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In my previous article I pointed out that, contrary to popular belief, stocks are not cheap (or expensive) based their 12-month forward PE.

Nevertheless, many analysts argue that a proper analysis of PEs must take interest rates into account. On this basis, many of these analysts argue that given the extraordinarily low levels of interest rates, stocks are cheap.

I agree with the first part of the argument. However, the second part of the argument is simply incorrect, both logically and empirically.

Misery Does Not Make Good Company

Long-term government bond yields are very low because the prices of these bonds are very dear. Few knowledgeable people would deny the fact that government bonds are extremely expensive and bond yields are extremely low relative to reasonable expectations of real returns and inflation.

Thus, to say that stocks are cheap compared to bonds (that are expensive) is not saying much.

The fact that bonds are expensive does not make stocks cheap. Stocks may very well be expensive, just less expensive than bonds.

How Expensive Are 10-Year Treasury Bonds?

Yields on 10-year bonds are expensive by any measure.

For example, the average real (inflation-adjusted) yield on 10-year Treasury bonds since 1871 has been 2.58%. The after-inflation yield on 10-year Treasury Notes since 1960 has been 2.58% as well. The comparable figure since 1992 has been 2.43%.

If we take the long-term historical real yield (2.58%) and add it to the latest inflation reading (CPI) of 2.71% the "normalized" nominal yield on 10Y Treasury Notes would be 5.29%.

As of the close on April 23, 2012, the yield on the 10Y Treasury note was 1.94%. This is ridiculously low compared to the normalized yield of 5.29%. This is a dramatic illustration of just how expensive 10Y Treasury bonds are.

As everyone knows, government bond yields are expensive and bond yields are at historically low levels (negative real rates) largely because of U.S. Federal Reserve policy. As an emergency measure to counteract a severe national and international crisis, the Fed is actively intervening to maintain interest rates artificially low. This Fed policy may continue for some time.

However, it is clear that the ability of the Fed to keep bond yields artificially low will not last for more than a few years, at most. Yields will eventually rise to normal levels and/or beyond, one way or another. The only scenario in which bond yields will not normalize is actually terrible for stocks (more on that later in the essay).

Stocks have extremely long duration - hundreds of years. Thus the yields on stocks must be compared to a reasonable expectation of what long-term bond yields will be over very long periods of time. Since there is no doubt that over the long-term bond yields probably rise to normalized levels or beyond (in any scenario that is plausibly favorable for stocks), then it simply is not true that stocks are cheap on the basis of today's artificially low interest rates. Stocks may be less expensive than bonds based on current interest rates. However, stocks are not necessarily cheap when one makes a reasonable estimate of long-term interest rates.

Stock And Bond Yields In Historical Perspective

My own estimate of normalized earnings per share (EPS) for the S&P 500 is around $85. Please note that this estimate is quite high (optimistic) compared to the most commonly cited estimates of normalized EPS. For example, the best known estimate of normalized earnings is that of Yale Professor Robert Shiller, which currently stands at $61.44. Figures cited by John Hussman and Crestmont research oscillate between the mid to low $60s.

Using the April 23 closing S&P index value of 1367 and my normalized earnings estimate of $85 implies a normalized PE of 16.02 and an earnings yield of 6.22%. As pointed out previously, a reasonable estimate for a normalized 10Y bond yield would be 5.29%.

Thus, the spread between the normalized S&P 500 earnings yield and the normalized 10Y bond yield is 0.93%.

The average earnings yield spread (gap) between the S&P 500 earnings yield and the 10Y note yield since 1871 has been 2.81%.

Thus, by long-term historical standards, the current earnings yield spread is quite low, which means that stocks are quite expensive.

Note that I do not believe that the appropriate benchmark for the earnings yield spread should be 2.81%. I personally think that this historical spread does not represent "fair value."

However, the central point that I am making is that is simply not credible to argue that stocks are "cheap" relative to bonds based on the historical record.

The Catch 22 Of Citing Low Bond Yields As An Argument For Stocks

Many analysts have argued that low interest rates reduce the discount rate at which equity cash flows are discounted, thereby raising the value of stocks. Alternatively, analysts argue that low interest rates simply make stocks look attractive on a relative basis.

However, to argue that exceptionally low bond yields make stocks attractive for investment is a logical contradiction.

There are two reasons that bond yields are exceptionally low, and both actually constitute arguments against investing in equities.

