Wednesday, October 22, 2014

The Earnings Yield, Interest Rates, and Leverage

In some previous posts I have shown how high PE ratios and profit margins can, ironically, be a reflection of lower risk.  Given a set level of operating profits, and, say, an 8% required return on the unlevered firm's assets, a firm facing 3% interest rates with a 5% equity premium, at the optimal allocation of capital, will have lower leverage, higher net profit margins, and a lower share price and a lower PE ratio, than the same firm facing 5% interest rates and a 3% equity premium.

Low Interest Rates High Interest Rates
High Equity Premium Low Equity Premium
Leverage Low High
Net Profit Margin High Low
Share Price & Enterprise Value Low High
PE Ratio Low High

This is complicated in a business cycle shock because frequently firms experience operational dislocations and/or are pushed out of their optimal capital allocation targets.  But, at this late point in a cycle recovery, when dislocations have been generally repaired, when interest rates go up, leverage will go up, profit margins will decline, and share prices will increase from both revenue growth and multiple expansion.

This might seem counterintuitive in some ways, but this should follow from a Modigliani-Miller framework where corporate income is taxed.  Where I think intuition is wrong is that we tend to conceive of debt in a consumption context.  Debt tends to be described as a risky and greedy attempt at overconsumption, or for corporations, a dangerous way to create false growth that exposes them to higher risk.

Of course, a firm leveraged imprudently would face high risk.  And, firms that have been exposed to deep revenue shocks tend to meet their ends when they can't pay the interest payments on their debt any more.  But, I think what we see mixes with these perceptual biases in a way that creates a false interpretation.  If a firm didn't have any debt, it might fail at the point when it couldn't pay its workers anymore.  Would we say that hiring workers is a risky proposition that, generally, causes firms to fail?  I suppose in any failure we can claim that workers were overpaid or unproductive.  But, generally, clearly, firms need workers to produce.  So, while hiring workers inefficiently would be a problem, workers themselves are not a source of risk.  I propose that debt is the same.  It can be handled poorly, but it is simply a part of the stakeholder structure of the firm, and is not, in and of itself, a risk.  Some workers might have fixed salaries while others receive wages tied to profits or revenues in some way.  And, some capital (debt) receives a fixed payment while some capital (equity) received residual payment.  All firms must decide on a mixture of fixed and variable costs, but there will always be a reasonable level of fixed costs above zero.....Anyway, I'm going on too long.

Over time, total required real returns on firm capital appear to be fairly stable.  Generally, when interest rates fall, equity risk premiums rise.  This suggests that there are fairly stable factors regarding delayed consumption and the myriad other factors that create profit for investment and that within the ownership claims on investment, there is a risk trade between debt and equity.  Debt holders trade risk with equity holders.  So, instead of having a single class of owners in a unlevered firm, there are owners with a certain payout structure and owners with the remaining residual payout structure.  Because certainty has value, debt holders accept a discounted payout, and thus, the equity premium is always positive.

The long term balance between debt and equity does seem to follow the trends I described in the table above, and this can be explained with the Modigliani Miller framework as a product of corporate taxation.  But, note, this also aligns with a risk-trading perspective.  Low interest rates are a sign that investors have become risk averse, and they are willing to trade away a higher discount from the unlevered return on assets to the remaining equity holders in order to minimize local risk.  We might imagine that the demand for low risk ownership would push debt levels up.  But, this would leave a bifurcated set of investors - many investors with low-return/low risk payouts, and few investors with very risky payouts.  It may be more realistic to imagine a normal distribution of investors where the mean level of risk aversion has increased, and the entire body of investors has shifted or skewed.  So, when investors as a group become more risk averse, driving down interest rates, the marginal investor in the switch between equity and debt will also be more risk averse.  Corporate deleveraging changes the nature of equity, making it less volatile, and thus low interest rates are associated with falling debt levels as the marginal investor is attracted into the less volatile equity position.

Earnings Yield

If there is any truth to my framing above, the comparison of the earnings yield on equities and the yield on bonds is not very helpful.  There may be a tendency for earnings yields to decline when interest rates are low.  But, this may be related to the deleveraging of equities, so that the lower earnings yield simply reflects the lower relative risk of equities in that context.

