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While stocks are not in a bubble today, inevitably a bubble will form at some point. Some say you can't spot a bubble when you are in it, largely because of disagreements over what constitutes fair value. The Risk Premium Factor Model can identify bubbles by comparing actual to intrinsic value.

I define a bubble as the stock market, the S&P 500, sustaining a 20% overvaluation for several months followed by severe corrections. By this definition, bubbles are rare events with only two bubbles since 1986:

  1. March 1987-October 1987 where valuation peaked 64% over fair value
  2. February 1999-August 2000 where valuation peaked 48% over fair value

Under this definition, it is not a bubble when the market crashes due to recession or other events. For example, 2009 was not a stock bubble, since the market declined when the popping of the housing bubble triggered a severe recession. The market decline was actually consistent with economic expectations. Another period of overvaluation from May 1991 to November 1992 was also not a bubble since predicted valuations caught up with the actual as interest rates declined and the economy improved. The latter period will be discussed at the end of this article.

Establishing Intrinsic Value

Obviously, determining overvalue requires the establishment of intrinsic value. Financial assets produce cash flow and that cash flow can be valued. The price of bonds fluctuates directly with interest rates and perceived risk. The prices of equities are based on future projected cash flow, interest rates and risk. At any point in time, we can estimate the intrinsic value of equities and determine whether they are in a bubble.

About The RPF Model

The Risk Premium Factor Model (RPF for short) is used to determine the intrinsic value of the market to help identify bubbles or buying opportunities. (If you are a regular reader, the inset material below will be familiar.)

Determining whether the market is fairly valued is simple matter of looking at its price relative to earnings and the P/E ratio. The Risk Premium Factor (RPF for short) Model shows that the fair value P/E ratio at any point in time is determined relative to long-term interest rates and not based on a simple historical long-term average as some would argue.

Determining whether the market is fairly valued is simple matter of looking at its price relative to earnings and the P/E ratio. The Risk Premium Factor (RPF for short) Model shows that the fair value P/E ratio at any point in time is determined relative to long-term interest rates and not based on a simple historical long-term average as some would argue.

In short the model says that:

Intrinsic Value of the S&P 500 Index =

S&P Operating Earnings / (Long-Term Treasury Yield x 1.48 - 0.6%)

The model shows that equity prices (NYSEARCA:SPY) move inverse to yield. In this simplified version of equation, 1.48 is the Risk Premium Factor and 0.6% is the difference between long-term expected growth and real interest rates. I've written about the model numerous times, so rather than repeat my entire overview of the model, you can read about it in my book or on Seeking Alpha where you can find the expanded equation as well.

Today it shows that the S&P 500 is fairly valued, not in a bubble and priced for continued growth with higher long-term bond rates already factored in. Fairly valued means that investors can expect annual equity returns of about 11%. This is a long way from a bubble.

Using a rough estimate of normalized long-term interest rate of 4.5% (2% real plus 2.5% inflation) to adjust for the Federal Reserve's artificially depressing long-term rates by keeping short-term rates near zero, the model shows the S&P 500 is fairly valued. (If you care to read my past articles, they indicated that the S&P 500 was undervalued.)

Alternatively, the RPF Model implies the fair value yield on 10-year Treasuries is 4.37%.

The chart below shows predicted versus actual levels of the S&P 500 Index since 1986. Bubbles are indicated by periods where there is a large gap between predicted and actual levels. This also illustrates the strong historical performance of the model compared to actual continuing to revert back to predicted levels.

(click to enlarge)

This chart uses normalized yields on Treasuries of 4.5% (2% real plus 2.5% inflation) from August 2011 through the present. It also shows the recent several year period where the S&P 500 was significantly undervalued.

RPF Model and Bubbles

While the market often deviates from the intrinsic value determined by the RPF Model, it regresses back to predicted values. This makes it a tool for bubble identification. Looking back historically, the chart clearly shows the bubbles in 1987 and 2000.

The cause of decline in predicted value in the 1987 crash was overall P/E multiple expansion combined with an increase in long-term interest rates from 7.25% in March to 9.25% in October. Instead of declining the market continued to rise and P/E ratios continued to expand and the stock market continued to rise, until the bubble popped.

The 2000 bubble was a similar story. Yield on the 10-year increased from 4.6% to 6.2%, driving down the predicted values but, again, P/E continued to expand. This was further compounded by earnings continuing to rise despite the NASDAQ bubble having popped in March 2000. The S&P actually peaked in August 2000, bottoming out more than a third lower in October 2001. During this period S&P Earnings declined from 56.79 to 42.02, making this a bubble followed by a recession driven decline.

Possible Causes of the Next Bubble

It is almost a certainty that a bubble will develop at some point in the future; since we don't know when, the key is knowing how to see it. Here are three scenarios that could lead to a bubble:

  1. The fruit of loose monetary policy comes home to roost. As many fear, the loose money policy of the past several years could lead to a spike in inflation causing the Fed to react and driving up long-term rates in general. Long-term rates at 6% would equate to a predicted value of 1,295 for the S&P 500 - 30% below today's level.
  2. Irrational exuberance and continued P/E multiple expansion. Strong economic growth and reduced unemployment could set the stage for another bubble by making investors over optimistic and driving the P/E higher. The P/E on operating earnings is about 17 today. If it expanded to 25, it would push the index up to 2,680 and overvalued by about 34%. This is the fear the Robert Shiller and others have expressed. Not that we are in a bubble today, but one could form if the trend of P/E expansion continues.
  3. The "Perfect Storm" of high interest rates and P/E expansion. The term "Perfect Storm" is overused, but still applicable to a rare convergence of events. A combination of interest rates rising to 6% due to a strong economy and inflation and P/E expansion to 25 would put the market to be almost double fair value with a predicted value of 1,295 compared to an actual value of 2,680 for a P/E of 25 on today's level of operating earnings.

Before dismissing these scenarios, consider that the S&P has ended 41 of the 337 months since January 1986 above 25 - that's roughly 10% of the time. Long-term interest rates of 6% only require inflation of about 4% and the Fed's willingness to allow them to be set by the market which is what would happen if inflation spiked. The 10-year yield has ended a month above 6% in 140 months since January 1986. The point here is not to imply some probability but only suggest that metrics at these levels are not uncommon.

The good news is that bubbles tend to persist. In 1987, a bubble was indicated by the RPF Model for six months before it corrected. In 1998/9 it persisted for 18 months. The bad news is that using the RPF Model to exit the market in a bubble will surely cause you to miss the top.

Final Caution - Beware of False Positives

Using this tool also absolutely requires thought and analysis. The output cannot be followed blindly. Most of my analysis for publication is based on current actual values for earnings and interest rates. During one period since 1986, this would have given a false positive for a persistent bubble.

In May 1991, just as the economy was exiting the recession driven by the S&L crisis, the S&P was at 390, 19% above the predicted value of 316. This implied overvaluation persisted until the end of 1992 while the market rose 17%. Two factors stand out during this period: 1) The economy was in recovery and, 2) 10-year yields were trending down from 8.06% in May 1991 to around 6% in early 1993.

Incorporating these facts into a sensitivity analysis could have indicated that the market was priced to include forward earnings and interest rates, and while it may have been overvalued, it was not a bubble.

Source: 3 Scenarios For The Next Bubble