Beyond The CAPE: The Influence Of Interest Rates On Equity Valuation

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Knightsbridge Asset Management commentary for the month ended October 31, 2016; titled, “Beyond The CAPE'”

Also see


  • Q3 2016 hedge fund letters
  • Q2 2016 hedge fund letters


“I am wiser than this man, for neither of us appears to know anything great and good; but he fancies he knows something, although he knows nothing; whereas I, as I do not know anything, so I do not fancy I do. In this trifling particular, then, I appear to be wiser than he, because I do not fancy I know what I do not know.” — Socrates, 5th Century BC – Philosopher


This quarter we’re going to take a break from our usual practice of surveying the investment landscape and instead focus on a single topic which begins on the next page.

We have attempted to write in a manner interesting to students of the markets but still understandable by the layman. Most of the technical details behind our exercise will appear in footnotes at the end of this letter… we suggest casual readers skip these.

“How much should stocks go up when rates go down?”


“How I learned to stop worrying about valuation and love stocks.”

It is relatively common knowledge that when interest rates decline stocks ought to rise, and they typically do. We are far from the first investors to ponder the effect of interest rates on valuation, but the majority of the analyses we have seen have been empirical, i.e. more about what happened in the past. A good example is the following graph which compares 10-year treasury rates (bottom axis) with the earnings yield of the S&P 500 (inverse of the P/E) on the side axis. The image contains a linear “best fit” line, but it would be quite a jump to say that the market “ought” to price itself to be
on the line.


Given that the market rise of the past few years was probably somewhat justified by the decline in interest rates, we set out to try and demonstrate to ourselves just how much stocks should move when interest rates fall. The analysis is simple enough, but we hadn’t seen anyone else do it and wanted to see for ourselves. From here it is an irresistible step to ask “is the stock market expensive?” In preview, we answer with a rather qualified “no”.

Before we get started we must confess to a number of caveats.i First off, we are not forecasting future interest rates! We are agnostic, though we have been and continue to be very skeptical of the idea that “rates will rise because they have been lower than they were in the past”, as we have discussed in previous quarterly letters. Rates will definitely change in the future, one way or the other. (Those who believe rates can surely go no lower may wish to examine their rate forecasting track record.)

Secondly, in order to undertake this demonstration we had to make lots of assumptions. We didn’t try to necessarily make the “right” assumptions; we simply attempted to make reasonable and defensible ones. As reasonable minds can and will differ on these assumptions, we have published our dataii and underlying calculations on our website.iii

Finally, the biggest caveat is that we are about to demonstrate how value changes when you change one variable (interest rates) and leave all else equal. In the real world, when you change one thing, all else is never equal, and economic variables have a sneaky way of interacting in offsetting ways. Lower interest rates often come with lower accompanying earnings growth, which would have a large effect on stock market value if appropriately predicted. Earnings growth has and will change over time; we have not varied it in our exercise.iii

A stock receives its value from the future cash flows it will deliver to the company’s owners. The stock market is just a grouping of individual stocks, and in aggregate receives its value from all the future cash flows of all the underlying companies in the market. Without going through all the basics of the time value of money, one dollar of cash flow ten years from now is worth less than one dollar of cash flow next year. Just how much less is determined by interest rates, or discount rates as they are sometimes called. Thus, the same exact set of future cash flows has a very different present-day-value under a different set of interest rates.

To demonstrate the effect of interest rates on valuation, we constructed a “stock-market-like” set of cash flows growing at the average historical rate of real earnings growthiv… and only changed the interest rates we used to value those cash flows.v We dug up the real world U.S. interest rates that were recorded for every maturity in every month since 1953. We then used each set of different interest rates to value the same set of cash flows to come up with different present values for each historical month (i.e. discounting future period cash flows by the actual interest rates on the yield curve at that time during the 1953 to today period).vi Below we present the value of the “stock-market-like” stream of cash flows under the interest rate regimes which prevailed since 1953.

Beyond The CAPE

As you can see, changes in the interest rate environment alone have an enormous effect on value, all else equal. Indeed, today’s near-all-time-low rate environment would imply historically lofty valuations. Looking at the above chart, in today’s low discount rate environment a stock-market-like stream of cash flows is worth more than in any period since at least the 1950s. We went on to make a couple adjustments (that require a lot of assumptions) to instead use estimated real (after inflation) interest ratesvii and include an equity risk premium.viii This produced the more realistic absolute numbers which appear below… which send the same basic message.

Beyond The CAPE

Another way to present these results is to pick a base year and put the valuation implications of interest rates on a relative basis- how much more or less the same set of cash flows is worth under different interest rate environments. We chose March 1971 as our base period because its interest rate environment produced the median present value of cash flows in our above analysis, but choosing March 2000 or September 1993 would have yielded nearly identical results.ix Below is the effect of the interest rate environment on valuation relative to March 1971.

