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Closing at a record high, the S&P 500 is currently fairly valued with higher long-term bond rates already factored in. Fairly valued means that investors can expect annual equity returns of about 11%.

The S&P 500 closed at 1854.29 on February 27, 2014. This new record high eclipsed the previous record of 1848.38, set on January 15. Each new high prompts talk of a speculative bubble, but rarely do they indicate a bubble.

Record highs are both common and expected, while bubbles are rare. The long-term historical trend is for the economy to grow and market value grows with it. Since long-term growth in the market is expected, record highs must also be expected. Not only is growth expected, but the market is priced for expected growth. Bubbles are not simply the result of new highs but the result of extreme overvaluation. The key to bubble spotting is determining fair value.

The supposed evidence of a bubble comes from many sources.

Individual companies and sectors can be overvalued or in a bubble without the market being in a bubble. Some suggest that Facebook's acquisition of WhatsApp for $19 billion is an indication of a private company tech bubble. Clearly the price is high. Based on WhatsApp's current business model, if every human on the planet was a paid user, the price would still be 2.7 x revenue. Even so, others argue that other sources of revenue are contemplated or will emerge, so the price was reasonable. Either way, this not an indication of a broad market bubble.

The most absurd bubble arguments are that the market is at a bubble, simply because it is at a new high. When Googling "market bubble" today, the first entry was "this is no recovery, this is a bubble - and it will burst" from The Guardian. This hyperbole filled article from a British national newspaper, authored by a Cambridge professor, includes arguments like:

"The Standard & Poor 500 stock market index reached the highest ever level, surpassing the 2007 peak (which was higher than the peak during the dotcom boom), despite the fact that the country's per capita income had not yet recovered to its 2007 level. Since then, the index has risen about 20%, although the US per capita income has not increased even by 2% during the same period. This is definitely the biggest stock market bubble in modern history."

The argument that the market is in a bubble because it reached a new high is absurd. The market is driven by earnings and interest rates. Earnings rise with the economy, which has had an upward long-term trajectory since the dawn of civilization.

Simply looking at the chart below of S&P Operating Earnings since 1986 makes the point that long-term growth is the norm.

(click to enlarge)

Determining Intrinsic Value

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 a 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 a 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 4.32%.

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 the actual - continuing to revert back to predicted levels.

(click to enlarge)

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

Today the market is slightly overvalued based on trailing earnings and the implied 4.5% 10-year yield. Given 4.5% is a very rough estimate, I would not use it to make a granular valuation call and consider the market fairly valued today.

This also means that higher long-term rates are already factored in.

From both perspectives, the model tells the same story - while the market often deviates, it regresses back to predicted values. The implication for holders of long-term bonds is an expected loss when the Fed allows interest rates to return to market. Equity prices have already factored in higher long-term yields.

What does this mean for equities long term?

The model calculates expected returns (cost of equity) as Long-Term Treasury yield + Equity Risk Premium, where the Equity Risk Premium equals Long-Term Treasury yield times the Risk Premium Factor. That is, 4.5% + 4.5% x 1.48 = 11.6%. At fair value, the market can be expected to yield at total return of 11.6%.

Using the S&P's forward estimates for operating earnings and assuming long-term rates stay at 4.5% or less, the RPF models show considerable upside for year-end 2014.

S&P 500 Operating Earnings

Index Actual

Index Predicted

27-Feb-14

107.13

1,848

1,768

31-Dec-14

121.90

Estimated

2,014

Of course, this is completely contingent on both earnings meeting projections and interest rates remaining 4.5% or less.

Bottom line: The market is fully valued but not in a bubble.

Source: Absurd Bubble Talk

Additional disclosure: Short long-term treasuries.