The age-old question: is the S&P 500 overvalued or undervalued? Are you interested in markets? You too will be forced to reckon with this dilemma. It has been reported that Bank of America/Merrill Lynch recently found that the S&P 500 was overvalued on 18 out of 20 metrics! A quick look through these measures makes me really wonder what good they really are. (See also, S&P 500 Overvalued on Almost Every Metric.)

Among other things, BoA/ML concluded the S&P 500 was expensive against the 10-year U.S. Treasury yield. Fascinating! I've carried out this analysis myself countless times, using the very same metric. In fact, by my analysis the S&P 500 is not overvalued against the 10-year U.S. Treasury yield, it's undervalued, and quite significantly.

Let's identify a few reference points: it's safe to say that around March of 2000, the S&P 500 was in a bubble, no? It's also safe to say that in March 2009, the S&P 500 was oversold. It's very hard to argue with that. Additionally, using the S&P 500 chart below, it's safe to say that from around 1955 until 1980, the S&P 500 saw an enormous move higher—with a few bumps in the road—while U.S Treasury yields headed higher as well.

^SPX Chart

^SPX data by YCharts

Now that we've established a solid frame of reference, we can obtain a solid analysis. Using YCharts, I found the monthly dividend for the S&P 500 going back to 1953, and divided it by the price of the S&P 500, to come up with the S&P 500 dividend yield, which you can see at the bottom of the chart below.

S&P 500 Dividend Chart

S&P 500 Dividend data by YCharts

Next, I took the S&P 500 dividend yield and divided it by the yield on the 10-year U.S. Treasury. See the chart below:

This chart tells us the S&P 500 is not overvalued compared to its average, which since 1953 is 0.63. Why? We have established the S&P 500 was expensive to the 10-year yield in 2000—we know equity markets were in a bubble in that fateful year. We also know that equity markets were cheap to treasuries in the 1950s, 60s, 70s, because the S&P 500 yield was higher than the 10-year rate, and both rose for the next 27 years. After that, treasury rates began to collapse. As rates came down on the yields, S&P 500 dividends grew to keep the ratio in balance. Then in the late 1990s, the S&P 500 dividend yield began to sink, due to the stock market bubble. The financial crisis low told us equities were cheap to 10-year yield because S&P 500 yields were higher than treasuries once again. So if the average is 0.63 and we know that a number less than 0.63 is expensive and a number greater than 0.63 is cheap, how can 0.8 be expensive!? I

The explanation above may be hard to follow. In the chart below, I've inverted the ratio and made it much easier to understand:

It's fairly obvious at which point of the cycle we are in right now. At its current ratio of 1.25, the S&P 500 is cheap. The average is 2.04, with a Standard Deviation of 0.93, which means we are towards the lower bound of the average. In fact, even if rates rose to 3 percent, the ratio would only be 1.5. Treasury rates could rise to 3 percent on the 10-year and the S&P 500 dividend yield would have to fall from today's near 2 percent to 1.5 percent. With a current dividend of $46.38 per share, the index would trade at nearly 3,100 to get back the ratio of 2:1.

This tells us one of two things: either equity prices are cheap relative to bonds, or bonds are expensive to relative to equities. It's totally up to you which way you wish to look at it. One thing we can say for sure: equity prices are not overvalued to bonds.

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