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.
"But everyone else thinks they're smarter than average, and half of them are deluded"
ReplyDeleteJohn, I'm glad you are incorporating concepts from Behavioural Economics.
If by average is meant "mean" then it is not necessarily true. After all, almost all of us have more than the average number of legs.
Delete+1. Median is the correct term, not mean.
Delete"can't all hold more or less gold than average". John used italics on the word "all" as if he anticipated this question. He didn't say "almost all".
Delete"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?""
ReplyDeleteWhat you mean is, how much more or less than _other people like me_ should I hold? And what makes me different from _other people like me_?
The market average is not especially relevant, since it's heavily weighted to the atypical. What do the investing habits of central banks, for example, have to do with me?
But everyone else thinks they're smarter than average, and half of them are deluded.--Cochrane.
ReplyDeleteActually, all of them are deluded! In any particular period (say, year) you might be smarter--actually, luckier---than your peers. But as we see from hedge fund managers....call it EMH.
Gold? The price is set by retail buyers in India and China, where the bulk of gold is sold. Mostly for traditional gift-giving, but also as a means to escape taxes, on the part of Indians.
But my grandaddy once told me, "Son, all gold is fool's gold."
He's been right so far.
Actually, some people will beat the market, if only through random variation. The EMH is not literally true.
Delete"[L]ong-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..."
ReplyDeleteNope. For fixed rate bonds (which I assume is what you're talking about), the reason the yield has gone down is not because future coupons have increased but because the base against which you're measuring the future coupons (the price of the bond) has decreased. So a $1 coupon paid in a year is 10% of a bond worth $10 but 20% of a bond worth $5. Are you saying you'd be happy to get the 20% if it means the value of your bond is cut in half?
John, you're surely familiar with the postulates on which your average investor findings rest.
ReplyDeleteLike “non-Euclidean” geometry that starts from different constraints than classical geometry, the “average investor” approach can bust apart pretty quickly once you realize that, for example, shorting incurs substantial costs, or that borrowing to buy stocks can't be done at the risk-free rate. Markowitz himself has written, even presented on the impact that these assumptions make on efficient diversification. This is neither new nor heretical.
But like your complaints against Mankiw, the violations of EMH actually strengthen the argument against gold. Gold is disproportionately held in countries with weak legal protections, enough to compensate for the substantial security/warehousing costs. Gold certificates may reduce the costs, but they'd be worse than useless if global order utterly breaks down — so, not there when an NYT reader really might think that some shiny metal could get them a basement full of canned beans. So the proportion of one's portfolio in gold might be compared to other investors who face the same set of opportunities and risks, reducing the share even further.
'Practically anything does better' than mean-variance optimization?
ReplyDeleteAs the word 'optimization' implies, within its rules and constraints, it finds the portfolios that, in the past, would have yielded the best return for a given risk.
So what are the rules and constraints where 'practically anything does better?'
Certainly, mean-variance optimization assumes the past is like the future, so when that's not the case it will be wrong. Since it assumes any variance not captured in the model is unsystematic and cancels out, it underestimates risk.
But if 'practically anything does better' then a lot of people who use it as a framework, if not an actual portfolio construction practice, for lack of anything better, are wrong...surely worth elaboration, or a blog post?
I think Mankiw phoned that one in. But for a mainstream economist, just to say gold is a natural hedge and worth a look is kind of a big deal.
CT, I think you're taking John's claim to mean something more general than it is. The claim is that practically anything does better than *measuring historical means and variances* and plugging these into the Markowitz formula to choose portfolio weights. This isn't about whether the past is like the future, but rather about the fact of life that these quantities are difficult to measure statistically whether the past is like the future or not.
DeleteThe claim is as follows. Go download twenty years of daily stock returns from Yahoo. Estimate means and variances on the first fifteen years and construct the Markowitz mean-variance efficient portfolio. Compare its performance to a value-weighted or 1/N weighted portfolio.
Maybe the past is the same as the future, maybe it's different, but after the exercise the question John wants you to ask is: do I want to base the amount of gold I hold on my portfolio using no data except the historical mean and variance of gold returns?
"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."
DeleteWith all due respect, why would anybody use a historical return in a portfolio optimization?
I was quite clearly taught that it was expected returns, and that historical returns are not expected returns, particularly at the security and/or sector level.
Textbooks certainly do not suggest using historical returns.
