Comments on: The equity premium and the Stern Review http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/ Out of the crooked timber of humanity, no straight thing was ever made Sun, 27 May 2012 00:43:58 +0000 hourly 1 http://wordpress.org/?v=3.3.2 By: Barry http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181754 Barry Sun, 10 Dec 2006 04:48:12 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181754 OK, I think that I see now. Radek, thanks for the reminder - I was thinking about optimal outcomes, not optimal expected values. OK, I think that I see now. Radek, thanks for the reminder – I was thinking about optimal outcomes, not optimal expected values.

]]> By: radek http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181750 radek Sun, 10 Dec 2006 03:48:29 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181750 Also, I was under (perhaps mistaken or inaccurate) impression that to the extent that we can estimate eta independently it comes to somewhere around 2 but generally higher than 1 which Stern uses (Brad says sensitivity analysis should use values of 1 to 5) (eta = 2, gives a simple utility function of u(w)=-(1/w), where w is wealth) I'm also not convinced that setting pure rate of time preference to 0 is any more "ethical" than setting it equal to 1. Not that I know what the correct delta is in this context. Alan Rogers has an argument that for evolutionary reasons delta is 2.5 (AER 94). Also, I was under (perhaps mistaken or inaccurate) impression that to the extent that we can estimate eta independently it comes to somewhere around 2 but generally higher than 1 which Stern uses (Brad says sensitivity analysis should use values of 1 to 5)

(eta = 2, gives a simple utility function of u(w)=-(1/w), where w is wealth)

I’m also not convinced that setting pure rate of time preference to 0 is any more “ethical” than setting it equal to 1. Not that I know what the correct delta is in this context. Alan Rogers has an argument that for evolutionary reasons delta is 2.5 (AER 94).

]]> By: radek http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181749 radek Sun, 10 Dec 2006 03:29:13 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181749 Barry, that's the 'expected' in expected utility theory Barry, that’s the ‘expected’ in expected utility theory

]]> By: John Quiggin http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181746 John Quiggin Sun, 10 Dec 2006 01:54:58 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181746 Expected utility is fine in this case, Barry. More importantly, suppose A happens and that there are three possibilities (themselves involving uncertainty), conditional on A, for time t2, call them Aa, Ab and Ac, such that you can choose, at A, which you want. With dynamic consistency, if you had made a plan at t0 which involved choosing Aa if A occurred at t1, you would always want to follow through. Without dynamic consistency, you might end up preferring Ab at t1, and this might cause you to regret the choices that led you to A. Expected utility is fine in this case, Barry.

More importantly, suppose A happens and that there are three possibilities (themselves involving uncertainty), conditional on A, for time t2, call them Aa, Ab and Ac, such that you can choose, at A, which you want. With dynamic consistency, if you had made a plan at t0 which involved choosing Aa if A occurred at t1, you would always want to follow through. Without dynamic consistency, you might end up preferring Ab at t1, and this might cause you to regret the choices that led you to A.

]]> By: Barry http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181741 Barry Sat, 09 Dec 2006 23:50:38 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181741 John Quiggin: "Marcel, you’re a step ahead here. The dynamic consistency properties of EU depend crucially on the (false) assumption that you’ve anticipated all possible contingencies. The problem of what to do when you haven’t anticipated all possible contingencies is very hard and is the focus of my current research." This still doesn't make it understandable to me. For a simple example, let's say that there are three possible outcomes - A, B and C, with associated probabilities assumed, all at t0. Then, at time t1, one of the outcomes will be no longer possible (e.g., A), or it actually happens. How can an expected utility hold then? John Quiggin: “Marcel, you’re a step ahead here. The dynamic consistency properties of EU depend crucially on the (false) assumption that you’ve anticipated all possible contingencies. The problem of what to do when you haven’t anticipated all possible contingencies is very hard and is the focus of my current research.”

This still doesn’t make it understandable to me. For a simple example, let’s say that there are three possible outcomes – A, B and C, with associated probabilities assumed, all at t0. Then, at time t1, one of the outcomes will be no longer possible (e.g., A), or it actually happens.

How can an expected utility hold then?

