Financial Mathematics Text

Monday, January 20, 2014

CAPE - An Alternative Calculation

Today I want to look at an alternative way to calculating the Cyclically Adjusted Price to Earnings Ratio or CAPE for short. The standard approach to CAPE suffers from a few drawbacks and I think the calculation I'm proposing can address some of those drawbacks.


The CAPE calculation has been popularized by recent Nobel prize winner Robert Shiller. In Irrational Exuberance, Shiller used the measure to indicate overvaluation in the stock market. You can view a regularly updated of this chart here. The data is updated by Robert Shiller here.

The calculation behind this is to take the earnings figures for the last 10 years in order to "normalize" them and then look at that price ratio:
$$\text{CAPE} = \frac{\text{Price}}{\text{Average 10 Years Earnings}}$$
The idea behind this is that if you're looking to buy a business, you're not just interested in earnings were last year; you want to see how earnings behave over an entire business cycle. That's where long-term value lies.

Now Shiller actually looks inflation adjusted numbers (more on that below). Here's what the chart looks like:

Observe that the nominal CAPE calculation is often higher than Shiller's inflation adjusted one especially during periods of high inflation (e.g. late 70's to early 80's).

You can find a version of this chart (CAPE Real) updated daily here.

This idea goes back to Graham and Dodd in Security Analysis. There is even a suggested general strategy:
Can the analyst exploit successfully the repeated exaggerations of the general market? Experience suggests that a procedure somewhat like the following should turn out to be reasonably satisfactory:
  1. Select a diversified list of leading common stocks, e.g., those in the "Dow-Jones Industrial Average."
  2. Determine an indicated "normal" value for this group by applying a suitable multiplier to average earnings. The multiplier might be equivalent to capitalizing the earnings at, say, twice the current interest rate on highest grade industrial bonds. The period for averaging earnings would ordinarily be seven to ten years, but exceptional conditions such as occurred in 1931-1933 might suggest a different method, e.g., basing the average on the period beginning in 1934, when operating in 1939 or later.
  3. Make composite purchases of the list when the shares can be bought at a substantial discount from normal value, say at 2/3 such value. Or purchases may be made on a scale downward, beginning say, at 80% of normal value.
  4. Sell out such purchases when a price is reached substantially above normal value, say, 1/3 higher, or from 20% to 50% higher on a scale basis.
So that would be one way one might use CAPE.

CAPE Criticism

Now CAPE is not without its criticisms. One consideration, and one that Graham was well aware of, was whether or not the historical average is a good indication of the future.

But there are other problems which I think Jesse Livermore has laid out a nice case for: Fixing the Shiller CAPE: Accounting, Dividends, and the Permanently High Plateau.

The two main issues here are as follows:

1) Accounting practices have changed over time and earnings are no longer measured the same way.

What this amounts to is a different operational definition is used to define earnings across time. So there is no reason to suppose that the measures are even comparable. Livermore suggests that using Pro-Forma earnings provided by Bloomberg may be preferable here.

2) Dividend Payout / Growth

A company that is significantly growing earnings will ultimately have a higher CAPE than a company which is not growing. Since companies now have lower dividend payout ratios, we should expect to see higher earnings growth (either from higher investment or EPS growth via share buybacks) and therefore higher CAPEs.

Proposed Solutions to Criticisms

So far I've seen two solutions which attempt to address the first criticism. None of the solutions proposed have addressed the second criticism.

The first I've already mentioned and that is to look at a different measure of earnings. This is what Jesse Livermore proposes here.

A second solution is proposed by Eddy Elfenbein and that's looking at Cyclically Adjusted Dividend Yield. Here's what the chart looks like (using both nominal and inflation adjusted figures):

This addresses the accounting issue. But it suffers from two considerations related to growth.

1) As you can see in the difference between nominal and real dividend yield calculation, periods of high inflation result in lower CADY (analogous to what we saw with CAPE).

2) Dividend payout ratios are much lower now. This means that companies are retaining more earnings and therefore should have higher dividend growth rates in the future.

This I largely believe has more to do with an increase in share buybacks. So total payouts (dividends + share buybacks) may be about the same since buybacks are roughly equivalent to reinvested dividends.

In any case, both proposed solutions fail to address the second criticism regarding growth.

CAPE - An Alternative Calculation

I'm proposing a solution which will address the second criticism (and the idea can be combined with either Livermore or Elfenbein's solution to the first criticism to address both). This proposal offers a different approach to "normalizing" earnings.

The key insight here is that earnings are driven by earning a return on book value (ROE). So instead of averaging earnings we're going to average ROE and then multiply that by current book value:
$$\text{Normalized Earnings} = \text{Average}(ROE) \times BV$$
While I came up with this approach independently, it is not without precedent (see here from Prof Damodaran1).

The implicit assumption here is that past ROE figures will be a decent indicator of future ROE. And the earnings we can expect are, therefore, going to be ROE multiplied by the current book value.

This addresses the growth problem because the company now has more assets (factories, stores, restaurants, etc) which it can generate problems now than it did 10 years ago. 

So what does this new CAPE look like? Here's a look at it:

It's fairly well correlated with Shiller's CAPE, at least for the time period for which I had data. The book value data was taken from here.

Ideally we'd want to look at a longer data series than what I have access to.2

In case you're curious, here's what the ROE calculations looked like:

In any case, there are some criticisms of this alternative CAPE that are worth pointing out.

1) It's still subject to the criticism that our measurement of earnings is not the same across all periods. So using something like the Pro-Forma earnings or dividends (total payouts including buybacks as well) might address that issue.

2) Another consideration that may come up is whether or not there is consistency in balance sheet data. If there are differences in accounting practices, the book value data may not be consistent across time.

3) I've already mentioned this in a footnote, but it's possible that ROE metric will vary as companies increase or decrease leverage. This has the added effect of making companies more or less risky. Presumably, the CAPE should be lower (higher) when more (less) leverage is used.

Concluding Remarks

In any event, I think this approach has advantages over the typical calculation and should be given consideration. It also has the advantage of working better for individual stocks, especially when there is a significant amount of growth involved.

1 Prof. Damodaran uses ROIC and invested capital. It's basically the same idea, however, it has the advantage of using an unlevered return on capital metric. ROE will vary as companies vary leverage.
2 If someone has a longer series on book value for the S&P 500, please do the calculations or send me the data and I'll update the blog. Thanks.

No comments:

Post a Comment

Some common OpenID URLs (no change to URL required):