Portfolio theory and the business cycle: Determining ideal allocation to stocks?
Historically, there is a level of mean reversion with stock prices. So the expected return of a market portfolio changes with boom and bust periods.
Is there a generalization of portfolio theory that incorporates the business cycle? So for example now since there has been several years of good performance in stocks, it seems sensible to hold somewhat higher percentage of bonds than I have during worse times. Is there a precise formulation of this?
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Economic cycles are highly predictable, but it takes many years of study, and there are many variables involved.
Obviously, upon examination of the historical returns of the market, being only half correct about buying near bottoms and selling near tops is more profitable and less variant than buy & hold.
If you've spent many decades on this Earth and are honest with yourself, you can sense the various times. Try now: are we closer to the top or the bottom? It should be obvious.
Standard Markowitz's portfolio optimization takes trend into account, not mean reversion.
Otherwise, since a portfolio is a linear combination of your individual assets, you could 1st model them separately and than establish a second-layer criteria for weighting.
For the 1st layer, mean reversion (as well as trend) of returns can be captured with a ARIMA model, and for the 2nd layer, you could use the Kelly criterion, for instance.
A more direct approach to mean-reversion portfolio selection is working with pairs trading. I'm not linking any materials as those topics are plentiful on the web.
...If that's still not the answer you're looking for...
The problem with predicting economic cycles is that, they are long, and we hardly have a sufficient measured history to forecast anything reliable. In order to predict the mean reversion of a stock or bond market cycle, you've got to measure their long-term mean first. And there you'll have disagreements right on the start...
Some researchers (see Jeremy Siegel) have tried to measure the long-term mean of returns for various asset classes. Some argue that stocks are the long-run winners and that CAPM explains that, but others say that's just questionable, since measurements go just as far as the western countries (US, UK, etc.) have thrived. Other countries have much more recent economic records.
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