]]> By: Barry http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181740 Barry Sat, 09 Dec 2006 23:47:36 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181740 Also, Maynard, from what little I know, there's a time-horizon issue. If one can assuredly hold stocks for the long run (i.e., past a recession and it's sluggish aftermanth), then one is in a different position from those who can't be sure of that. And the market will, of course, be a mix of both types, plus those who simply don't see the long run, and make their decisions on the short run. Also, Maynard, from what little I know, there’s a time-horizon issue. If one can assuredly hold stocks for the long run (i.e., past a recession and it’s sluggish aftermanth), then one is in a different position from those who can’t be sure of that. And the market will, of course, be a mix of both types, plus those who simply don’t see the long run, and make their decisions on the short run.

]]> By: Maynard Handley http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181739 Maynard Handley Sat, 09 Dec 2006 23:27:20 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181739 I have heard a claim, which sounds quite reasonable to me, that the equity risk premium is easily understood as a liquidity premium. The idea is that by holding bonds, when trouble comes, you can sell those bonds for something close to principle, and have the cash you need. (Of course long bonds are subject to interest rate risk, but that is a known issue.) When it comes to stocks, when trouble comes and you need to raise cash, chances are everyone else is also selling, and you're liable to take a substantial loss. The difference versus the bonds case is the extent to which your need to raise cash (or at least desire to flee stocks) is correlated with everyone else's simultaneous desire to flee stocks. The implication is that this premium is covering a real risk, one that is not diversified by owning the S&P500 rather than a single company, and one that is a real problem *for certain classes of actors* but not for others. If you are an entity that requires a certain level of cash flow over short terms, or at least is vulnerable to this sort of mass panic, you have to figure this risk against the premium and decide how the two compare; if you are not such an entity, you can ride the risk premium to greater wealth. (Note, as always, this discusses a limited issue in finance. Relevance to a specific situation, eg should I buy stocks today, requires paying attention to other issues, for example the risk that US dollars will be worth a whole lot less ten years from now than they are worth today.) This strikes me as an eminently reasonable explanation of the risk premium. An ideal solution would involve real numbers (fluctuations in the values of stocks over quarters, the fraction of the market that are sensitive to these fluctuations, etc) but this seems a worthwhile project. I have heard a claim, which sounds quite reasonable to me, that the equity risk premium is easily understood as a liquidity premium.
The idea is that by holding bonds, when trouble comes, you can sell those bonds for something close to principle, and have the cash you need. (Of course long bonds are subject to interest rate risk, but that is a known issue.)
When it comes to stocks, when trouble comes and you need to raise cash, chances are everyone else is also selling, and you’re liable to take a substantial loss. The difference versus the bonds case is the extent to which your need to raise cash (or at least desire to flee stocks) is correlated with everyone else’s simultaneous desire to flee stocks.

The implication is that this premium is covering a real risk, one that is not diversified by owning the S&P500 rather than a single company, and one that is a real problem for certain classes of actors but not for others. If you are an entity that requires a certain level of cash flow over short terms, or at least is vulnerable to this sort of mass panic, you have to figure this risk against the premium and decide how the two compare; if you are not such an entity, you can ride the risk premium to greater wealth.
(Note, as always, this discusses a limited issue in finance. Relevance to a specific situation, eg should I buy stocks today, requires paying attention to other issues, for example the risk that US dollars will be worth a whole lot less ten years from now than they are worth today.)

This strikes me as an eminently reasonable explanation of the risk premium. An ideal solution would involve real numbers (fluctuations in the values of stocks over quarters, the fraction of the market that are sensitive to these fluctuations, etc) but this seems a worthwhile project.

]]> By: John Quiggin http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181733 John Quiggin Sat, 09 Dec 2006 22:16:09 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181733 Marcel, you're a step ahead here. The dynamic consistency properties of EU depend crucially on the (false) assumption that you've anticipated all possible contingencies. The problem of what to do when you haven't anticipated all possible contingencies is *very* hard and is the focus of my current research. But dynamic consistency isn't just a matter of reputation, which, as you say doesn't matter in this context. It's a desirable property for individual decision-making. If it doesn't hold, it means that you will predictably reach situations where you would, if you could, change your past decisions. Also, it creates a dependence of current decisions on things that might have happened but didn't - this gets very complicated. Marcel, you’re a step ahead here. The dynamic consistency properties of EU depend crucially on the (false) assumption that you’ve anticipated all possible contingencies. The problem of what to do when you haven’t anticipated all possible contingencies is very hard and is the focus of my current research.