Beyond The CAPE

This measure shows the same exact asset would be worth double today what it would have been worth in 1971, 1993, or 2000! In other words it shows the change in interest rates implies a justified doubling of investment multiples such as price to earnings or price to sales. (That being said we’re not suggesting stocks will actually trade to those levels, not least of which because stocks were not necessarily at justified levels previously. Even we admit in the current environment there is more scope for rates to rise which is an increased risk). This magnitude of valuation increase stands in stark contrast to some off-the-cuff estimates we sometime run across which posit that the market should trade 10-15% higher than “normal” due to the current rate environment. Interest rates make a bigger difference than that.

Let’s turn our attention to today’s U.S. stock market… is it expensive or not? First, a short disclaimer on what “expensive” means for the market. Market valuation should not be used as a timing tool! “Expensive” does not mean “will go down in the future”, not least of which because overpriced assets can and do become more overpriced for very long periods of time. Furthermore, the market would be expected to have a general rate of advance over time as the economy grows, and so even a pricey market might still be expected to appreciate, just perhaps not as fast as it would under a less exuberant valuation.

In any case, in our opinion the best measure of whether the stock market is cheap or expensive is Professor Robert Shiller’s “Cyclically Adjusted Price to Earnings Ratio”, or CAPE, which we have mentioned a few times in previous quarterly letters. This measure takes the price of the market and adjusts it for the average earnings of the market for the last ten years (adjusted for inflation), based on the idea that earnings can swing so much from year to year that a longer term average is a better measure of true earnings power going forward. An updated graph appears below.

Beyond The CAPE

While not at all-time highs, by this measure the market appears to be in expensive territory.x

However, the CAPE doesn’t take into account the interest rate environment. Isn’t it therefore likely that some of the market’s expensiveness is “justified” by the rate environment? How much? To answer this question we can again choose a base year and then adjust the regular CAPE values up and down according to our earlier exercise demonstrating the effect of interest rates on value.xi This modifies the original CAPE to come up with a “Cyclically Rate Adjusted PE”, or CRAPE. We present the results atop the next page.

Beyond The CAPE

In this updated measure, when the interest rate environment is taken into account, today’s market doesn’t look so expensive… in fact the current CRAPE value of 13.51 is below 77% of all the observations since 1953. Despite being near all-time absolute highs, the stock market no longer appears “frothy” or wildly overvalued.

So are stocks expensive? It depends on what you adjust for. If you only adjust for earnings, then yes, stocks do appear expensive. But, if you adjust for earnings as well as interest rates, then stocks do not appear expensive.xii

What does this mean? It means that if you believe either 1) rates are staying where they are or 2) rates are equally likely to go down as opposed to up or 3) you have no wish to place a bet on rates because you have no insight better than the bond market’s, then… stocks are reasonably valued and perhaps on the cheap side, when compared to your other main alternative, the bond market.xiii There are other conclusions as well. For those who say, “I don’t want to adjust for interest rates”, then yes, stocks are expensive… but bonds are REALLY expensive. If you are worried about stocks because you think rates will rise, then you ought to be even more worried about bonds. Another conclusion is that because our CRAPE measure ends somewhat below the median range, rates could indeed rise to some degree and stocks would still be cheap (our ballpark estimate is that even if rates rose around 1% across all maturities, stocks would still be reasonably valued).xiv Alternatively stated: stocks perhaps didn’t rise enough when rates fell so they wouldn’t fall if rates rise (or at least not nearly as much as bonds).

We have heard many complaints in recent years that “stocks are expensive, bonds are expensive, real estate is expensive… everything is expensive.” And…? This is the same thing as saying worldwide interest rates in general are “too low”… and carries few practical implications unless you also believe “this will change”. If assets are too expensive, then must one hold cash or nothing in order to “buy” what’s cheap? Holding cash is only beneficial if asset prices fall… which is possible, but over time that is a losing proposition, and is tantamount to timing the market. (We continue to hold some cash because it allows us to be opportunistic and for risk management purposes).

Finally, we must address those who would protest “but rates ARE going up.” They very well might be… or they might not… or at least even if they do, the pace and magnitude are unknown. Much like Socrates, we do not know, and we are aware that we do not know. Those who think they do know when and how rates will return to “normal” would do well to look at 1) Japan’s ultra-low rates of the past 20 years 2) the even-lower negative rates in Europe and 3) the history of interest rates in the U.S. in the decades around the turn of the 19th century (hint: low for a very long time).

In any case, the real question for equity holders isn’t “are rates going to rise”, it is rather, “are rates going to rise with enough magnitude to send the stock market lower, and in a short enough timeframe such that it will be worth sitting in cash during the wait.” We definitely do not know the answer to this. We do admit that the forward return profile for stocks at present does not match the average of the last 10, 20, or 50 years. Still, when viewed against bonds or cash, we believe stocks are the best game in town. We thank our clients for the continuing trust you place in us.

John G. Prichard

Miles E. Yourman

P.S. Special thanks are due to our summer intern, Alex Pearce, who helped extensively with the arranging of the data and the construction of the spreadsheet behind this exercise. Good luck in your senior year!

See the full PDF below.


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