Long Term Equity Valuation: Replacing the P/E for the DR3

By: Francois Soto | Mon, Nov 2, 2009
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Is the S&P 500 undervalued from the current level? To answer this question, one might be tempted to look at the actual P/E (Price / Earnings) and establish a comparison with its historical data. You most likely have seen this chart before:

Source: Bloomberg, EMphase Finance

The chart above is using operating earnings for the P/E calculation. Standard & Poors publishes two earnings formats: operating earnings and reported earnings. Operating excludes write-off charges while reported includes them. In other words, operating earnings are higher and reported earnings are lower.

P/E Advantages

P/E Shortcomings

Proposed Solution

Is there a better metric for long term equity valuation than the P/E? Yes, the Dynamic Real Required Return - DR3. The result is displayed on this chart:

Source: Bloomberg, EMphase Finance


The DR3 is simply the real risk-free rate + real expected market risk premium.

DR3 vs. CAPM

You probably recognized a part of this equation and said: Hey, you just wrote the CAPM equation! Yes, but there are two major differences: 1) CAPM is keeping the parameters static (except beta) while the DR3 is making them dynamic. 2) CAPM is using nominal returns while the DR3 is using real returns.

DR3 = Dynamic Real Required Return.
β = Beta is equal to 1 because we are valuing the S&P 500. In this case, it can be removed from the equation without a problem.
Infl = Inflation using the CPI All Items. It is estimated with a trailing CAGR (Compound Annual Growth Rate) over the last ten years.
E(Rm) = Expected return on S&P 500. It is estimated with a trailing CAGR (Compound Annual Growth Rate) over the last ten years.
Rf = Risk-free rate using the US Government 10-Year yield. It is estimated with a moving average over the last ten years.

DR3 Advantages

DR3 Shortcomings


When investors are greedy and require too much real return on equity (more than ten percent), this signals markets are overvalued. It does not mean the markets will collapse right away, although it might be the case as seen in 1929 and 2000. The DR3 should be used in conjunction with other indicators.

When investors are fearful and think the real return on equity is going to be grim (less than ten percent), this signals markets are undervalued. In theory, no rational investor would invest when expected real return on equity is declining and negative but they still do. Market participants are risk seeking and irrational.

When the DR3 goes from overvalued to neutral, equities should underperform treasury bills or bonds or gold. When the DR3 goes from undervalued to neutral, equities should outperform treasury bills or bonds or gold. Further analysis is required to learn more about the other properties of the DR3.

The DR3 barely touched the undervalued level in March 2009 and is now increasing slightly since then. Historically, the DR3 previously reached readings as low as -17% twice. Consequently, it is not impossible to see further declines in the future and reach valuation levels that will be more attractive.



Francois Soto

Author: Francois Soto

François Soto
EMphase Finance

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François Soto, Chief Investment Strategist of EMphase Finance, fsoto@emfin.com 300 Ave. Des Sommets, Suite #1213, Montreal, QC, Canada, H3E-2B7, 514.984.9155

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