Do Low Inflation or Low Interest Rate Environments Justify Paying More For Stocks?
In this era of high valuations one of the standard justifications given for buying stocks has to do with the perception that investors should be willing to pay more for stocks during low inflation environments such as we have seen the past few years. When inflation is low the net present value of stocks is supposed to be higher when one invokes the dividend discount model. Briefly, this model states that the present value is equal to the inflation adjusted sum of all future cash flows discounted to present. This means that one should be willing to pay more for a stock in a lowinflation environment since present value will be eroded less relative to its value some years out, all other things being equal and assuming that nominal earnings are unaffected by changes in the inflation rate. And since the riskfree interest rate tends to be lower when inflation is low some will argue that one should be willing to pay more for stocks in order to achieve the same return in excess of the risk free rate. At times of low inflation investors also tend to feel that the prospects for economic expansion are good and that the quality of earnings may be higher. First of all, let's look at what kind of returns one can expect when investing in the market at various PE ratios: Graph 1
As most investors know, subsequent returns tend to be lower when one pays more for stocks and Graph 1 above bears this out. I picked inflationadjusted threeyear annualized returns for analysis. Fiveyear returns were also looked at but since the graph is very similar I didn't include it. Although there is quite a bit of dispersion in the dataset, in general the investor would have had aboveaverage returns when investing at low PE ratios and below average returns when the PE ratio was higher. No surprises here. Next I wanted to see if it was in fact true that investors pay more for stocks in low inflation environments. I took Schiller's data for the S&P 500 dating back to 1871 and plotted the PE ratio relative to the inflation rate. To calculate the inflation rate, I took the CPI and divided by its value 12 months previously to give a yearoveryear inflation rate: Graph 2 As you can see, there is a pretty weak correlation between the PE ratio and the inflation rate (Rsquared equals 0.05). During times of low inflation, say around zero to 3%, investors tend to pay about 15 times earnings for S&P 500 stocks. However, in higher inflation periods the PE ratio is not that much lower. For example, looking at the trend line on the chart, the PE ratio is tends to be around 13 or so when the inflation rate is between 10 and 15%. Thus, investors really haven't paid that much more for stocks historically when inflation is under control although you would not know that by the way some of the commentators on CNBC Squawkbox or Rukeyser's show carry on about how we should be content to pay 20, 30, or even more times earnings in times of low inflation. This is a bad idea, as I'll explain in a minute. By the way, note that the PE ratio tends to be a little higher in times of deflation which at first blush seems curious since deflation usually is associated with very poor economic conditions, often severe recessions or depressions. However, along with severely crippled business conditions come very low profits thus there is very little "E" (earnings) to go along with "P" (price) in the PE ratio. Therefore, the PE ratio tends to be relatively high in periods of deflation, not because prices are particularly high but because earnings are so very low. Okay, so what happens when investors pay more for stocks at all levels of inflation? What I did was take the data from Graph 2 and look at the threeyear returns separated into two groups by the regression line. Roughly half of the dots are above the regression line (red area in Graph 2a below) and the other half are below it (green area). These two groups were looked at separately when calculating the subsequent threeyear annualized real return. Graph 2a
The results again prove that valuations do matter, or at least they have in the past. The average threeyear annualized real return for the entire period was about 7.4%. However, for the high PE ratio group (red area above the line) annualized returns were only about 4.4% versus 9.4% for the low PE group (green area below the line). Thus collectively, at all inflation levels, subsequent returns are definitely influenced by current valuation levels. I repeated the same exercise using the PE10 ratio rather than the PE ratio and the results were almost the same (4.1%, red area vs. 9.2%, green area). What about longer time periods? I looked at 20 year periods and found similar numbers (3.9% vs. 8.1%). This is all well and good but the question at hand is whether or not it is smart to buy equities at higher PE's in times of low inflation. To answer this question I arbitrarily chose to define low inflation as 0% to 3%. I isolated this area and studied it separately as the dark shaded region in Graph 2b: Graph 2b The results are really no different than what was shown for the whole series collectively. The high PE region (red, dark shaded) had a 5.3% annualized 3 yr. real return as compared to a 10.4% return for the low PE region (green, dark shaded). Annualized 20 yr. real returns were 3.9% for the shaded high PE region vs. 7.0% for the shaded low PE region. Using the PE10 ratio for the 20 yr. periods yielded even more disparate returns of 3.1% and 7.8% for the shaded high and low PE areas, respectively. It would appear, then, than one is much better served by investing at below average PE's whatever the inflation rate happens to be at the time. The folks at CNBC won't like it but it rarely is a good idea to buy the broad market at times of above average valuations, even when inflation looks to be under control. Invest at prices 20, 30, or more times earnings at your own peril! Next I wondered if there was any advantage to investing in the market during times of high inflation versus low inflation, all other things being equal. To do this, threeyear annualized real returns versus the yearoveryear inflation rate were plotted: Graph 3
It is apparent from Graph 3 that there is almost no correlation between the current inflation rate and subsequent annualized threeyear real returns (Rsquared = 0.01). Somewhat surprisingly, it would appear that deflation is associated with very slightly higher returns versus inflationary periods. I guess this is to be expected since deflationary environments tend to be the gloomiest and perceived risk is the greatest  i.e. investors are afraid to buy stocks and thus demand higher returns in order to participate in buying equities. So what about the infamous "Fed Model" which relates the current yield on 10 Treasury bonds to the earnings yield or E/P ratio for stocks? There are various incarnations of this model, some of which use the forward 12 months earnings estimates for the stock market. Earnings estimates are notoriously unreliable and overly optimistic. I prefer to look instead at the actual trailing 12 months earnings versus the treasury bond yield. I was only able to find monthly treasury yield data going back to 1953 to study. I then plotted the result of subtracting the 10year treasury bond yield from the earnings yield versus the 10year forward annualized real return: Graph 4 It would appear from looking at Graph 4 that the Fed Model is essentially worthless in predicting forward stock returns (Rsquared 0.0008). I repeated the analysis using the inverse of the PE10 ratio and got much the same results. This Fed Model relationship has been looked at in much more detail by Cliff Asness in his recent Fight the Fed Model paper which I highly recommend to any of you out there who still think that "undervaluation" as defined by the Fed Model is a good rationale for buying stocks. In summary then, investors do tend to pay slightly more for stocks in low inflation environments but it is generally not wise to buy equities during periods when the PE ratio is above normal, even in periods of benign inflation. The "Fed Model" relationship between earnings yield and 10year Treasury bond yields is also probably useless as a valuation indicator or predictor of future stock market returns.
Last edited: 04/21/2005 