For example, Bodie Kane & Marcus, 9th edition, pages 234-236 (ironically, it has gold on the cover):
"As we discussed in Chapter 5, estimating expected returns using historical data is unreliable...In Chapter 8 we will establish a framework that makes the forecasting process more explicit"
John,
ReplyDeleteplease give us that missed out on the gold bounce 5 years ago, but now have asymmetrical market monetary info, some bunker portfolio advice. What about M0 cash? cold hard currency, both foreign and domestic, in small denominations for food, alcohol, checkpoint bribes, standing in line bribes, etc. the cash machines will be the first to go, the FDIC will have strings attached (only whole grain food you little peasants).
Thx
Jim
I think one of the best assets for a SHTF scenario is miniature liquor bottles. They are smaller denominations than a fifth or a pint and they are sealed so there is proof against tampering or dilution. Would you rather be paid with an opened half pint of vodka in a bottle labeled Grey Goose or several small unopened bottles labeled Grey Goose?
DeleteIf the S never does HTF you'll have all this booze you can party with. Plus I'll bet the price goes up on those bottles.
Booze: It's both fun and fungible.
JB McMunn,
DeleteBe sure to store lots of guns with your liquor. The first thing a new government will no is try to disarm you and then tax your liquor (See U. S. Whiskey Rebellion circa 1791).
John,
ReplyDelete"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."
"Second, deeper, Greg forgot the average investor theorem."
Third, Greg forgets that not all investors are passive investors. If you were an active equity investor in company XYZ and that company had a bad year, what might you do? You might at the annual shareholders meeting vote the current management out of their jobs. Similarly, if a company has a really bad year(s) and has problems making timely payments on its debt, then the company may be forced into bankruptcy where shareholders are wiped out and bondholders become the new shareholders.
Stocks and bonds are not the only cases. Few people own houses solely as an investment. They also receive utilitarian value from a roof over their heads. And so when that roof starts leaking, people have an incentive to repair the roof beyond maintaining / improving the market value of the house.
John,
ReplyDelete"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."
That theorem only works for assets that are supply limited - for every buyer of a good that is anticipating higher prices based upon demand exceeding supply, their is a seller of that good that is anticipating lower prices based upon demand being less than the supply.
For financial contracts (like stocks and bonds), there is no explicit limit on supply. And so the issuer / redeemer of those financial contracts can state the price that those contracts are bought and sold at. If the issuer feels that market prices are too low, he buys AND sells at a higher price. If the issuer feels that market prices are too high, he buys AND sells at a lower price.
Professor Cochrane, with all due respect, you state:
ReplyDelete"But long-term bonds have a magic property: When the price goes down -- bad return today -- the yield goes up -- better returns tomorrow."
In real terms - the terms that should matter to investors - this is simply untrue as a general statement.
If bond prices drop as a consequence of increases in expected inflation, do real expected returns increase?
Of course not.
If bond prices drop for credit-related factors, do real (or nominal, for that matter) expected returns increase?
Of course not.
I'm not famous, but I sure know bonds.
Weirdness,
DeleteI would tack one other possibility on - if bond prices drop due to prepayment risk, do real expected returns increase?
That's a very good one, Mr. Restly.
DeleteProbably even better than the corporate example.
(Risk premiums may increase for lower quality bonds, if increased credit risk implies increased systematic risk)
Weirdness,
DeleteI only bring it up because CAPM models use a risk free rate of return. The asset class used to model the risk free rate of return is sovereign government debt. A sovereign does not bear credit risk, but by choice in can induce prepayment risk - for instance by running a surplus and simultaneously reducing its long term debt (See Clinton administration). The buyer of long term government debt thought he / she had bought a "risk free" security but it turns out he / she did not - debt was retired before maturity.
Nothing wrong with a sovereign running a surplus and nothing wrong with treating sovereign debt as credit risk free, but for CAPM models to hold true over any significant time period, a government surplus must be coordinated with the expiration of existing debt.
I think a blog post on dynamic portfolio choice would be interesting.
ReplyDeleteAnyway, I'm not sure how relevant the average reader would find the average investor theorem. On a practical level, the average investor may hold the market portfolio, but how does the average investor obtain market cap weights? Do they have subscriptions to Bloomberg and Factset? If you've ever tried to implement the Black-Litterman model incorporating commodities, you'll be well aware that it can be difficult even for professionals to find market capitalization data on commodity holdings.
