On Au

Greg Mankiw has a cool New York Times article and blog post, “On Au” analyzing the case to be made for gold in a portfolio, including a cute problem set. (Picture at left from Greg’s website. I need to get Sally painting some gold pictures!)

I think Greg made two basic mistakes in analysis.

First, he assumed that returns (gold, bonds, stocks) are independent over time, so that one-period mean-variance analysis is the appropriate way to look at investments. Such analysis already makes it hard to understand why people hold so many long-term bonds. They don’t earn much more than short term bonds, and have a lot more variance. But long-term bonds have a magic property: When the price goes down – bad return today – the yield goes up – better returns tomorrow. Thus, because of their dynamic property (negative autocorrelation), long term bonds are risk free to long term investors even though their short-term mean-variance properties look awful.

Gold likely has a similar profile. Gold prices go up and down in the short run. But relative prices mean-revert in the long run, so the long run risk and short run risk are likely quite different.

Second, deeper, Greg forgot the average investor theorem. The average investor holds the value-weighted portfolio of all assets. And all deviations from market weights are a zero sum game. I can only earn positive alpha if someone else earns negative alpha. That’s not a theorem, it’s an identity. You should only hold something different than market weights if you are identifiably different than the market average investor. If, for example, you are a tenured professor, then your income stream is less sensitive to stock market fluctuations than other people, and that might bias you toward more stocks.

So, how does Greg analyze the demand for gold, and decide if he should hold more or less than market average weights? With mean-variance analysis. That’s an instance of the answer, “I diverge from market weights because I’m smarter and better informed than the average investor.” Now Greg surely is smarter than the average investor. But everyone else thinks they’re smarter than average, and half of them are deluded.

In any case, Greg isn’t smarter because he knows mean-variance analysis. In fact, sadly, the opposite is true. The first problem set you do in any MBA class (well, mine!) makes clear that plugging historical means and variance into a mean-variance optimizer and implementing its portfolio advice is a terrible guide to investing. Practically anything does better. 1/N does better. Means and variances are poorly estimated (Greg, how about a standard error?) and the calculation is quite unstable to inputs.

In any case, Greg shouldn’t have phrased the question, “how much gold should I hold according to mean variance analysis, presuming I’m smarter than everyone else and can profit at their expense by looking in this crystal ball?” He should have phrased the question, “how much more or less than the market average should I hold?” And “what makes me different from average to do it?”

That’s especially true of a New York Times op-ed, which offers investment advice to everyone. By definition, we can’t all hold more or less gold than average! If you offer advice that A should buy, and hold more than average, you need to offer advice that B should sell, and hold less than average.

I don’t come down to a substantially different answer though. As Greg points out, gold is a tiny fraction of wealth. So it should be at most a tiny fraction of a portfolio.

There is all this bit about gold, guns, ammo and cans of beans. If you think about gold that way, you’re thinking about gold as an out of the money put option on calamitous social disruption, including destruction of the entire financial and monetary system. That might justify a different answer. And it makes a bit of sense why gold prices are up while TIPS indicate little expected inflation. But you don’t value such options by one-period means and variances. And you still have to think why this option is more valuable to you than it is to everyone else.

From Livestock to the Stock Exchange

From Livestock to the Stock Exchange. © Sally Cochrane All Rights Reserved

Artist’s description: This is a brief visual history of trade, reading left to right. The first “money” was cattle, represented by the cheese. Ancient Mesopotamians kept track of their cattle exchanges on cuneiform tablets like receipts (we have some at the Oriental institute of Chicago!). The root of the word “pecuniary” comes from the root “pecu” meaning “cattle.” Cowrie shells were another early form of currency for trade, and beaver fur, which was very valuable, was used in barter when Europeans discovered the New World. The coins and stock ticker tape represent the modern end of the history. July 2013. 8"x 16" oil on canvas.

Original here with many other sizes.

Sally says the beaver fur was inspired by a Russ Roberts EconTalk podcast, interviewing Timothy Brook on his book Vermeer’s Hat. “Part of the book talked about how valuable beaver fur was for making hats that ended up in the Netherlands during Vermeer’s lifetime.” I don’t know how many other artists listen to EconTalk while painting…

The Value of Public Sector Pensions

The unfunded promises of public sector pensions are in the news, with the Detroit bankruptcy. Josh Rauh at Stanford and Hoover has a nice blog post on the subject titled “Public Sector Pensions are a National Issue”. (Josh and Robert Novy-Marx wrote a very influential paper (ssrn manuscript) alerting us to the size of the state and local pension bomb.)

Josh’s baseline number for the value of underfunded pensions: $4 trillion. Why so big, and why is this a surprise? Because many governments calculate their funding by assuming they will earn 8% per year. Discounting a riskless liability (pensions) at a risky rate is a basic error in finance. It’s made all the time. University presidents are notorious for demanding their endowments “reach for yield” in order to “make our rate of return targets.”

Reading this piece sparks a few thoughts about the risks posed by pensions and other unfunded liabilities.

