P/E Ratios & Interest Rates: A Formula for Fair P/E Ratios Incorporating Interest Rates - Sure Dividend

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P/E Ratios & Interest Rates: A Formula for Fair P/E Ratios Incorporating Interest Rates

Updated August 22nd, 2018 by Ben Reynolds

The 10 Year T-Bonds hit all time yield lows of 1.5% in July of 2016.  To say we have been in a period of low interest rates is an understatement.

With that said, interest rates are now rising.  The current 10 Year T-Bond rate is now 2.8%, 1.3 percentage points higher than lows reached in July of 2016.

The bullet points and image below give a general idea of the range of T-Bond rates over time.

Source:  Multpl

In theory lower interest rates cause asset prices (including stock prices) to rise.  Here’s how.

Imagine a stock yields 4% and T-Bonds yield 8%. The stock has a lower yield because it is expected to grow over time, resulting in higher dividend income and capital appreciation.  Now imagine that the T-Bond yields drop to 4%.  Now the stock’s yield looks very attractive.  Investors will pile on and bid up the share price, reducing the stock’s yield back to equilibrium with the T-Bond yield.

If theory holds true, it stands to reason that the S&P 500 will have a higher price-to-earnings multiple on average when interest rates are lower.


But how much higher should the price-to-earnings ratio be?  Is the market really overvalued given today’s ultra-low interest rate environment?

This article takes a look at the relationship between interest rates and price-to-earnings ratios to determine if the market is truly overvalued today on a historical basis taking into account interest rates.

Who Controls Interest Rates

Before going further, it is important to note that interest rates are not dictated by the free market.  If they were, there’d be no need to study their relationship with price-to-earnings ratios as they would always move in or near equilibrium thanks to market forces.

Instead, interest rates are controlled by the Federal Reserve.  The Federal Reserve’s primary tool in setting interest rates is controlling the Federal Funds Rate.

The Federal Funds Rate is the rate at which banks lend funds held at the Federal Reserve to each other on a short-term (overnight) basis.

The Federal Funds rates indirectly determines borrowing rates for the entire United States economy.

The Federal Funds Rate was slashed to a range of 0% to 0.25% (virtually free bank borrowing costs) to stimulate the economy in 2008.  It was held at that rate until 2015.  Movement in the Federal Funds rate from 2015 onward is below:

The Federal Funds rate has gone from a range of 0.00% – 0.25% prior to December 2015 to 1.75% – 2.00% today.  More increases are likely over the coming months and years as long as the United States economy remains strong.

With the Federal Funds Rate on the move, it’s important to examine the historical relationship between the stock market’s price-to-earnings ratio and the 10 Year T-Bond rate (which is a good general gauge of interest rates).

We will explore the correlation of the stock market’s price-to-earnings (P/E or PE) multiple with 10 Year T-Bond yields in the modern financial era; since the United States abandoned the gold standard in 1971.

Correlation Between Market Valuation & Interest Rates

From 1971 through 2015 the S&P 500’s price-to-earnings ratio and PE10 has been highly correlated with the 10 year T-Bond rate.

Note:  The PE10 ratio or ‘Shiller PE ratio’ divides the current price by average earnings over the last decade.  This ‘smooths out’ the price-to-earnings ratio and is a better gauge of valuation during recessions.  As an example, the S&P 500’s P/E ratio in 2009 was 70.9, which would be wildly overvalued.  In reality earnings were depressed causing a high P/E ratio even though market sentiment was negative.  The PE10 ratio was at 15.2 in 2009, well under its mark of 24.0 the year earlier, accurately showing the better valuations during the depths of the Great Recession.  This article uses both P/E and PE10 ratios for thoroughness.

Source:  Data from Multpl

There is a clear inverse relationship between the market’s valuation multiple and interest rates.  The higher interest rates go, the lower the S&P 500’s valuation multiple will be, all other things being equal.

What’s a Fair Valuation Today?

What is a fair price-to-earnings ratio for the S&P 500 today given ultra-low interest rates?

Running a linear regression on the data above gives the following:

Using the slope and intercept above combined with the current 10 Year T-Bond yield of 2.82%, we get the following:

Using PE10 tells a similar story:

Based on today’s still low interest rate, the market is actually trading around fair value today using the P/E ratio.  It is somewhat overvalued using the PE10 ratio, in part due to depressed earnings near the end of the Great Recession, and in part due to higher earnings today from lower corporate tax rates.

All in all, the market certainly doesn’t look extremely overvalued when one factors in current interest rate levels.

What if Interest Rates Continue to Rise?

10 Year T-Bond rates fell from their high in 1981 to record lows in 2016.  Since then, T-Bond rates have slowly risen.

The trend of rising interest rates is likely to continue as long as the United States’ economy remains strong.  I expect 1 to 2 more Federal Funds rate increases this year, with potentially more in 2019.

Higher interest rates put a damper on the economy.  While the United States’ economy is growing, high levels of government debt and liabilities make it impractical that interest rates will rise to 1980’s levels.  As interest rates rise, the United States’ economy is likely to grow slower, which will result in a halt in rising rates – and potentially even rate reductions if we enter into another recession.

If the federal funds rate reaches 4% – roughly double today’s current level, I would expect 10 Year T-Bond’s to yield around 5%.  Using 5% in our equation above implies a fair price-to-earnings ratio for the S&P 500 of 21.7 and PE10 of 22.8, respectively.

This would mean a 12.6% decline in market levels due to P/E valuation multiple contraction from current levels.  So in the event the federal funds rate rises to levels seen around 2005, we can expect a decline in the S&P 500, but not a massive shock.

Final Thoughts

Is the market overvalued based on an absolute historical basis?  Absolutely.  Is the market overvalued given current low interest rates?  No.  It is trading around fair value.

The conclusion I draw from this data is that the stock market is trading around fair value given our current low interest rate environment, and that the artificially low interest rate environment will likely be with us for the foreseeable future, albeit with moderate increases.

Regardless, the prerogative for long-term buy and hold investors does not change:  Invest in high quality dividend growth stocks with strong competitive advantages trading at fair or better prices.  When the market trades for a lower price-to-earnings ratio this is easier, but it is still possible today.

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