I also think it's a bit of a logical leap to go from the truism that the average investor holds the market portfolio to the argument that an average investor should hold the market portfolio. Even assuming away your nuance about what makes the investor different from average, I don't really know who the average investor (and how do you know if you're average?). We may know what people's portfolios are in aggregate, but that doesn't tell you much about the approaches they used to prepare them. Do we average their return and covariance estimates? Do we average their time horizons? Their taxes? Their constraints?
In general, I find a Bayesian approach to portfolio management to be clearer than looking at it from an average investor. You could set up your prior, as in Black-Litterman, so that if you have no views then your portfolio optimization would lead you to the market portfolio if you have the risk appetite and time horizon that was used to back out your priors (or you could use other priors). Being different from a prior makes more sense to me than being different from average.
On a side note, I basically did what Mankiw was suggesting (without incorporating any fancier effects, such as time-varying volatility) and got a minimum variance weight of 5% for precious metals, with smaller holdings (to zero) as the return target increases.
Yes, just what I need in case of calamitous social disruption is an electronic record stating that I am the beneficial owner of some metal stored on a different continent...
ReplyDeletePeople who have those concerns hold physical gold nearby.
DeleteWhat I love is the arguing with John about the one thing that he actually knows everything about ! People, please argue with him about macro and policy just don't argue with him about finance and weights, he can outfinance any you. Oi Vei
ReplyDeleteI know this may come off wrong, but considering the failures in economics we might as well as the tooth fairy if we should,hold gold
ReplyDeleteI think even buying it for calamity insurance is probably going to be pointless- if the monetary system comes down there is no way the government will allow gold hoarders to keep their gold.
ReplyDelete"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."
ReplyDeleteGreg comes down to 2%, the fraction of trading (?) gold in the sum of gold, stocks, and bonds. The value including central bank and jewelry gold is 9%, though. So shouldn't you hold 9%, including in that the value of your jewelry (a sensible way to hold it).
Even if it's 2%, that's worth noticing. My pension fund has 0% in gold, not 2%. It would be interesting if *everybody* is holding the wrong amount of gold--- the gold bugs way too much, everyone else a little too little (average investor theorem again?)
This excludes other assets such as housing and automobiles and silver. I don't know what implication that has.
Sorry wait, am I correct that Proff Greg did not leave the option to comment on either the blog you link or the nyt article he links? hopefully this is not correct and just a result of me having the the technological prowess of a Ludite.
ReplyDeleteAnyway, John, I have no idea why you spend all this time talking about average this average that and why we need x reason to deviate from the average etc. In the best case, this amounts to nit picking at the author when he puts such jucier prey on the table for us (note you even inspired the first few posters to begin picking back at you in their fascinating mean vs. median debate).
Meanwhile (pun intended), did you not notice that the Chairman of Economics at the world's top ranked educational establishment thought he was telling us something novel by pointing out that we should give a low portfolio allocation to an asset with low expected relative returns but high expected relative volatility? Surely this is the scandal that we should be focusing on? Further he then goes on to claim its a tough problem because a 200 year sample of data isn't enough to form a useful return expectation? oh brother. Why don't you call him out on the underlying assumption that historical returns are at all relevant to expected returns for such a volatile and regime dependent asset class? whats that? you kind of did? well not to worry, the charismatic Ranter that I am entails that will continue to be often wrong but never in doubt; Why didn't you then go on to scold him for perpetuating these myths regarding optimal time independent portfolios, that in reality are only optimal for the sogiest of fatalists incapable of forming a view of the world in pragmatic terms and acting on it, yet still willing to devote their lives to discussing irrelevant abstracts that serve only to alienate them from all that is beautiful? what's that? you kind of did? Well all I can say is that as a grumpy economist I hope you can learn to be far less tactful in the future. that is all.
Gold is special in the sense that it has a very elastic supply in the long run, I believe much more so than the stocks and bonds. You just go and dig more. If the price of gold would be expected to run at $1500 plus cpi, then we'd see a huge number of new projects in the works.
ReplyDeleteIt's of course correct that one should think in terms of deviations from what the average investor wants. But it also matters greatly to the gold supply and price dynamics what the average investor wants.
The real magic property of long term treasury bonds and of gold is that their prices bob about in a way that doesn't correlate positively with stock prices. So you can sell them to buy stocks when stocks are cheap. Keeping a portion of regularly rebalanced portfolio as such assets improves the Sharpe ratio. That may throw pet theories out of the window but theories can be wrong.
ReplyDelete