A low earnings yield may not be a signal to a risk-insensitive investor to switch to bonds.  It may be a signal to leverage up or beta up her equity portfolio.

First, please let me know if anyone knows a source for S&P 500 debt/equity ratios that goes back further than 1952.  I'd love to see how it looks with a longer time frame.

Regarding the graph, the earnings yield looks like it tracks with leverage as much as it tracks with interest rates.  (Note, as an aside, the unusual behavior during two demand shock recessions in the 2000's, where revenue shocks caused earnings to decline and leverage to increase, both temporarily, as corporations were thrown into disequilibrium.)

One could say that leverage and earnings yield track simply because they both have equity value as the denominator.  That is true.  It is interesting that debt as a proportion of net operating profits is fairly stable over time, and that is what leads to this co-movement.

On the other hand, the co-movement of the earnings yield and bond yield is problematic for another reason.  The bond yield includes an inflation premium.  The earnings yield is simply a measure of the trailing earnings.  The inflation premium will come from future nominal growth of earnings and share price.  When this adjustment is made, these indicators don't move together as tightly in the high inflation 1970s.  In fact, using an equity risk premium (which takes growth expectations into account) instead of an equity yield, there tends to be an inverse relationship so that inflation adjusted interest rates and equity premiums tend to add up to a fairly stable return level.

I suspect there are times when a low relative earnings yield should signal higher weights in bonds and other times when a low relative earnings yield signals higher weights in equities (to make up for low leverage).  I don't know if there is a coherent way to decipher the signal.  As such, I'm not sure how useful earnings yield relative to bond yield is as an allocation tool.


  1. TravisV here.

    I love this topic! It's challenging to do probability analysis for what will happen to all these variables that influence asset prices. But anyone with significant money on the line needs to think seriously about scenario / probability analysis.

    I think you agree with me that if NGDP growth expectations and interest rates rise (to, say, 4% on the U.S. 10-year treasury), P/E ratios will not collapse. If fact, they'll probably increase. So Asness's has it exactly backwards in Fortune Magazine re: interest rates and P/E ratios.

    Now, what if our current negative demand shock deepens and the yield on 10-year U.S. treasuries goes to 1.5%? Earnings growth would certainly slow. But would P/E ratios collapse? Would they even fall below the median P/E ratio of the 1970's and 1980's (thinking about Shiller's misleading CAPE reasoning)?

    After all, think about (r - g). If NGDP expectations fall, expected growth falls, but so do interest rates (to a lesser extent).

    According to my intuition, U.S. stock P/E ratios might fall, but only slightly.

    Kevin, what do you sense would probably happen in the following scenario: if a negative demand shock drove the yield on 10-year U.S. treasuries to 1.5%, how much would U.S. P/E ratios generally fall (on, say, the S&P 500)?

    1. That article is terrible. The result from the 2003 paper is just a product of the arbitrary 10 year holding period. So, basically, if they are describing the paper correctly, he shows that rising rates are a bad time to invest because we have tended to have decadal business cycles. So, you shouldn't buy stocks today if rates go up because in 2022 there will be a recession.

      Here's S&P 500 performance after the initiation of rate increases:

      The horror!

      In the previous two cycles, these stock market gains came with stable or slightly falling PE ratios during most of the recovery. It was only very late in the cycles when long term rates and leverage began to move up again that PE ratios started to increase.

      In the first post of my series on risk & valuations, I show a simple operational model where the PE ratio increases somewhat as leverage declines. And, I think this is something to consider. But, in the cyclical context, there are a lot of things happening with growth expectations, earnings and capacity utilization, changing rates and risk premiums. Lower equity premiums will naturally be associated with higher PE ratios. So, while as a start, lower leverage would lead to a higher PE ratio, when I looked at a more dynamic model in part 4, it showed higher PE ratios when the leverage was associated with lower equity premiums. But leverage and growth expectations would have effects on equity and price ratios that get a little messy and end up being the product of the relative scale of various competing effects.

      To be honest, I haven't developed a strong intuition for PE ratio movements within this model I've been describing. My best guess would be similar to yours - a slight fall in PE ratios.

  2. Kevin, I think this post and the next one are terrific. In particular, the idea of looking at including corporate leverage is a useful addition to the discussion I hadn't considered.