Let’s report risks

How to make the error clearer? Perhaps focusing on present values and arguing about discount rates obfuscates the issue. Let’s talk about risk. Maybe it would clear things up if pensions had to report a “shortfall probability” or “value at risk” calculation like banks do. OK, you are assuming an 8% discount rate because you’re investing in stocks. What’s the chance that your investments will not be enough?   Coincidentally, when I saw Josh’s piece I was putting together a problem set for my fall class that illustrates the issue well.

Here is the distribution of how much money you will have in 1, 5, 10, and 50 years if you invest in stocks at 6% mean return, 20% standard deviation of return. I added the mean in black, the median (50% of the time you earn more, 50% less) and the results of a 2% risk free investment in green. (The geometric mean return is 4% in this example.)

(Note: there is a picture here. I’ve noticed this blog is getting reposted here and there in text-only form. Go to the original if you want the pictures)

The mean return looks pretty good. After 50 years, you get $20 for every dollar invested, or contrariwise an accountant discounting a promise to pay $20 of pensions in 50 years reports that the present value of the debt is only $1. But you can see that stock returns (these are just plots of lognormal distributions) are very skewed. The mean return reflects a small chance of a very large payoff.

In these graphs the chance of a shortfall is 54, 59, 62, and 76% respectively. As horizon increases, you are almost guaranteed not to make the projected (mean) return! The median returns – with 50% probability of shortfall, in red – are a good deal lower. And the modal “most likely” return is below the riskfree rate in each case.

How is it that people get this so wrong? Let’s look at the distribution of annualized returns in each case. Remember, these are exactly the same situations, we’re just reporting a different number.

In these pictures, the distribution of annualized returns is symmetric, the mean and median are the same, and the distributions get narrower and narrower for longer horizons.

Comparing the two graphs, you see that annualized returns are profoundly misleading about the risks you’re taking. Annualized returns have a standard deviation that goes down at the square root of horizon. But the actual return has a standard deviation that goes up at the square root of horizon, and exponentiating makes it skewed with the larger and larger chance of underperformance. Money matters, not annualized returns.

So as usual, when arguments are getting nowhwere, perhaps we need to shift the question: please report your shortfall probabilities. And your plans for what you do with shortfalls.

In  many of those cases, the plan for shortfall  comes down to “the Federal Government bails us out” (or ERISA bails out private plans.) Well, if that’s true, then we have a different and interesting discounting question. Maybe 8% is the right number if someone else pays the losses!

Finance also teaches us to think about “state contingent payoffs.” What does the whole world look like in the bad events? If cities and states can’t pay their pensions, this very likely because stocks have performed badly, and because we’ve had 20 years of sclerotic growth, no growth in tax revenues, to fund the pensions. Stock returns are not uncorrelated with other aspects of state, municipal, and corporate finance. Investing in stocks to fund pensions is like selling fire insurance on your house, rather than buying it. If the house burns down, then you pay the insurance company.

What debt really matters?

Even $4 trillion is not all that huge in the grander scheme of things.  The official Federal debt is $18 trillion. But if you add the present value of unfunded pensions, social security, medicare, Obamacare, and so on you can get numbers like $50 trillion or more. Which, it should be perfectly obvious, are not going to get paid, especially if we stay on the current slow growth trajectory.  But how important is this present-value observation?  Should we routinely add up all the unfunded promises, discount them properly using the Treasury yield curve, and report the grand total?

I worry most about runnable debt. Promises to pay people trillions in the far off future are a different thing than rolling over marketable debt every year. If it looks likely we won’t be able to pay pensions in 20 years, there’s not all that much pensioners can do about it. If it looks like we won’t pay off formal short-term debt, markets can fail to roll over, leading to an immediate financial crisis.

So, much as I value Josh’s calculation, and zinging those who want to minimize the necessity of ever paying off debt, it does seem there is a difference between marketable debt that needs to be rolled over every year and promises to pensioners and social security that may eventually be defaulted on, but can’t cause an immediate crisis.

The cash flows do matter. If the government has promised to make pension and other payments that on a flow basis drain all its revenues, something has to give. As it has in Detroit.

A too-clever thought

A good response occurred to me, to those cited by Josh who want to argue that underfunding is a mere $1 trillion. OK, let’s issue the extra $1 trillion of Federal debt. Put it in with the pension assets. Now, convert the pensions entirely to defined-contribution. Give the employees and pensioners their money now, in IRA or 401(k) form. If indeed the pensions are “funded,” then the pensioners are just as well off as if they had the existing pensions. (This might even be a tricky way for states to legally cut the value of their pension promises)

I suspect the other side would not take this deal. Well, tell us how much money you think the pension promises really are worth – how much money we have to give pensioners today, to invest just as the pension plans would, to make them whole. Hmm, I think we’ll end up a lot closer to Josh’s numbers.

Details

I used a geometric Brownian process, dp/p = mu dt + sigma dt with mu = 0.06 (6%) and sigma = 0.20 (20%). The T year arithmetic return is then lognormally distributed R_T = exp( mu - 1/2sigma^2)T + sigma root T e) with e~N(0,1). It has mean E(R_T) = exp(mu*T)=exp(0.06*T), median exp[mu-1/2sigma^2)T] = exp(0.04*T) and mode exp[(mu-3/2*sigma^2)T] = exp(0)=1.

