factors returns in asset pricing and how do we construct them?
# When are factors returns in asset pricing and how do we construct them?
I am very certain that the temperature in New York's Central Park plays a super-significant role in stock returns, so I take its daily averages and I want to test it in factor model.
Cochrane (section 12.2, p. 235) says I can use cross-sectional regressions to test this whether my "factor" is a return or not. However, to use time-series regressions I must make my new factor a return. How do I make my factor a return?
Next, suppose I know each stock's headquarter's building average daily temperature. I sort the stocks every day based on their temperature. I construct the Hot-minus-Cold factor by subtracting the (equally-weighted) averaged return of the 1000 coldest stocks from the 1000 hottest stock. This Hot-minus-Cold is a return, right? Is this type of process the only way to construct factors that are returns? In the last case, when is it necessary to use excess returns?
## Answer by RandyF (score 2)
https://quant.stackexchange.com/a/25030
When he is saying that the factor analysis requires returns, he is considering how the change in one asset would imply a change in another asset. You can model this the same way by modeling a change in temperature day over day, in which the "returns" would be $temp_t - temp_{t-1}$ or $\frac{temp_t}{temp_{t-1}}-1$.
However, if you believe the stock market performs worse at lower temperatures in general, you could just model the temperature and not consider just the change. In this case, you would be predicting stock price movements by looking at the actual temperature. In this case, the explanatory variable would just be $temp$. Finally, you could model the significance of the effect on returns under adverse conditions by using a Boolean for extreme temperatures. For instance, you could use 1 as your explanatory variable if the temperature is above 100 degrees or below 32, and 0 if it's a nice comfortable (32, 100).
The hot minus cold index that you are looking at is interesting, but I believe is unnecessary, and I'm not sure what it would add.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.