Monday, October 23, 2017

The Upside Down CAPM and Lawrence Summers

I think there is a lot of value in turning the CAPM upside down.

Normally, we think of it as:  ER = R(f) + B*ERP

The expected return of the broader stock market is the risk free rate of return plus the equity risk premium - the premium investors demand for having exposure to cash flow that is volatile over the business cycle.  The expected return on a given equity is its "beta" - its sensitivity to broader market volatility.  The broader market, by definition, has a beta of 1.

I prefer to think of equity market expected returns this way:  R(f) = ER - ERP

It's a simple algebraic reformulation, so it seems like it can't make that much difference.  But, the key is that (1) expected returns (ER) seem to be pretty noisy (or unknowable) around a stable mean, so that ER can generally treated as a sort of mysterious constant and (2) the real risk free rate is generally negatively correlated with expected real growth and does not have a stable mean.

When secular growth expectations decline, R(f) tends to decline and ERP tends to rise.  Expected returns aren't a product of R(f).  It's more accurate to say that ERP is a product of R(f), so that, lower growth expectations cause equity holders to demand higher returns relative to R(f).  Comparing equity yields to real bond yields gives us little information, and comparing equity yields to nominal bond yields is less than useless.  (We are currently in an odd time, because what amounts to financial repression in mortgage markets has pushed real long term interest rates lower than what we might call broadly the "natural" rate.)

I was recently listening to Lawrence Summers on David Beckworth's great podcast series.  Here, I think Summers has presented an example where this framing would help.  He is talking about whether it would be beneficial now to have a US sovereign wealth fund investing in equities:
If it were all about risk premiums then you'd think this was a particularly attractive moment to invest in stocks relative to bonds because there was an extraordinarily high risk premium . I think most sophisticated people in markets kind of think the opposite. Some people think the stock market's a bubble, some people think it's not. I don't know many people who think it's unusually cheap, which would be the corollary of the view that the risk premium is extremely high. So I don't particularly relate to the safe asset paradigm. If you had that paradigm, then you would say that if the spread between bond yield and stock yields was super wide. This was a good moment for the government to issue bonds and buy stocks. But I don't find that a plausible guide to my own investment behavior. And so I'd be hesitant to inflict it on the government.
Now, in ERP terms, clearly there is a high equity risk premium.  Clearly, expected returns on equity are much higher than risk free returns.  Summers is speaking about risk premiums, but he seems to be thinking in terms of absolute valuations.

If equities perform poorly, though, it will be the result of unforeseen real income shocks.  It will have little to do with valuations, because valuations, in terms of total expected returns, don't actually change that much after taking account of cyclical changes in growth expectations.  Thinking of equity valuations as a fairly stable long term variable with a lot of short term and mid-term variability, then it is much less confusing.  Clearly the equity risk premium is high, and we don't need to know much more than that real long term interest rates are low to realize that.  After cyclical adjustments (which are large for equities, make no mistake), it will take some sort of epic regime shift in the American economy to keep equities from vastly outperforming real bonds over the next 30 years or so.


Later in the interview, a couple of other items caught my attention.  On QE:
I'd also say, whatever you thought a few years ago, fact that we stopped QE and interest rates kept falling, it has to lead you to think QE is less effective than whatever you thought before we did that experiment.
This comes from thinking of monetary policy through interest rates.  Clearly, to me, the fact that interest rates fell after the QEs were ended is a sign of how QE was effective and had kept rates from falling while QE was on.

But, then, he follows up with this comment about raising rates moving forward:
And I don't see the financial stability rationale either. I'm not sure that markets are extraordinarily overvalued. If I believed with confidence that markets were a bubble, I'm not sure that would be a reason to tighten policy. It might be a reason to ease policy. 'Cause when the bubble bursts, we're gonna have a real problem. And so, I might as well get some stimulus into... Behind the economy. So, I don't see the case for tightening.
Can I nominate Summers for Fed chair in 2006?


