The cyclically adjusted PE ratio (CAPE) is a modification of the PE ratio to account for the effect on profits of the economic cycle.
The PE ratio calculated at any point in time is affected by the current state of the economy. This effect is, of course, particularly strong in the case of cyclical shares.
The simplest, and most widely used approach is to use a simple average of annual EPS over a long period, usually ten years. It is also common practice to adjust the EPS into real terms, essentially making this a long term PE corrected for inflation. Only the EPS needs adjustment, not the price.
The cyclically adjusted PE often compared over several years to look at historical trends and, especially, to identify the level it would go to if it reverts to mean. When doing this each year's number is calculated using the previous ten years, so the end result is a moving average.
There are more sophisticated methods of cyclical adjustment available than simply using a ten year period and hoping that it is long enough to average out the effects of the economic cycle. These may be difficult to apply to the available data given how volatile markets are and how many different variables affect them.
Uses of the cyclically adjusted PE
The cyclically adjusted PE is most commonly used as a measure of the level of markets. The expectation is that it will revert to mean, so the current level is a good indication of whether markets are over-valued or under-valued. This use of CAPE is similar to how Tobin's q is used. They can be used in conjunction to see whether they both provide the same signal: they tend to do so, and graphs of the two are often very similar.
Unlike q, cyclically adjusted PE is also useful as a valuation ratio at the level of particular shares. In this context, it is just the long term PE, possibly adjusted for inflation. It would not be usual to look for mean reversion in this contest, and it is used in much the same way as other variants of the PE ratio.