Are equities overvalued?

It’s a common proposition that prevailing market valuations are unreflective of underlying fundamentals. Some say that we’re living through an outright bubble and are in for a correction, and others that markets will be lethargic and stagnant over the next few months, without much room to grow at historical rates.

On the other hand, extremely low interest rates – not just in Treasuries, but safe(r) assets in general – suggest anxiety about future growth. If growth potential really is so fantastic, it doesn’t make sense to crowd into risk-free assets that have almost no claim on that growth. One explanation could be a decline in the risk premium, which militates in favor of the “lethargic and stagnant” view – that we’ve rerated valuations with a lower discount rate, but shouldn’t expect exceptional growth.

A decline in the risk premium would suggest a host of projects that were otherwise unprofitable become feasible, resulting in increased business investment across the board. This may be the case (and we can’t examine the counterfactual) but, somehow, this doesn’t sit well with the prevalence of cash and highly liquid assets piling up on corporate balance sheets.

One simple (if unsatisfying) explanation might be that markets aren’t efficient. There are two types of inefficient. The sort that persists temporarily, and that is bidded away as investors and arbitrageurs profit on the discrepancy, and the sort for which there isn’t an obvious correcting mechanism. The latter, I would argue, is rarer but one can definitely contrive explanations that make sense of the situation.

A possibility that I find appealing stems from a simple principal-agent dilemma. The risk profile for high-level managers (who are – as a baseline – compensated extremely well) aggressively pursuing projects that become viable on the margin is asymmetric. If lots of cash is lost, the manager risks his job. If it succeeds, given that it is a marginal investment, the effect on his bonus would be minimal. The literature on CEO salaries outlines incredible bonuses as an incentive to take big risks – but big risks with big payoffs (and big losses), not necessarily those that are merely better than nothing.

There is some real evidence that this sort of managerial kerfuffle is real:

Importantly, the hurdle rates are often left unchanged for years, even when interest rates drop. A paper included in the latest Reserve Bank Bulletin reports that some hurdle rates have not changed in years.

They were set when interest rates were “far higher than they are today”.

The bank’s findings match those of a survey by Deloitte that found that two-thirds of corporations recalculate their hurdle rate less frequently than they recalculate their cost of capital. Nearly half change their hurdle rate “very rarely”.

Among the reasons businesses give are that changes to the rate might “send the wrong message to staff proposing projects”. Another reason is that changes in the hurdle rate “require board approval”.  Or that keeping the rate high protects against the type of economic uncertainty likely to be present when interest rates are low.

One could argue that this risk aversion should befall investors and managers. Unfortunately, high-level managers have a much less diversified implicit portfolio (including the returns from their labor) than investors, and cannot diversify the idiosyncratic risk that emerges from projects that are profitable on the margin (wherever EV is all the investor would care about).

This outlines at least one possible case of “persistent inefficiency”. You might even argue that inefficiency is cyclical – spare me a few moments of speculative rambling before we get to real data. In a sense the “market” is like a public good. We put into it by performing due diligence on stocks, commodities, and countries to arbitrage any mispricing and more efficiently allocate capital. We take from it by holding its value as a given and using models to infer useful information. Implicit volatility. Inflation expectations. Future price probability distributions.

There’s a tension between the two that becomes especially pronounced when one takes from one pond and puts it into another pond. If you’re a fundamental investor discounting future cash flows, you might take the forward Treasury curve as a starting point to measuring the WACC. (In fact, unless Janet Yellen tells you what she’s up to, you don’t have much of a choice but to take the forward yield curve as a given).

There is some “fundamental” work that goes into generating the forward curve which currently underprices the Fed’s dot plot. The market is telling you that certain economic and geopolitical gravities are conspiring against the Fed’s chosen choice of action – to increase interest rates. It’s come to this conclusion under the guidance of thousands of macro investors who have studied these forces to the extent they can.

Then your value investors are taking this work and applying it to their valuations of individual companies. If the market is wrong, and the Fed is right, the discounted value of S&P cash flows would be lower than valuations imply. But David Einhorn and George Soros do very different things and, in a vague sense, rely on each other for their fundamental work.

This doesn’t really solve our problem. If markets are underpricing the Fed because they think its optimistic about wage growth and international stability, this would be reflected in lower earnings for American companies and be a “short equities, long bonds” moment.

But maybe there isn’t a paradox. And maybe markets aren’t really overpricing anything. That, at least, is the theory I’d like to forward.

