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Seeking Alpha contributors Skyler Greene and James Kostohryz recently submitted dueling articles outlining the bull and bear cases that can be made from ultra-low interest rates, particularly the strong bids for treasury bonds. James focused on the risks that are causing investors to bid up treasury bonds, while Skyler focused on the valuation of stocks relative to bonds and found stocks to be more attractive as a result.

I wondered after reading these two articles if any historical trends could be drawn from the relative prices of bonds and stocks to predict future market performance. For my analysis, I began by looking at the rate of the 10-year U.S. Treasury bond against the earning yield of the S&P 500 index, termed the risk premium. The earnings yield of the S&P 500 is simply the inverse of its P/E ratio, subtracting the risk free rate gives the risk premium. Unfortunately, this value measured against future performance of the S&P 500 failed to give any discernible trend. Perhaps the earnings yield is simply too volatile, so the 10-year normalized earnings yield against the 10-year Treasury was also analyzed. While the 10-year CAPE, as popularized by Shiller does have predictive value, the normalized earnings premium did not.

In a previous article, I analyzed the ratio of stock to bond prices and showed that this ratio displayed predictive power over a period of two years. This led me to conclude that the S&P was attractive at 1330 about one month ago; it has traded up by 5.3% since. I wondered if the stock/bond ratio could be used for longer periods of time to predict how much upside a stockholder could expect from the S&P 500. The task is somewhat more complicated over longer periods of time. To derive the price of a 10-year note relative to its final return one should calculate the price as: V = 1/(1+Treasury Rate)^10. Thus if a 10-year note yields 1.60%, a buyer today pays about 85 cents to receive one dollar in 2022.

For a 10-year note trading at 1.60%: V = 1/(1 + 0.016)^10 = 0.853

However, comparing this value over a long period of time is complicated by inflation. In 1881, the purchaser of a 10-year note would have paid 70 cents to receive a dollar in 1891, but the value of an 1881-dollar is very different from a 2012 dollar. To compensate for this difference, the value paid to receive a dollar 10 years hence was multiplied by the CPI index. This then yields the inflation adjusted price the purchaser of such a note paid, which is defined as the Real Bond Price. The Real Bond Price then was applied as the denominator, and the real price of the S&P 500 index was applied as the numerator in the following equation:

Stock Bond Ratio = Real S&P 500 Price/(CPI*1/(1+ 10 Yr Rate)^10)

So to calculate the current ratio with the S&P 500 at 1400, the CPI at 230 and the 10-year at 1.60%:

Stock Bond Ratio = 1400/(230*1/(1+0.016)^10) = 7.1

This CPI, real S&P 500 price and Treasury rate were obtained from www.multpl.com. I used years between 1881 and 2002 and plotted the stock bond ratio versus the forward annualized 10-year return of the S&P 500 without dividends:

(click images to enlarge)

The predictive power of this ratio to the forward return of the S&P 500 index is astonishing. When real stock prices are lower and real bond prices are higher, the imbalance is generally resolved to provide stockholders with above average returns. My initial reaction to the discussion of risk premium was skepticism. However, it seems from this correlation that very expensive bond prices do tend to favor good returns on stocks.

The top five years according to this metric were: 1920 (10.7% real return), 1921 (10.4% real return), 1948 (8.7% real return), 1949 (11.6% real return), 1950 (10.7% real return) and 1994 (6.6% real return). 2009-2012 all rank in the top years, although the 10-year forward returns are not yet known. Right now, treasuries are impossibly expensive relative to stocks. Historically, this has tended to result in good returns.

There is one aspect of the equation above that I am still not satisfied with. Since the real price of the S&P 500 has appreciated above the rate of inflation, shouldn't the equation have some term offsetting this growth? I attempted to correct for this, either by averaging the real price lower at a set rate, or by adding real GDP to the denominator of the equation. In either case, the correlation broke down. This still puzzles me, and I would like to come up with a better rationale for why such an adjustment doesn't fit.