The first reason that bond yields are exceptionally low is because the prospects for economic growth in the future are so weak. However, if economic growth in the future will be below trend (which it almost certainly will be), earnings growth will almost certainly be below trend. This means that current PE ratios should be below the historical mean both in absolute terms and relative to interest rates. However, they are not.

The second reason that bond yields are low is related to the first: The US. and much of the rest of the world is experiencing an unprecedented economic emergency and the U.S. Fed is intervening in order to keep the economy on "life support" by manipulating bond yields to artificially low levels.

The problem is that in the midst of all the drama surrounding the economic crisis and the responses by economic policymakers, many investors have simply lost a proper sense of perspective.

It needs to be clearly understood that Fed intervention is a symptom of an economic disease; this intervention hardly constitutes a reason to be getting excited about stocks or to be jumping up and down claiming that they are undervalued. Under current high-risk circumstances, PEs should be trading below their historical averages, both in absolute terms and relative to interest rates. They are not.

The bottom line is that investors cannot have their cake and eat it too. If investors believe that current bond yields will be sustained at currently low levels due to Fed intervention and/or low economic growth, they must necessarily believe that future earnings growth will be well below par. Using this set of assumptions, investors cannot use low bond yields as an argument in favor of stocks.

If investors believe, to the contrary, that bond yields will normalize, then as demonstrated earlier, stocks are not actually cheap at all.

Either way, investors that try to argue for purchase of stocks on the basis of low bond yields are engaged in a logical contradiction.

Other Arguments

Many other attempts have been made to refute the notion that stocks are cheap on the basis of low interest rates. I have not mentioned all of those arguments here, in large part because I believe many of these arguments are not sound.

To illustrate this point, many analysts have harshly criticized the so-called Fed Model, which explicitly compares earnings yields to interest rates. Many, if not most, of these criticisms do not hold up to scrutiny.

For example, it is frequently asserted on empirical grounds that the only time that the relationship between PEs and interest rates held was during the 80s and 90s. This argument is simply false. This relationship is actually quite strong and it has held fairly well most of the time between 1871 and the present - excepting the highly unusual (war and post-war) circumstances prevailing between 1914 and 1960.

Another argument is that the Fed Model is theoretically flawed. The truth of the matter is that while no model is perfect, the so-called Fed Model has much to recommend it from a theoretical point of view. Analysts can reasonably differ about whether the earnings yield should precisely equal the risk free interest rate. What cannot really be argued reasonably is that the basic formula that underlies the comparison of stocks and bonds implicitly embedded in the Fed Model is unsound. This formula is very sound theoretically.

Conclusion

Readers should note that in contrast to other analysts that are currently arguing that stocks are not cheap, I have not contended that that it is theoretically illegitimate or empirically unproductive to compare PEs to bond yields. I believe that interest rates, along with a host of other factors, need to be taken into account when valuing stocks.

The central point that I wish to make in this essay is that the analysts that are currently making the claim that stocks are cheap because bonds are expensive are typically engaging in logically unsound and even contradictory arguments. Perhaps even worse, the people making these arguments usually do not have their facts straight: Historically speaking, stocks are not cheap compared to bonds.

Ultimately, my cautious stance toward equities at the present time is not premised on their current valuations relative to historical averages. On this basis, stocks on aggregate are not expensive or cheap enough on a historical (backward-looking) basis to make a substantial difference.

My cautious stance toward stocks is forward rather than backward looking. For reasons that I will detail more fully in future articles, it is my view that economic growth for the next 10-20 years will be slower than the historical mean. Furthermore, it is my view that macroeconomic volatility will rise considerably relative to what it has been for most of the past 30 years. Given these assumptions, along with the current level of extraordinary risks that permeate economic and financial conditions, stock PEs should be cheap.

In particular, stock earnings yields should be high compared to the risk free long-term interest rate represented by an estimate of the normalized 10Y Treasury yield in order to adequately compensate investors for the near certainty of sub-par growth in the future, as well as for taking on extraordinary present and future risks.

In sum, historically speaking, stocks and index ETFs such as (NYSEARCA:SPY), (NYSEARCA:DIA) and (NASDAQ:QQQ) are currently not cheap relative to 10Y bonds (NYSEARCA:TLT). And stocks are certainly not cheap relative to bonds when the prospects for future growth are properly assessed and when myriad macroeconomic risks are factored in.

Source: Do Low Interest Rates Make Stock PEs Cheap?