But dynamic consistency isn’t just a matter of reputation, which, as you say doesn’t matter in this context. It’s a desirable property for individual decision-making. If it doesn’t hold, it means that you will predictably reach situations where you would, if you could, change your past decisions. Also, it creates a dependence of current decisions on things that might have happened but didn’t – this gets very complicated.

]]> By: aaron http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181729 aaron Sat, 09 Dec 2006 20:54:38 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181729 (for a no AGW senario). (for a no AGW senario).

]]> By: aaron http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181723 aaron Sat, 09 Dec 2006 19:35:39 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181723 I think trying to model a discount rate is silly. Just use the straight up expected real gdp growth rate. I think trying to model a discount rate is silly. Just use the straight up expected real gdp growth rate.

]]> By: marcel http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181711 marcel Sat, 09 Dec 2006 15:05:17 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181711 Why is time-consistency important here? It was first raised as an issue in a context where reputation influenced outcomes. Consider this example, which I think is relevant to climate change. 1) We have very incomplete information about the future: considerable ignorance about not only the probabilities of potential outcomes, but also of the contents of the event space - the set of possible outcomes. 2) Nevertheless, it appears that some action is a wise step. 2a) Based on current knowledge, including recognition of our ignorance, we choose an action that appears most prudent, i.e., optimal in light of what we know and know we don't know (shades of Rumfeld). 3) At a later date, with more information, we see that a different choice would have been better. With this greater information, we can see that even with the choice previously made, it is now possible to improve the (likely) outcome by modifying our prior decision; i.e., choosing a new action. Of course, assumption (1) makes EU theory inappropriate, since that requires a complete listing of both possible outcomes and their associated probabilities. (Step (3) may as well, but that's not relevant here.) Nevertheless, I don't see the importance of reputation in determining the outcome, and more to the point, I don't see the importance of time-consistency. JQ, enlight me. Why is time-consistency important here? It was first raised as an issue in a context where reputation influenced outcomes.

Consider this example, which I think is relevant to climate change.

1) We have very incomplete information about the future: considerable ignorance about not only the probabilities of potential outcomes, but also of the contents of the event space – the set of possible outcomes.

2) Nevertheless, it appears that some action is a wise step.

2a) Based on current knowledge, including recognition of our ignorance, we choose an action that appears most prudent, i.e., optimal in light of what we know and know we don’t know (shades of Rumfeld).

3) At a later date, with more information, we see that a different choice would have been better. With this greater information, we can see that even with the choice previously made, it is now possible to improve the (likely) outcome by modifying our prior decision; i.e., choosing a new action.

Of course, assumption (1) makes EU theory inappropriate, since that requires a complete listing of both possible outcomes and their associated probabilities. (Step (3) may as well, but that’s not relevant here.) Nevertheless, I don’t see the importance of reputation in determining the outcome, and more to the point, I don’t see the importance of time-consistency.

JQ, enlight me.

]]> By: Michael Greinecker http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181710 Michael Greinecker Sat, 09 Dec 2006 14:19:30 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181710 No, martingales are certain stochastic processes. The idea of time consistency is that if you prefer two apples tomorrow to three apples the day after tomorrow, you shouldn't change your mind tomorrow and trade in the two apples for three apples the day afterwards. No, martingales are certain stochastic processes.

The idea of time consistency is that if you prefer two apples tomorrow to three apples the day after tomorrow, you shouldn’t change your mind tomorrow and trade in the two apples for three apples the day afterwards.

]]> By: thetruth http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181703 thetruth Sat, 09 Dec 2006 08:12:41 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181703 "if you make a plan, anticipating all possible contingencies, you’ll want to continue with that plan over time, whichever contingency arises" That's called a martingale, isn't it? “if you make a plan, anticipating all possible contingencies, you’ll want to continue with that plan over time, whichever contingency arises”

That’s called a martingale, isn’t it?

]]> By: talboito http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/comment-page-1/#comment-181702 talboito Sat, 09 Dec 2006 06:22:51 +0000 http://crookedtimber.org/2006/12/08/the-equity-premium-and-the-stern-review/#comment-181702 It seems Mandelbrot's <a href="http://www.amazon.com/Misbehavior-Markets-Benoit-Mandelbrot/dp/0465043550" rel="nofollow">argument</a> about all this <i>equity premium</i> stuff says equities are actually much much riskier than standard models would claim. It seems Mandelbrot’s argument about all this equity premium stuff says equities are actually much much riskier than standard models would claim.

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