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The Mystery of Treasury Yields and Stock Market Valuation

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The 10 year treasury yield rose roughly 130 bps from its May low without a material impact on the equity market.  Although there has been a great deal of focus on Fed tapering and rising interest rates, the S&P 500 remains near its May high and seems more concerned about politics in Washington and the outlook for earnings.

Looking at theory:

Given the ability of the S&P 500 to weather the up in treasury yields, it might be worth reviewing the relationship between interest rates and equity prices.   From a theoretical standpoint, the value of a stock is based on the discounted value of earnings or cash flow.  As a result, as interest rates rise the value of a stock should fall and as interest rates fall the value of a stock should rise, holding earnings constant.

The table following illustrates the impact of interest rates on the discounted value of $1.00 of earnings.   Here is an explanation of the table:

(click table to enlarge)

The earnings line displays a $1.00 of earnings.

The discount rate represents the interest rate.  If you want, think of this as a 10 year treasury yield or corporate bond rate.

The value is the discounted value of earnings to perpetuity.  The value for the first column is $1.00/1.50% or $66.76.

The multiple is the discounted value without the dollar sign.  It can be akin to a PE ratio.  It is the multiple that an investors could pay for $1.00 of earnings at a given interest rate.  

The graphic below displays the relationship between interest rates and the multiple  Notice the relationship is non-linear and the multiple gets exceedingly higher as interest rates fall and flattens as interest rates rise.  At some point, when interest rates fall sharply, the multiple or valuation gets hard to embrace.  


The chart following displays the relationship between the 10 year treasury yield and the 4-quarter trailing PE ratio for the S&P 500 based on Generally Accepted Accounting Principles.  Extreme PE ratios over 40 were eliminated and occurred during the recent Great Recession and 2001 recession time frames.  By excluding these values, it is easier to see the relationship.  Earnings fell off sharply in these periods, making the PE ratio not very meaningful.  

Furthermore, the graphic looks at the relationship since 1970 and separates the PE ratio by 10 year increments.  In other words, the PE ratio 10 year treasury yield relationship was broken out by the 1970’s, 1980’s, 1990’s, 2000’s, and 2010’s.

The graphic provides a number of insights.

First, there is a loose relationship over time between the level of the 10 year treasury yield and the PE ratio on the S&P 500.    Using an exponential fit, the 10 year treasury yield explains about 41% of the movement in the PE ratio across all periods.

Second, the relationship between the 10 year treasury yield and the PE ratio shifts over time.  It is not stable.  The relationship looks “tightest” in the 1970’s and 1980’s.  In the 1970’s, the 10 year yield explained about 66% of the movement in the PE ratio, while in the 1980’s the 10 year yield explained 77% of the movement in the PE ratio.   The 1990’s were less strong with the 10 year explaining 46% of the movement in the PE ratio.

Third, the current relationship between the 10 year yield and the PE ratio is weaker than it looks quantifying it statistically.   The 10 year treasury yield has explained just 16% of the movement in the PE ratio.  Moreover, the relationship seems out of line with the other years.

Fourth, the curves on the graphic look like demand curves.  In other words, they seem to suggest the willingness of investors to own equities for a given set of interest rates.   For example, investors were willing to pay more for equity at a 9% interest rate in the 1980’s compared to the 1970’s.  Similarly, investors desired to pay more for a stock in the 1990’s compared to the 1970’s at a given 10 year yield.  The political and geopolitical environments were friendlier for equities in the 1980’s and 1990’s relative to the 1970’s. Remember, the 1970’s saw two oil price shocks.  The 1990’s saw much of the world embrace free markets and capitalism.

Fifth, the relationship between interest rates and equities was very variable in the 2000’s. The end of the bubble, the super cycle in commodities, and the interest in EM investing may have played a role in confusing the relationship, although a number of quarters could be lumped together to highlight a relationship.  It almost looks like the demand for equities was falling for a given interest rate during the period, but the PE ratio ratios were very distorted by bubble period in the early 2000’s.


The question may come to mind:  Why is the trade not paying more for equities now given the historically low level of interest rates?  It seems like the PE ratio should be much higher.

It is hard to directly answer this question, but here are a few ideas:

First, the market is well aware of the Fed Reserve’s actions to provide stimulus and artificially lower interest rates.   The market may see the Fed’s actions at transient and be reluctant to price a high PE ratio.  In other words, the market is actually priced at a much higher rate structure.

Second, investors have been burned by equities twice in the 2000’s with the financial crisis in 2008 and the bubble around 2000.  There has been a major investor shift to bonds in recent years.  Some of this psychology and investor shift may be showing up in a low PE ratio relative to interest rates.   Demographic factors could also be at work.  Baby boomers have aged and may be more defensive favoring fixed income, for example.

Third, the graphic displays the relationship between the 10 year treasury yield and the PE ratio, but the 10 year yield may not be the correct discount rate for equities.  The 10 year treasury is backed by the printing press of the U.S. government.  One could argue the quality of the government paper given the circus in Washington, but most textbooks view treasuries as the risk free rate.  There is an equity risk premium which is not displayed in the scatter chart.

There are times when the equity risk premium rises and periods when it falls.   When investors discount earnings to value a share, the discount rate is based on the risk free rate plus some risk premium.   The equity risk premiums changes over time.  It may be relative high in current times.  Certainly politicians across the Global have not been able to generate strong economic growth, regulation has been a burden, and the geopolitical land scape is uneasy. These factors argue for a high risk premium.

Fourth, since the PE ratio interest rate relationship gets “silly” at extremely low interest rates, the market may be just looking more at the average PE ratio to value stocks.  The current PE ratio on a GAAP basis is set to be about 17.8 at the end of Q3.  This is slightly above the longer term average which is just below 16.0. Going forward, the PE ratio is ripe to decline below average based on current profit estimates.

Fifth, it is possible that the equity market has “value” and is pricing caution.  This may open the door to higher returns in the coming years.  Put another way, the equity risk premium could shrink.  The scatter seems to suggest the PE ratio could easily be in the 20's given the current level of the 10 year treasury yield.

The fixed income market is also pricing more risk:

The spread between the Moody’s Baa corporate and the 10 year treasury was 2.70% a few days back.   A Moody’s Baa corporate is neither highly protected nor poorly secured. It is a median grade corporate note. Going back to 1970 and using monthly data, the spread has averaged 2.19% with a median of 2.06%.  Like the equity market, the corporate debt market seems to be cautious about embracing the low yield in the treasury market.   In other words, the risk premium in the corporate market also seems high compared to average.  The same result is present when using a ratio spread between the Baa and 10 year treasury in order to adjust for the rate structure.  The ratio spread was 2.02 compared to an average of 1.43 and a median of 1.30.

One might loosely, off the cuff, draw the conclusion that the corporate debt market thinks treasury yields are roughly 50 bps too low.  It is fair to think that the spread relationship would be near average with corporate profits expanding, the economy growing, and the rate structure low.

Summing it up:

The relationship between the 10 year treasury yield and the PE ratio on the S&P 500 is unstable overtime.  In theory, investors should pay more for stocks when rates are low and less for stocks when rates are high.  However, the equity risk premium tends to cloud the relationship between treasury yields and the PE ratio, and empirically speaking the relationship between stocks and interest rates is much looser than we would like to think. 

Stocks look cheap compared to the level of the 10 year treasury. This may be a piece of good news for stock bulls. An up in interest rates may not have as much of an impact on the market’s valuation as feared.  The outlook for earnings and the environment for economic growth may be much larger factors in stock market pricing in the coming months.

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