  1. Great post.

    (We are currently in an odd time, because what amounts to financial repression in mortgage markets has pushed real long term interest rates lower than what we might call broadly the "natural" rate.)--KE

    Then, there is this from John Cochrane: "Our central bank is taking in $2.2 trillion from banks, and is paying them a higher interest rate than they can get elsewhere. Right now, the Fed is paying banks 1.25% on their reserves. But Treasury bills are 1%. Even commercial paper is 1.13-1.2%. It looks every bit like a bank that is pushing rates up. And has been doing so for a long time."

    So, is the Fed both raising short-term rates and crimping long-term rates?

    On QE, I think there is ton of motion under the water, and looking at nominal rates and QE (as you note) is not fruitful.

    In fact, maybe QE made people think, or even resulted directly in real economic growth being stronger, raising rates. Then ending QE brought lower rates.

    I am beginning to think macroeconomics and shamanism are equal careers.

    Though perhaps shamans have fewer taboo topics.

  2. So is there a free lunch here whereby you own equities (where Rf is irrelevant) and shorting risky corporate debt (where presumably there is a tighter link to Rf?)? If so, how does that free lunch arise?

  3. I guess another way of phrasing my question is should the ERP resemble corporate debt spreads? Both are indicators of the required return to take on the risk of corporate cash flows. Is this currently being violated?

    1. I don't know if anything is being violated. Equity and bonds have different risk exposures. Mostly, equities are exposed to changing cash flows (mostly cyclical) and changing valuations (again mostly cyclical). For investors who are not particularly sensitive to those risks, they currently earn a very high premium for accepting those risks.

      It could be that regulatory factors push some money into bonds, so that the premium doesn't fully reflect unbiased risk preferences. In any case, it seems pretty clear to me that there would be few better times for doing something like starting a sovereign wealth fund invested in equities. From a risk-adjusted gains perspective, the government is already highly short bonds. Pairing that with a long equity position would be profitable. I think someone could argue that this is what social security should have done all along. If social security savings had gone into private accounts, it's certainly where much of it would have, or should have, gone.

    2. To me it would certainly seem to be a violation of market efficiency if equities dramatically outperformed high-yield corporate bonds. You are being compensated for default risk and therefore are very sensitive to corporate cash flows. Historically, HY bonds have been highly-correlated to equities (except for certain "odd" periods like the dot-com bubble), with about half the volatility.

    3. The CAPM is based on a spread with the risk free yield. As you say, HY is a sort of hybrid between the risks of low risk bonds and equities.

    4. Right, so with HY spreads at very low levels doesn't his mean that the ERP must be at a very low level?

    5. I see your point. It seems like HY spreads would be higher. It is strange that VIX is low and default risk seems to be low, yet ERP is high. But, I'm not sure these measures are closely related enough to consider this a "violation" of some sort of no-arbitrage relationship. HY spreads are more of a cyclical measure that reflects short term default risk. ERP reflects required returns on cash flows.

      You have made me think about this a bit. I suppose one difference is that HY spreads reflect idiosyncratic risks of the individual firms that are borrowing, whereas ERP only reflects systematic risks. Possibly this is another sign of a sort of stagnant, limping economy, and systematic risk is high while idiosyncratic risk is low. That is the opposite of what we would want. Unfortunately, during the crisis, the imposition of systematic risk, as if it was a useful substitute for idiosyncratic risk, was popular. Maybe we are seeing the shadow of those broad policy preferences.

  4. "Clearly, to me, the fact that interest rates fell after the QEs were ended is a sign of how QE was effective and had kept rates from falling while QE was on."
    *I could not agree more. I wish I could get Summers or Beckworth or Krugman to address directly why they don't see it the same way as you and I.

    1. Yes. I'm no macro-economist, so who am I to say, but this seems like one of many reasons why thinking of monetary policy in terms of interest rates - especially long term interest rates - is confusing. I have some follow up posts planned on this, because I think my upside-down CAPM idea is a useful way to think about this.