In my previous post Is the Earnings Yield Divergence Unprecedented? we saw that the current differential in the earnings yield of the S&P 500 relative to the yield of the 10 year Treasury is large, but not unprecedented. This post will hopefully provide a bit more insight into the relationship of yield to both fixed income and equity returns.

First, let's start with bonds...

*Bonds*The beauty of a traditional bond is that yield wins in the long run... while performance may fluctuate year to year, if you buy a bond and get the credit work right (i.e. it doesn't default), you get a nominal annualized return roughly equal to the yield over a period that matches the duration of the bond (this is the main reason I called out those claiming bonds were in a bubble around this time last year... don't hear much from those guys these days).

The chart below details this feature using bond data from Shiller going back 140 years. To be specific, it shows the Treasury yield at each point in time, then the forward return on an investment in a bond index eight years forward (close to the average duration of a ten year Treasury). While the below does show some noise due to a fluctuating durations (when yields are low, duration is higher) and reinvestment risk, the correlation is 0.92 over that 140 year period (i.e. strong to quite strong). In other words, do not expect to earn more than 2% annualized from an investment in a ten year Treasury bond.

*Equities*Equities are a much more difficult beast. There have been countless studies on whether equities actually have duration (one such study showed that equities have a duration of more than 20 years with a standard deviation of 30 years). For this post I ran the 140 years of equity data through an analysis to determine which duration provided the highest correlation between earnings yield and annualized return.

As the following chart details, the winner is.... 10 years.

So.... is there a value in comparing the relative attractiveness of equities to fixed income? Sure. I would say the likelihood of equities outperforming Treasuries over the next eight years is high. But don't confuse relative attractiveness and attractive. Ten year Treasuries are currently yielding just 2%, so the 4% "excess" yield of the S&P translates to only 6% on a non-cyclically adjusted basis (using cyclically adjusted earnings it's less than 5%). As the chart above indicates, there have been plenty of occasions where equity performance has significantly under performed its yield, even over extended periods.

While ten years was best, eight years was close (and the duration used above for fixed income). Another thought was that if we are to compare earnings yield to the yield of a Treasury bond for relative value, we need an apples to apples comparison... so the chart below uses eight years.

And what do we find... a chart with a pretty strong (~0.45 correlation) relationship. The difference of course lies in the fact that an investor in equities is guaranteed nothing (earnings can fall) and is at risk to multiple (i.e. P/E) contraction, but also shares in the "upside" (i.e. earnings growth) and potential for multiple expansion.

So.... is there a value in comparing the relative attractiveness of equities to fixed income? Sure. I would say the likelihood of equities outperforming Treasuries over the next eight years is high. But don't confuse relative attractiveness and attractive. Ten year Treasuries are currently yielding just 2%, so the 4% "excess" yield of the S&P translates to only 6% on a non-cyclically adjusted basis (using cyclically adjusted earnings it's less than 5%). As the chart above indicates, there have been plenty of occasions where equity performance has significantly under performed its yield, even over extended periods.

Source: Irrational Exuberance