If, at a first pass, Price = Earnings/(Risk-free Rate + Risk Premium – Growth), then G_implied = D + RP – (E/P). To my surprise, the picture you get really isn’t that crazy.


The blue line is market implied earnings growth, and the red line is smoothed (realized) NGDP growth. I took a market risk premium of 4.5%. The two aren’t perfectly aligned for three key reasons:

  1. Primarily, the rough estimation I used is incorrect. We should discount by the forward curve instead of the spot rate. Today this would increase the implied growth rate but not meaningfully.
  2. Implied earnings growth is ex ante whereas NGDP growth is ex post. Markets aren’t always correct, there are always random, exogenous, and significant events (wars, draughts, etc.) that couldn’t be predicted before, after which the market corrects. This explains why the two series aren’t perfectly equal, but more in generally the same direction (after the information is released, the market revalues as necessary, changing the implied earnings growth).
  3. And implied earnings are a level above growth (of which profit is a component) because capital’s share of GDP is increasing (and profits, hence, grow faster than the economy itself).

Otherwise, as expected the two series track each other pretty well.

In the long-term, nominal earnings growth in the 4-5% range, or real growth in the 2-3% range does not seem absurd – especially if you believe an increasing share of the economy will accrue to capital owners. Those who argue that the Fed is keeping the market artificially inflated may want to look at how the curve shifts if the forward curve steepens a bit. We will likely be well into 2017 by the time interest rates are even 1%, and even a 1% increase in G_implied may not necessarily be absurd.

And that’s assuming the Fed’s decision isn’t endogenous to economic factors that influence earnings. Very likely, if the forward curve steepens, it is a result not of a negative supply shock (runaway inflation requiring an increase in interest rates, for example) as much as a positive demand shock, where better-than-expected global trade and growth result in an increase in earnings to maintain valuations at a higher interest rate.

This post was meant as a composite of a number of thoughts that I’ve been playing with recently, many of which deserve their own blog post. A particularly interesting tangent would consider the effect delayed IPOs and exclusion of public investors from lucrative returns has on this analysis. My initial guess is “not much”. While it is a deeply interesting, and important, trend, it doesn’t effect public valuations much. Most of Facebook and Uber’s returns might have been captured in the private market but the valuation is slash will be reflected in the public market. And that’s what we’re concerned about here, not returns specifically.

  1. Anoop said:

    What did you use for risk premium?

    • 5%. G_implied only shifts linearly up and down though, so you can mentally adjust as you wish. Thanks for pointing this out, I should have mentioned this. >

  2. Clayton said:

    Impressive model. Great to see someone actually run the numbers.

    Two high-level thoughts:

    1) Does the model use nominal variables? Make sure you’re not using explanations that depend on low real performance (like growth) just because you see low nominal performance. I think any place where Sumner recommends “never reason from a price change” would apply here.

    2) I assume your model doesn’t depend on any particular explanation. If so, I recommend you separate the two or at least leading with the model. I don’t think your explanation is very compelling (details below) and am left wondering if the model depends on it. If you lead with the model, there’s no doubt that the interesting conclusions about stock prices stand on their own.


    I don’t see how Principle-Agent concerns…

    1) Explain the failure of managers to take other actions — like stock buybacks and dividend increases — that historically (if not theoretically) increase the value of shares.

    2) Prevent the “bidding” away of this arbitrage by entrepreneurs, venture capitalists, and private equity. Indeed, the large number of so-called unicorns could indicate this process at work.

    An alternative explanation for corporate decisions is government (especially tax) policy.

    According to this article (, Apple was holding around 2/3 of its cash internationally. We know that Apple recently borrowed $6.5b as part of an initiative increase dividends ( We don’t need a theoretical model to make this case — hard evidence is readily available.

    1) If we look at it more abstractly, companies must find investments that exceed (1) the interest on cash, (2) the risk premium, and (2) the tax impact. Even if they must eventually pay the tax, deferral is profitable (for the same reason you use tax deferred savings accounts).

    2) This theory has the added benefit of reducing the “bidding away” of this arbitrage since domestic tax rates have a similar effect on domestic investment.

    The latter seems far more parsimonious given the evidence — even if we might disagree about the best strategy to overcome this particular (dis)incentive.

    • Yes, my explanations (which I highlight as speculative) are entirely separate from the chart, which is purely derived as the implied earnings growth necessary to justify current valuations. I agree corporate tax concerns probably play an important role in emergence of cash piles, but I think this is restricted to a few big corporations (notably Apple).

      To clarify, the chart simply shows the time series of growth the market is expecting to justify its valuation given a very simple discounted cash flow model.

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