A standard technique for selling anything is to make it seem like a bargain. For something that is not actually a genuine bargain, this can be done by comparing it to something that is even more outrageous, or by just lying about the contents. To increase sales of a $40 bottle of wine, a retailer might prominently display a $200 bottle of wine, never intending to actually sell the $200 bottle to anyone. Since both are in the same sized bottle, naturally, people will gravitate to the $40 bottle. We tend to forget that what's inside the bottles are not the same. For equities, the item for comparison is usually a bond. To compare equities with bonds, the so-called Fed Model converts a P/E ratio into an earnings yield, which is simply the inverse of the P/E ratio. Instead of dividing P by E, we divide E by P. Intuitively, one wants to buy the asset with the highest yield.

Unfortunately, equities are not bonds. Relative yield does not predict relative return, and never has, but it is interesting to examine why it does not, even though, intuitively, we think it should. The scatter graph below, based on monthly data of the S&P500 and 10- Year Treasuries, shows that the correlation between interest rates and earnings yields is statistically equivalent to zero.

This graph confuses a lot of people. How can interest rates not be related to the P/E ratio, you might ask? When interest rates go down, the value of my house goes up because it costs less to pay the mortgage. It seems common sense that when interest rates go down, the value of other assets must go up. Unfortunately, what appears to be common sense is nothing more than an illusion, even for houses. Interest rates are at an all-time low, and if you checked the value of your house recently, you know that it is not at an all-time high. The question I want to deal with is "Why?"

If we look at a linear chart of the same data, we can see that stocks clearly yield much more than bonds now, but before 1962, it was normal for stocks to yield more, and the current differential is not exceptional by any measure. We also see that during the past 30 years or so, earnings yields seem to have been more correlated with bond yields than before, but checking the scatter graph again for only the data after 1962, we find that even during this later period, the level of interest rates explains only 50% of the level of the earnings yield. One possible conclusion would be that low interest rates are less correlated with earnings yield than high interest rates, but this is only an important clue. It's not the full explanation.

The answer is that interest rates do affect asset prices, but they are only part of a much larger equation. Like all valuation models, the Fed Model is just a simplification of the discounted cash flow model. Simplifications are easier to work with, but you have to understand what you are giving up in terms of accuracy.

The discounted present value for any asset can be expressed as:

V = F/(d-g)

where

*V*is the discounted present value of the future cash flow;*F*is the nominal value of a cash flow amount in a future period;*g*is the growth rate.*d*is the discount rate, which reflects both the cost of tying up capital and the risk premium associated with the possibility that the expected growth rate might not be achieved.

The Fed Model focuses exclusively on near-term earnings and the risk-free interest rate, excluding both the rate of future growth and the risk premium. The Fed Model works when either of these factors are constant or when they cancel each other out. It just so happens that they tend to cancel each other out when interest rates are high. In high-interest rate environments, higher growth tends to be associated with higher risk just because it creates a higher hurdle rate. If you can count on these two factors to move in opposite directions then they cancel each other out and the only thing you need to know is the current earnings and the risk free rate.

Low interest rate environments are different. The lower rates are caused by significantly lower growth expectations and thus, instead of canceling each other out, the growth and risk premium amplify each other. This is why you see the earnings yield rising to much higher levels during low-interest rate environments than it ever does during high-interest rate environments. For the next decade or maybe longer, the risk premium is probably going to create wild swings in share prices that are totally unrelated to either earnings or interest rates. A model that ignores this is going to be wrong almost all of the time.

## Or You Could Just Lie About It

The second way you sell a $15 bottle of wine for $40 is to just flat-out lie about what is inside the bottle. This is effectively what people are doing when they use current earnings in their equation. Stocks are a claim on all future earnings, of which, the current earnings are but a very small fraction. Whenever you use a price to current earnings ratio, you are making the implied assumption that future earnings are correlated to current earnings and therefore, not relevant. This is just a lie. Earnings in the US are so cyclical that they are actually inversely correlated to future earnings, and it turns out that they actually predict themselves quite well. Current earnings, as a percent of GDP, actually explain 70% of the subsequent 5-year earnings growth. At the current level of 5.2% of GDP, earnings are at nearly all-time highs and there are no examples in history of earnings being this high and not declining precipitously over the subsequent five years.

If we stretch this data out into a line graph and plug in the forecast, we see that the model is projecting the most aggressive decline in earnings since the data became available. Be careful of long-term charts however. For one thing, the peak in earnings is not as close as it looks. According to the model, earnings should peak in the third quarter of 2013 and don't really turn significantly lower until the second quarter of 2015. Between now and then, earnings are actually more likely to go sideways. On the other hand, it is important not to expect too much accuracy from the model. It only explains 70% of the changes. Earnings in the 1st Quarter of 2012 are already higher than the expected peak. Conceivably, earnings have already peaked, but even if not, the best case scenario is that earnings muddle along for the next 12-18 months and then completely collapse.

The most important take-away point from all of this is that any ratio of price to current earnings today is pretty meaningless. It is still important to simplify because, after-all, we don't know what the risk premium or the exact growth rate will be. We have to make guesses, but those guesses tend to be far more useful if we start with reasonable assumptions, and assuming that current earnings are sustainable just doesn't count as reasonable.

The last chart illustrates this point. In this chart we show for items all adjusted for inflation:

1. Stock prices

2. Current earnings multiplied by the long term average of 14

3. Trend earnings multiplied by the long-term average of 12

4. Forecast earnings multiplied by 14.

While the current price and current earnings may seem to be roughly in line with each other, they are both well above trend and using the forecasts from the discussion above, can be expected to come down well below trend. If these projections prove accurate, it will be a very long time before equities become attractive investments again.