### P/E Ratios In Low Interest Rate Environments

Published July 12th, 2010 in Valuation*The following is a guest post by Charles H. Dow Award winner, Wayne Whaley (CTA) of Witter & Lester. If you would like to be privy to his daily market comments and model ratings via daily email, free of charge, email him at wayne[AT]witterlester.com with the subject title “ADD ME TO DAILY EMAIL”.*

I presented a study recently showing the historical relationship between the equity earnings and interest rate yields. The current spread was shown to be the widest since 1980. Although back-tested trading of such models (Fed Model derivations) have not proven extremely successful (except at extremes), it is this person’s opinion that this approach has more utility than simply valuing the market at P/E levels, void of any other relevant variables.

I read a comment on a financial site this week from a reader who stated that in regards to valuation, all we know is that the market has historically sold between 10 and 20 times earnings, which implies that the current market, with S&P 500 trailing earnings of $65, should sell between 650 and 1300 - depending on your outlook for earnings growth for the rest of the year. My thought was that we can do somewhat better than a 650-1300 range and it prompted me to do the following update to my previous study. I wanted to look at P/Es as a function of the level of interest rates and see if we could at least narrow the 650-1300 range to a 90% confidence band of P/E levels.

Recall, that for my interest rate variable, I default to an average interest rate (AIR), where AIR is the average of the 3 Mt T-bill, 5 Year Note, and 30 Year Bond on any given day. The current (as of July 9th, 2010) AIR is 2.08%. For our study, let’s classify three different levels of AIR where “Low” is when AIR is below 5% and “High” when AIR is above 7.5%. Scanning my 40 years of earnings and interest rate data, I was able to make the following table of observations:

**Price to Earnings Ratio vs Interest Rate Levels (1970-June 2010)**

Since 1970, the average P/E, where E is calculated on trailing 4 quarter earnings, has been 19.55, slightly higher than the 15 most of us were trained to expect as the norm a couple of decades ago. The trend higher in trailing P/E’s is due largely to the collapse of earnings in 2008, that shot P/E’s temporarily into the triple digits, thus distorting averages, and secondly due to the fact that, as you can see in the table, stocks ‘tend to’ trade in a higher P/E plane when interest rates are extremely low, as they have been over the last decade. Anomalies, such as the 08 fourth quarter earnings collapse are the reason a lot of statisticians prefer to reference medians instead of averages. The median P/E since 1970 is 17.24.

The S&P 500 closed at 1078 on Friday (July 9, 2010). Trailing one year earnings, through the first quarter of 2010, were 60.83. We will have a better handle on second quarter earnings in a couple of weeks, but if we conservatively estimate that 2nd quarter earnings are simply equal to first quarter earnings, the trailing 12 month earnings go to at least 65.0, which would put today’s P/E at 1078/65 = 16.58, which is below the 90% confidence range (17.55-46.47) for low AIR periods.

The 90% confidence bands are very wide at all levels of interest rates and leave a lot of room for both Bulls & Bears to reside. I don’t know anyone that is anxious to pay 46.47 times earnings to own the S&P 500, regardless of the level of interest rates, so I added a table column, I called “Wayne’s (P/E) Band”, that seemed to simply make common sense given all considerations I have studied. So my take is that with interest rates extremely low, I’m inclined to view the market as cheap at 15 times earnings and expensive at 22.5 times earnings. Using trailing earnings of 65, that would put us in a S&P 500 range of 975 to 1462.5.

**The Bearish Case**

Why stocks should indeed be selling at the low end (S&P 500 at 975) of the historic low (15) of the P/E range focus around the arguments that, although the market looks inexpensive at these levels of interest rates:

- Stocks are expensive relative to future earnings which will suffer greatly in the upcoming deflationary environment that lies ahead. Or conversely,
- Fed policy is inflationary and we are headed for much higher interest rates, which would not justify such high P/E’s, or
- If you go back to the 1950s or 1930’s you can find cases where the above interest rate/earnings relationship fails.

All duly noted.