I am still confident of the overall conclusion, because the trend works well over shorter periods where large changes in real price are less significant. For example, the model successfully predicts the best years from 1881-1921, 1922-1962 and 1962-2002. The most significant drop off in correlation occurred during the 1970s, when stocks became extremely cheap due to inflation and bonds suffered a massive bear market.

This model shows that near the end of a cyclical bear market, several things happen. First, real stock prices decrease over a number of years, even as nominal prices trade within a range. Second, real bond prices increase. They do so through inflation over the cyclical bear and investors bid up the price of bonds, preferring the guaranteed return of a bond to the uncertain return of a stock.

The graph below shows the progress of the S&P 500 Index over the past one hundred years. Let us examine the Real Stock/Bond Ratio toward the end of each cyclical bear market:

The cyclical bull of the 1920s began in 1921 from a Real Price of 86 and a stock/bond ratio of 7.4. The earnings yield of the S&P 500 was 10.6% and the 10-year note traded at 5.1% vs. its recent low of 4.1% in 1916.

The cyclical bull of the 1940s began in 1948 from a Real Price of 144 and a stock/bond ratio of 7.7. The earnings yield of the S&P 500 was 11.1% and the 10-year note traded at 2.4% vs. a previous low of 1.9% in 1941.

The cyclical bull of the 1980s began in 1982 from a Real Price of 286 and a stock/bond ratio of 11.8 (it was elevated due to the bear market bonds experienced during the 70's stagflation). The earnings yield of the S&P 500 was 12.9% and the 10-year note traded at 14.6% vs. its recent low of 7.2% in 1977.

We are currently at a Real Price of 1400, an earnings yield of 6.9% and a stock/bond ratio of 7.1 with the 10-year note trading at 1.6%, somewhat up from its recent record low of 1.39%.

The end conclusion is one factor that causes investors to bid-up stocks and break the cyclical bear is bond prices that are horrendously overvalued relative to stock prices. A period in which the 10-year note trends lower in price generally precedes a very strong surge in the price of stocks.

Another observation is that toward the end of a cyclical bear, investors become very comfortable with benchmark risk. They say things like: "the S&P has gone nowhere for a long time, I'm sitting this year out, stocks never go anywhere." Add money on the sidelines, to money being squeezed out of bonds, to stock investors who have weathered much worse and prices can rise, quickly. The remarkable resilience of the stock market in recent months is in no small measure due to the lack of alternative investment opportunities. If stock holders could sell and buy a Treasury note yielding 5%, the S&P 500 would probably be trading much lower.

I cannot predict the exact date on which a new cyclical bull will begin. That will come due to specifics of the economy or the European situation, which are ultimately unpredictable. In the 1920s and 1940s, shortages from two world wars and debts from the Great Depression finally gave way to a booming economy. In the 1980s, the ravages of inflation subsided to yield the same. Our current anemic economy is waiting for consumers to heal their balance sheets and start spending again.

I will note that the current status of the market is out of balance, with stocks trading at relatively desirable valuations, while Treasuries trade at a very overvalued state. This is a field of tinder waiting on a match. The Real Stock Bond ratio predicts 6.8% real returns for the next 10 years, implying that the S&P 500 will be trading somewhere in the vicinity of 3000 by the beginning of 2023. Remarkably, these returns would be only slightly above average according to Siegel's constant, which predicts 6.6% real annual returns with dividends reinvested.

This prediction may be too bullish in light of the current valuation of the market. I am conflicted on this point. If the S&P 500 were priced at 1200 (12.5x earnings, 17x normalized earnings), I would be fully bullish. At 1400 (14.5x earnings, 20x normalized earnings), I am more agnostic over the short term, but still expect good performance over the longer term. However, I freely admit that normalized earnings may miss the point. The ratio presented above has far better correlation than Shiller's CAPE methodology. Value is a relative judgment. In a world where everything is expensive, perhaps we are too harsh expecting stocks to be dirt cheap.

Source: Ultra-Low Interest Rates Indicate Stocks Have Significant Upside