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

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“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

[drizzle]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?”

or

“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.

Beyond The CAPE

CAPE

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).

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