**The Bullish Case**

Why stocks should move back up into at least the middle (S&P 500 at 1218) of our defined low interest rate P/E range are:

- Not only are rates in our low interest rate level where high historic P/E’s are justified, rates are way below 5% and the current earnings yield on equities (6.0%) is nearly 3 times the yield of typical mid curve interest rates (2.08), a relationship spread we have not seen in over 30 years.
- If you look at the trend in S&P 500 quarterly earnings over the last 5 quarters, one can make the case that trailing four quarter earnings should improve or in the worse case stay at the level they are. For example (see table below), if S&P 500 earnings simply increase 50 cents a quarter for the next three quarters, earnings for 2010 would be 72.92 and at the current S&P 500 level of 1078, would produce a P/E of 14.78. This analysis is with conservative earnings projections, as it is not difficult to find earnings projections in the mid-80’s for 2010.
- It will be difficult to maintain the level of earnings growth that we have experienced over the last five quarters, but the argument for continuation of at least a positive trend gains additional support from Conference Board’s Leading Economic Indicators (LEI) which have been up 13 of the last 14 months.

**Summary**

During periods of extremely low interest rates, stocks can reasonably be expected to sell in a P/E range somewhat higher than the historic 10-20 range. It is difficult for me to envision the P/E’s going to single digits during this bear market cycle (as has been the case in many previous inflationary bear markets) - unless the single digit P/E’s come far down the road when interest rates are much higher (above 5%).

Based on historic precedent, stocks are trading at the low end of the range that would be expected with current low interest rate levels. However markets can, and do, stay under and overvalued for years at a time before reverting back to the mean.

Technicians will argue that the answer to the above debate lies in the tone and message hidden in the tape. Hopefully, we will get some additional insight in that regard shortly and a new story to share. Stay tuned.

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Babak & Readers,

If you get a chance for a last second edit, Under the Bullish Cash -2. should read earnings projections in the mid 80s instead of mid 1980’s.

Thanks for the post.

Horrible sample to draw any useful conclusions from.

Thanks for catching that Wayne - corrected now

Wayne,

Here is an interesting concept that I hope maybe you’ll apply your strong data analysis skills to.

Maybe P/E ratios are more tied to demographic factors, specifically the size of various generations who apply different magnitudes of buying and selling pressure to stocks.

Check out these links

In this study, Geanakoplos et al related demography to long-term stock returns. They found that P/E ratios were correlated to the ratio of middle-aged people to young adults, otherwise known as the MY ratio. When MY rises, the market P/E will tend to rise and when it falls, P/Es tend to fall.If the conclusions of the study are correct, then we should see a continued fall in P/E ratios with a long-term bottom in stock prices forming about 2018, or eight years from now.I’m wondering if this possibly explains the conundrum of very low P/E ratios in the 1940s and early 50s when interest rates were also very low.

On a gut level this makes sense to me. From 1995-2000, you had the biggest stock bubble of the century and maybe it was entirely driven by just the massive size of the baby boom generation being in their peak earning and asset accumulation years. Now we see all these articles about baby boomers abandoning stocks which perhaps will apply steady, downward pressure on P/E multiples.

Mike, thanks for bringing up the MY ratio, I talked about it back in 2009: Does Demographics Drive The Stock Market?. Focusing on the expansion and contraction of the P/E ratio is key because looking at earnings, as most tend to do is irrelevant since at different points in time, each $1 of earning is valued differently.

Why not also look at real interest rates?

Also, I wonder if it matters that today’s investors have more choice than stocks vs bonds i.e. various hedge fund strategies, private equity, emerging markets (not new, but easier to invest in today and their debt viewed as less risky), new derivatives markets etc.

Also, for private investors the “alternative investment” of paying down your debt may have become more attractive than ever before, not because such debt is necessarily high-interest, but because it is viewed as being simply too large given its huge size, ever rising expenses like healthcare, and uncertain outlook for income growth and house price appreciation.

brilliant piece you hit the nail on the head your predictions were 100% accurate, do you care to update this for 2011?

you were 100% correct do you care to update this for 2011? much appropriated i will publicize it if you do