*Price earnings*

#### It’s just a p/e

Graham and Dodd point out in their 1934 book *Security Analysis*, price earnings ratios can vary a lot because earnings vary a lot over the business cycle. Graham and Dodd suggested employing a multiyear average of earnings.

In 1988 John Campbell and Robert Shiller published a paper using a ten year average. Today Shiller publishes his CAPE, a cyclically adjusted (for inflation) price earnings ratio—sometimes referred to as the CAPE 10. It averages the most recent 10 years’ earnings and adjusts them for inflation.

Shiller says that: “The relation between price-earnings ratios and subsequent returns appears to be moderately strong…” and that, “We believe, however, the relation should be regarded as statistically significant.” (Shiller, 2005 Second Edition)p.187. There are some technical questions about the sample size.

Shiller’s idea was to use a long term average of CAPE as a benchmark. The determinant he selected as to whether CAPE is high or low is its 100 year average which today is about 16.5. Graham and Dodd’s idea was to use a multiyear average of earnings to smooth out the business cycle, not to use a 100 year average as a benchmark.

Nowadays CAPE is frequently referred to in the financial press and by market strategists in discussions about whether the stock market is expensive and what investors can expect in the years to come. It has a credibility that comes from the fact that its creator Robert Shiller has a high public profile and is a Nobel Prize recipient.

However, a statistically significant relation does not mean that by itself CAPE is a useful tool or indicator.

CAPE is a price earnings ratio. Price earnings ratios are a frail and shifting basis for determining fair value. They do not force investors to think through all the factors that go into a deep assessment of fair value. See my recent post: What is the right price earnings ratio?

What’s more, the 100 year average value as a benchmark is suspect.

**Back to basics**

Price earnings ratios are what some call a heuristic. That fancy word simply means a price earnings ratio is a rough rule of thumb. It is not the best way to assess the value of a business. Warren Buffett has written: “[Intrinsic value is] an all-important concept that offers the only logical approach to evaluating the relative attractiveness of investments and businesses. Intrinsic value can be defined simply: it is the discounted value of the cash that can be taken out of a business during its remaining life.” (Buffett W. E., 1998)p.187.

Note the words ‘can be taken out of a business’. This refers to Buffett’s concept of Owner Earnings discussed here.

The critical thing, for present purposes, is that in any valuation we are looking at the present value of future cash flows and a discount rate is required.

**Discount rates idea**

If you thoroughly understand discount rates you can skip this section.

A discount rate is simply a rate used to discount future cash flows to the present time. It represents the rate of return the investor requires on his investment to provide a suitable return and compensate for risk. It is made up of a risk free rate and an appropriate risk premium.

The risk free component is not as easy as one might think. As well, the risk adjustment is problematic.

The best way to understand how a discount rate and the ‘rate of return an investor requires’ connect up is to use a simple investment example. Suppose you have $200,000 to invest and choose to put $100,000 into a bond with an expected total return of 4% over five years and $100,000 into a stock with an expected total return of 8% over the same period. If the investments works out as expected, the bond will accumulate to $121,665.28; the stock to $146,932.80.

What this little calculation has given us is the future value of an investment we make today under two different total return assumptions.

The flip side of this is to calculate the present value of future cash flows. Instead of compounding forward we discount backwards. We solve an equation for the present value of future cash flows by using a discount rate. The discount rate is the ‘expected return’.

It is perfectly intuitive to understand that a 4% discount rate produces a higher present value of future cash flows than an 8% discount rate. Put another way, for an investor to receive any particular set of future cash flows, if the expected return is less, they need a higher present value.

Put yet another way, for an investment that only needs a 4% return to attract investors, the present value of the set of future cash flows is higher today. For an investment that needs a return of 8% to attract investors the present value of the set of future cash flows will be less.

The difference between the two, the 4% bond and the 8% stock, is the comparative riskiness of the two investments. For a given set of future cash flows the present value of the bond is higher because it is less risky and future cash flows are discounted at a lower rate.

There is an art to choosing the right discount rate for a Discounted Cash Flow (DCF) calculation valuing common stocks. The first component of the discount rate is the risk free rate. This is the pure and simple time value of money. The ten year U.S. Treasury bond yield is usually good market-based evidence for a long term risk free rate. However, it frequently needs to be normalized, such as in the climate of artificially depressed long term rates.

Once the analyst has a normalized risk free rate they need to add something to that rate to reflect the riskiness of common shares generally and the riskiness of the company in particular. For the stock market as a whole one uses the equity risk premium.

The DCF approach is superior to the use of ratios, like the price earnings ratio, for two reasons: firstly, it is the best way to assess the intrinsic value of an investment; and secondly, it forces the analyst to turn their mind to the key inputs, viz, the cash flows that can be taken out of the business for many years to come and an appropriate discount rate.

**Key point**

**Whether an individual stock or the stock market as a whole is overpriced, fairly priced or underpriced, is sensitive to an appropriate discount rate composed of a risk free rate and a risk premium. **That is, lower discount rates lead to higher valuations. The fair value of the stock market in part varies with interest rates, up and down. Note, I say, ‘in part’. It varies with other things as well.

As ten year treasury yields vary so do discount rates. A higher discount rate lowers valuations and should lower the benchmark for price earnings ratios and CAPE. Conversely, lower interest rates should increase the benchmark used for price earnings ratios including CAPE.

Let’s look at a chart of 10 year U.S. Treasuries from 1950 to the present. I have highlighted in green the tremendous rise in risk free rates from 1950 to 1982. I have also highlighted in green the relentless decrease in risk free rates from 1982 to the present.

No sane person would argue that an appropriate risk free rate today for use in a discounted cash flow valuations today should be the average of the rates over the last 70 years.

Now let’s look at CAPE. I have superimposed in green the rough slopes of the 10 year U.S. Treasury rates for the same periods.

It is quite clear that from 1950 to 1982 CAPE is generally going down. From 1982 to present, CAPE is generally going up. This suggests to me that CAPE is inversely correlated with 10 year U.S. Treasury bond yields.

https://ww.multpl.com/shiller-pe

Based on this, I think it wrong to think that an average CAPE taken from any period in history provides a good benchmark today. It suggests that like DCF valuations, CAPE is discount rate sensitive.

What follows is that a CAPE ratio of 26.91 does not prove the stock market is overpriced. The stock market today may be overpriced or underpriced. CAPE using a historic average as a benchmark just doesn’t tell us one way or another.

It could be argued that using a long term average of CAPE as a benchmark smooths out such things as changing interest rates, changing rates of inflation and different economic conditions. But, by smoothing out these differences, an average such as 16.5 loses the ability to be alive to a changing world. This doesn’t make sense to me.

**Conclusion**

One simply has to avoid getting hung up on the 16.5 long term average.

This post is the first of a three part series on the proper use of CAPE. The next two posts are Problems with CAPE – Part ll and Problems with CAPE Part lll

For readers wanting to dig deeper into the subject of how investors can deal with ever changing outlooks for investment returns take a look at Part 5: Asset Management

and specifically Chapter 28. Asset allocation

and Sections:

28.04 Other approaches to varying stock/bond allocation – CAPE,

28.06 Conclusion regarding CAPE

To read more about stock valuations, interest rates and ratios, see

Chapter 37. Stocks as disguised bonds and

Chapter 38. The Problem of Determining Intrinsic Value and

Chapter 39. Use of ratios to value shares and

Chapter 37.05 Stocks vs bonds – more and

Section 38.04 Discount rate

Section 38.06 Risk premium

Want to dig deeper into the principles behind successful investing?

Click here for the **Motherlode – introduction**.

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