Are we prepared for the next financial crisis?

This is the title of a very well-prepared video made by Hal Weitzman, Dustin Whitehead and the Booth “Capital Ideas” team, based on interviews with many of our faculty. Direct link here (Youtube)

Health Insurance and Labor Supply

I just ran across an interesting paper, “Public Health Insurance, Labor Supply, and Employment Lock” by  Craig Garthwaite,  Tal Gross and my Booth colleague Matthew Notowidigdo.

They study an interesting event

… In 2005, Tennessee discontinued its expansion of TennCare, the state’s Medicaid system. … Approximately 170,000 adults (roughly 4 percent of the state’s non-elderly, adult population) abruptly lost public health insurance coverage over a three-month period.

The result was

a large and immediate labor supply increase….we find an immediate increase in job search behavior and a steady rise in both employment and health insurance coverage. 

They call the phenomenon “employment lock.” This is different from “job lock,” people with preexisting conditions who stay with jobs they didn’t want in order to keep health insurance. “Employment lock” is the choice by healthy people to work at all in order to get  insurance, or put in academic prose, “strong work disincentives from public health insurance that are unrelated to strict income-based eligibility limits.”

The converse is a new danger for the ACA

Additionally, our estimates may provide useful guidance regarding the likely labor supply impacts of the ACA…

If such individuals could instead acquire affordable health insurance apart from their employer, many of them would exit the labor force entirely. As a result of employment lock, policies that expand access to health insurance apart from employers (such as the ACA) may have large labor market effects

… Using CPS data, we estimate that between 840,000 and 1.5 million childless adults in the US currently earn less than 200 percent of the poverty line, have employer-provided insurance, and are not eligible for public health insurance.Applying our labor supply estimates directly to this population, we predict a decline in employment of between 530,000 and 940,000 in response to this group of individuals being made newly eligible for free or heavily subsidized health insurance. 

They are quick to point out that this is not necessarily a bad thing.“the effects do not necessarily imply a welfare loss for individuals choosing to leave the labor force after receiving access to non-employer provided health insurance.” If people only work at a job they hate in order to get health insurance, then people may be better off not working. The policy world often just assumes more employment is always a great thing, which isn’t true.

However, less employment is not necessarily a good thing either. These are childless adults. How are they supporting themselves if they don’t work? Can it possibly be optimal for them to just sit around the house? We surely don’t want to compare employer-provided health insurance with highly subsidized individual insurance for the unemployed– that’s a subsidy to leisure and obviously skewing the scales.

Most of all, low-income single people face extraordinarily high marginal tax rates and other disincentives to work. So, an artificial incentive to work in order to get health insurance may offset some of the otherwise irresistible incentives not to work. (A good calculation for Casey Mulligan!)

And whether the people are in the end better off working or staying home and receiving larger subsidies, the government and taxpayers are clearly worse off, as the people and their employers are not paying taxes any more.

In sum, academic caution aside, inducing a million childless adults to leave legal employment doesn’t look like a good thing to me.  

The evidence is pretty cool. Here are some pictures lifted from the paper.

A Ray of Hope? Hospitals Post Prices

I was intrigued by news stories of an Oklahoma hospital posting prices for surgery – prices far below those offered by its competitors. Here is the article and the surprisingly low price list.  Several competitors felt the pressure to slash and post prices.


A fascinating tidbit: “Surgery Center of Oklahoma does accept private insurance, but the center does not accept Medicaid or Medicare. Dr. Smith said federal Medicare regulation would not allow for their online price menu. They have avoided government regulation and control in that area by choosing not to accept Medicaid or Medicare payments.”  Well, so much for the idea that regulations encourage competition and lower prices.

This is a ray of hope – that the sort of competitive free market health care I envisioned in “After the ACA” can emerge as people abandon the complete dysfunctionality of the highly regulated system.

I had seen the emergence of “concierge medicine,” and cash and carry doctors, who step off the highly regulated insurance and government treadmill. But if you get really sick, you need a hospital. And traveling abroad isn’t always an option. So the emergence of US cash and carry hospitals is interesting and encouraging.

This innovation clearly undermines the regulated system. A healthy young person knowing there are doctors who post reasonable prices and take cash, and now similarly reasonable cash and carry surgery, might be well advised to pay the Obamacare tax and skip out of the whole system. A bit of savings or a catastrophe only policy is enough. 

But before you cheer that Obamacare will die of its own weight, look hard at the other side. The government needs everyone in the system, especially the relatively healthy and solvent customers of this hospital.  It also needs hospitals and doctors to take medicare patients. The emergence of a two-track system is a financial and political disaster. So, how long can it last before the government bans it? Other countries have banned private practice to support their government health systems.  Ours will likely go down fighting, and this is the obvious move. In addition, the hospitals that don’t want to compete have strong political power to shut this down, and will make the same cherry-picking complaints that airlines and phone companies used to keep their protections in place. It will not survive easily. 

Readers: I’m back from a short vacation (national gliding contest), sorry for the silence.