Is the market fairly valued?

One of the advantages of not being in academia is that one can err generously and doesn´t have to prove itty bitty details by comprehensive empirical studies in order to conclude that “it all depends”. The downside certainly is that most writing can only be shared with an audience of one.

Since writing my seminal oeuvre “The impact of the 1987 stock market crash on the economy” (self published by type writing) I have been struggling with the concept of the equity risk premium (especially after reading Constantinides 1987 paper titled “a resolution to the equity risk premium puzzle”). After all, this is the observable but rather abstract difference between the total return of “the market” and the riskfree rate, giving us the actual or expectable earnings from investing in the market for risky assets.

Being academic, professional or amateur, we are at all time concerned by the question if the stock market is overvalued, undervalued or fairly valued. I would like to start off with a very simple metric: the stock market´s return with dividends reinvested over a long time period. To make life easy for myself, I choose the S&P500 and a twenty year time period (just because it´s a generational time frame and there´s plenty of publicly accessible data). I am aware that the S&P500 is an imperfect measure, and numerous broader measures for the market have been suggested, including bonds, real estate, commodities and stocks not only in the US (which is subject to a lot of idiosyncratic risk, being the US after all) but also in the remotest corners of the world. The point is that the market should be the broadest measure of investments which allow to diversify any kind of idiosyncratic risk. But I would argue that 2008 showed that there is no escaping when the bottom falls out. Everything fell into the same trough at equal speed.

Taking a “long” time period, gives us the advantage of being able to compare with seemingly reliable averages of 9-10% returns p.a., observed over >100 years by Dimson, Marsh, Staunton in their wonderful book “Triumph of the optimists”. Of course, we can never be sure that this is a predictive indicator, but in the absence of a crystal ball it´s all we´ve got. I would add that the last century has seen a lot ups and downs, with a couple of wars on the downside and several industrial and digital revolutions on the upside. No lack of risk there and no lack of opportunities either. Absent beliefs in “thought viruses” (Shiller) like secular stagnation, I am cautiously optimistic that the end is not nigh and we will continue to see those returns on average and over a sufficiently long time period like the 21st century.

The S&P500 has seen some wild rides since 1994, which happens to look like a good starting point to count.


We have to take dividends into account and assume that we are reinvesting them. Thanks to Shiller again, I have dividend history at my fingertips:


The S&P500 annual returns without dividends look much less smooth than indicated by dividends:


Considering dividends and reinvesting them, which in reality people never do, an investment in the S&500 on Jan 1, 1994 would have added an impressive 984 points to the index´s already significant 1972 points on Sept 30, 2014. Bear in mind that over a long period´s average, 100 points up or down in the SP500 don´t matter much for the compound annual return!

So now getting back to returns with dividends reinvested (which I derived through some highly clumsy computations) I derived a compound annual return for the S&P500 of 9.32% which is very much in line with what Dimson, Mash, Staunton, ever the optimists, would have predicted anyway.

Does this mean the market is fairly valued? According to my easy metric, it does. Not so much according to a wealth of literature and papers, which takes us back to the equity risk premium puzzle. The essence of the puzzle basically is that investors in risky assets get too much compensation for the risk that they bear, particulary in comparison to an investment in risk free assets. The rule of thumb used to be that the risk free rate is around 4-5% and so the risk premium was around 4-5% as well. This was of course before interest rates went into a secular decline and we started wondering which investment actually is risk free. It´s not the 10-year government bonds (returning 2.37% at last count) anymore, given their wild swings in price and it´s not the 5-year bonds either (returning 1.5%). On the other hand, the return on the 2-year note is so ridiculously low, at 0.375%, it makes me wonder who would bother to invest in them (apparently a lot of people and institutions and the Fed). Some people call the short end of the yield curve manipulated and it may well be, but that´s what we get when we ask for a risk free investment.


Obviously a declining and close to zero risk free rate gets us an increasing risk premium for equities, raising doubts about investors´ fair compensation in the same way as the question was asked in 1987.


Honestly, I am not sure what this means – it deserves the name puzzle! The 5 year average shows that 2003/2004 was a good time for investing and 2014 looks lofty, admittedly. But with a risk free rate at almost 0, anything else is prone to looking lofty. Clearly – when rates rise, we may see the risk premium abruptly converging toward its long term average of slightly above 5%.

Now back to the question of whether investors have been unfairly compensated by earning too much money while taking on little risk! There are numerous risks (wars, insolvencies, expropriation, financial shocks), but we prefer to measure risk in terms of volatility. Of course, this is a dubious academic simplification, but it´s handy and not totally wrong when measuring the market´s risk in retrospect. Without computing any numbers I can safely state that the market has been wildly volatile over the last 20 years. The problem with computations is that people can never decide about the appropriate time frame (years, quarters, months, days, hours, seconds, nanoseconds…) and calculating it and building conclusions on seemingly precise numbers perpetuates implicit flaws in the models. In my opinion, I would certainly feel just fairly compensated for riding out 2001 and 2008!

The problem with estimating the fair premium begins with the right starting point. Some have stated that we have been unfairly compensated by starting in 2003 or 2009. Hussmann has published some very lucid articles with titles like “Fast, Furious, and Prone to Failure” or outright “Yes, this is a market bubble” and impressive as they are, I have suffered some sizable losses from taking them too literally.

The basic idea is that investors should get high returns for high risks and low returns for low risks. People tend to forget that this is about expected volatility and expected returns. It doesn´t mean that your return goes up when risk increases (otherwise brilliant, but here a little misleading: Shefrin in “Beyond greed and fear”). It means that prices fall abruptly when risk increases in order to enable the next buyer to expect a return that is commensurate with the risk he accepts. Likewise a stock will go up when risk decreases, so that future buyers can only expect slim returns for a diminished risk.

Investors got amply rewarded after 2009 for a taking on a high expected risk. The risk premium which we observe is measured in retrospect and may be fully deserved. Naturally we cannot expect continuous rewards on the same level if the expected risk keeps decreasing, but markets will not crater in that case. If the expected risk increases, we will see abrupt declines and high future returns after those declines. The proper explanation for those declines will not be: “…told you so, the market was overvalued!” Let me finish this essay with the conclusion “it all depends”…

Max Nussbaumer, Chicago, Nov 1, 2014

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