    I'm not so sure about netting out inflation, however. It seems to me that we can net out 'expected inflation', but, prior to the introduction of TIPs, this was mostly guesswork.

    Anyway, a related point. I commented on a recent MR thread in which Tyler used the following title: "How much of financial fluctuations is behavioral?" (as opposed to rational or efficient, I reckon).

    I thought the link was very wrongheaded, but I would very much appreciate the opinion of someone like you, if you are so inclined. I went on to add a comment of my own at the bottom of the MR thread, and I am extremely curious to hear what you think about it, particularly anything I said that is obviously and embarrassingly wrong. Anyway, I will now spam you by copying a portion of my comment in order to underscore how desperately I would like intelligent feedback. Thank you and apologies for the length of this.

    Brian Donohue

    Excerpt of MR comment:
    I think there is much greater insight to be gained on the subject from following some homely wisdom from old school investors, in particular: “markets learn lessons very well in the short term, ok in the medium term, and not at all in the long term.”
    This seems obviously true to me. In the summer of 1932, the DIVIDEND yield on the S&P 500 was north of 10%, way higher than the available yield on bonds or cash. Why? Investors were scarred by the crash of 1929 and needed a helluva inducement to hold stocks. Very high equity risk premium available.
    This situation (S&P 500 dividend yield > long-term bond yield), as strange as it seems to us today, persisted through most of the 1950s, tapering off as memory of the crash receded.
    Still, the “risk premium” on the S&P 500 (earnings yield plus modest growth assumption minus long-term bond yield) persisted until the early 1970s. The market crash of 1973-1974 pushed the risk premium back up, but interest rates rose throughout the 1970s, so that by 1980 the S&P 500 risk premium was basically zero.
    Why? Bond investors had been clobbered by inflation and now THEY were demanding a premium.
    And they got it. Everyone remembers the bull market of the 1980s and 1990s as a great time to own stocks, but, in fact, long-term bonds were also producing double-digit returns over this period with a lot less risk, as inflation came in below expectations and rates started their long march downward.
    On January 18, 2000, the 30-year Treasury was yielding 6.75%. True rational agents (think forward-looking Warren Buffett, not the rearview mirror knucklehead in the paper) were extremely skeptical that the S&P 500 return could outperform this yield. But the rearview mirror crowd LOVED stocks in 2000. (Old man Buffett doesn’t get it!)
    And, of course bonds subsequently destroyed stocks. An investment in the S&P 500 in early 2000 earned less than 1% per year over the next 10 years, while bonds continued to rake on the strength of ever lower rates.
    In the pit of despair in March of 2009, the rearview mirror crowd HATED stocks, precisely as the equity risk premium had again reached salivating levels not seen since the 1950s.
    Those who understood this and had the intestinal fortitude, (Buffet: “By the time you hear the robins singing, spring is already here.”) have profited handsomely since then.
    Today, the equity risk premium is near its historical average, not because stocks are expected to go gangbusters, but because interest rates are near all-time lows (Buffett at the end of 2012: “Bonds should come with a warning label right now.)

    1. All great points, Brian. I wasn't quite sure what to make of the article Tyler posted. It seems like they are framing the issue as if a rational risk premium would be a constant, which is strange. As you point out, the world's a dynamic place. Risks change. Risk premiums are inherently behavioral, and while we might presume that they are a mixture of rational and irrational individual behaviors, to the extent that expectations can even be categorized cleanly into those categories, it didn't look like the article had developed a way to get at them. Admittedly, I gave up fairly early and didn't dig into their methodologies very deeply. It seems like the standard problem of EMH tests, that the test is also a test of your own model.

      I don't really have anything to add to your comment.

      As for the inflation adjustment, I agree that it's a bit of guesswork in pre-TIPS data, but the real bond rate, to the extent that we can estimate it, would be the rate to compare with. In my graph above, which shows the components of total asset returns, there are probably temporary fluctuations of a percent or two from year to year, but I think the relative movements over time are generally similar, whether you use TIPS spreads, Michigan inflation expectations, or real time inflation indicators. But, some work would need to be done to get a TIPS-quality indicator that goes further back in time. The other sort of fudge factor there is that equity risk premiums are also reliant on an estimate of growth expectations. I use data from Aswath Damodaran, but I'm sure there are many questions about that variable.