P/E Multiples vs (Past and Future) Returns and Volatility


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An eternal optimist, Liu-Yue built two social enterprises to help make the world a better place. Liu-Yue co-founded Oxstones Investment Club a searchable content platform and business tools for knowledge sharing and financial education. Oxstones.com also provides investors with direct access to U.S. commercial real estate opportunities and other alternative investments. In addition, Liu-Yue also co-founded Cute Brands a cause-oriented character brand management and brand licensing company that creates social awareness on global issues and societal challenges through character creations. Prior to his entrepreneurial endeavors, Liu-Yue worked as an Executive Associate at M&T Bank in the Structured Real Estate Finance Group where he worked with senior management on multiple bank-wide risk management projects. He also had a dual role as a commercial banker advising UHNWIs and family offices on investments, credit, and banking needs while focused on residential CRE, infrastructure development, and affordable housing projects. Prior to M&T, he held a number of positions in Latin American equities and bonds investment groups at SBC Warburg Dillon Read (Swiss Bank), OFFITBANK (the wealth management division of Wachovia Bank), and in small cap equities at Steinberg Priest Capital Management (family office). Liu-Yue has an MBA specializing in investment management and strategy from Georgetown University and a Bachelor of Science in Finance and Marketing from Stern School of Business at NYU. He also completed graduate studies in international management at the University of Oxford, Trinity College.

As I outlined in my previous post The Relationship Between Stocks and Bonds, the S&P 500 yields 3.7% at the current 27 CAPE (cyclically adjusted P/E), attractive from a relative basis to the sub 2% yield of the ten-year treasury. That said, a 3.7% yield is quite low by historical standards. Below is a framework for thinking about why returns should be expected to be lower AND more volatile than their long-term average given these low yields.

Thinking about stocks in terms of CAPE duration

While bonds, without embedded options, have a pretty well-known duration, there is much less certainty regarding the duration of stocks. That said, a framework for thinking about stocks in terms of their sensitivity to changes in their yield is informative. Stock valuations are highly sensitive to their required yield, with materially higher “stock duration” in the form of P/E multiple expansion at a lower earnings yield than at a high earnings yield.
  • Low yield = higher “stock duration”: For example… at a CAPE of 40, the “required yield” is 2.5% (1 / 2.5% = 40). This means (ignoring convexity), valuations change 40% for each 1% change in the required yield.
  • Higher yield = lower “stock duration”: On the other hand at a CAPE of 10, the “required yield” is 10% (1 / 10% = 10). This means (ignoring convexity), valuations change just 10% for each 1% change in the required yield.

Like bonds, the higher the duration (in the form of CAPE), means greater price sensitivity to a move in yield, which should be expected to result in higher forward volatility as well.

Historical returns drive the required yield and CAPE duration
The chart below looks at historical 5-year annualized performance of the stock market going back 50 years, bucketed into 10 distinct groups of ending CAPE values (<4% means the ending CAPE yield was less than 4%, which aligns itself to any ending periods with a CAPE above 25).
As the chart highlights, low stock yields (and high CAPE) have historically been the result of strong stock performance, as investors are lulled into forecasting low volatility and high returns given their recent experience, despite the poor valuations a low yield means.
The historical result of a low CAPE yield / high CAPE duration
Given the framework outlined at the beginning of this post, one would expect:
  • Low yields = low returns
  • High CAPE duration = high volatility


So… it should come as no surprise that forward returns based on a starting CAPE yield were in fact lower and risk was higher. In fact, when CAPE yields have been less than 4%, the forward average return has been only slightly above 0% over the next five years with materially higher volatility. At the current 3.7% earnings yield, investors in the S&P 500 should not only anticipate lower than normal returns, but higher volatility. Another reason to be diversified to higher “yielding” stocks abroad.

Source: Shiller, S&P


From http://econompicdata.blogspot.com/2015/04/the-relationship-between-cape-and.html


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