Friday, September 6, 2013

The Intuition for Wallace Neutrality, Part II: Why it doesn't Work in the Real World

My first post explaining the elusive intuition behind Wallace Neutrality was well received. In particular, I was happy to see it discussed in a post on the blog of the think tank Bruegel. Bruegel is a very large and impressive organization. It was the #1 think tank in Western Europe, and the #1 international economic policy think tank in the World according to a 2012 University of Pennsylvania report. It's a project of 17 EU countries, chaired, until recently, by Mario Monti, and now by Jean-Claude Trichet.

I mention their excellent post now, in part, because reading it a second time after being away from this material for a while finally really crystalized in my mind a key intuition for why Wallace neutrality won't work in the real world – and why quantitative easing can.

The Bruegel authors wrote at the time, "Richard Serlin will have a detailed post in the next few days detailing the problems when thinking Wallace neutrality actually occurs with QE in the real world. Stay tuned." Embarrassingly, a few days became a year! But I just could never really crystalize it, and nail it down the way I wanted to. Then, after putting it down for a year and picking it up again, it all came together. So, without further ado...

Why Wallace neutrality doesn't work in the real world, and thus quantitative easing can

The intuition came when I was reading, and reflecting on, Bruegel's paraphrasing of something I had written:
Richard Serlin (HT Mark Thoma) gives the bottom line intuition of Wallace neutrality. Consider that the government buys 100 million ounces of gold in a QE. The assumption is, of perfect foresight, perfect everything investors, that over the next several years, unemployment will go down and the Fed will reverse course, and then sell all of those 100 million ounces back again. Thus, the supply of gold in 10 years will be exactly the same as if the QE had never occurred. The gold just temporarily sits in government vaults (or with government ownership papers), rather than private ones, then goes back to the private vaults – No difference at all in 10 years. So, in 10 years the supply of gold is exactly the same, so the price of gold in 10 years will be exactly the same. If the price of gold in 10 years will be exactly the same, then its price today will be exactly the same, since with prefect foresight, perfect analysis, etc. investors, the today price is just the discounted 10 years from now price.
I had gone down various roads in thinking about why the neutrality that worked in Wallace's model would not work in the real world, and I just wasn't able to really nail down any of them the way I wanted to, at least not the ones I wanted to. But thinking about this again, the idea came to me. The intuition is this:

Suppose the Fed does buy up 100 million ounces of gold in a quantitative easing. And the people who are savvy, well informed, expert, and rational know that in some years the economy will turn around, and the Fed will just sell back all of those 100 million ounces. So, in 10 years, the supply of gold will be the same as it would have been if the quantitative easing had never occurred. The ownership papers will shift from private parties to the federal government in the interim, but will be back again to private parties like they never left in 10 years. So, no fundamental change to the asset's value in 10 years.

And if no fundamental change to the asset's value in 10 years, then no fundamental change to the asset's value today, as the value today, for a financial asset with no dividends, coupons, etc., is just the discounted present value of the asset's value 10 years from now.

Now, as should be obvious – especially with gold – not all investors are savvy, well informed, expert, and rational – let alone sane! So, when the price of gold starts to go up, some of them will not sell at that higher price, even though fundamentally the price should not go higher; nothing has changed about the long run, or 10 year, price of gold.

In the Wallace model, and commonly in financial economics models, no problem, arbitrage opportunity! Suppose there are investors who are less than perfectly expert, knowledgeable, and rational – or way less – and they don't sell when the government buys up the price a little. Who cares. It just takes one expert knowledgeable investor to recognize that there's an arbitrage opportunity when the price of gold goes up merely because the government is buying it in a QE, and he'll milk it ceaselessly until the price is all the way back down again and the arbitrage disappears.

What's the arbitrage? Well, we're pretending we live in the world of Wallace's model (and many models like it). Markets are 100% complete and frictionless. If the price of gold goes up by even one cent, when there's no change in its fundamental value, that is when there's no change in its payoffs in the various states ten years from now, then an investor can, first, synthetically construct and buy from the primitive and/or other assets in the market a combination that has the same exact payoff as gold in any possible state of the world ten years from now.

At the same time as the investor purchases this synthetic gold, he sells, or sells short, the natural gold.

Because we're assuming that the markets at the start of this QE are efficient, an ounce of the synthetic gold portfolio sells for the same as an ounce of the natural gold. But once the natural gold goes up by even one cent, arbitrage! That single expert informed investor sells (or sells short) the natural gold and buys the synthetic gold. And he does this for as many ounces, without limit, as it takes to bring back down the price of gold to where it was, undoing the government's QE 100%, no matter how large it was, no matter how many trillions the government spent.

Now, for this to work as advertised, first you need 100% complete markets, so you must have a primitive asset (or be able to synthetically construct one) for every possible state at every possible time in the world.

[using Chandler Bing voice] Have you seeeen our world? The number of states just one minute from now is basically infinite. Even the number of significant finitized states over the next day, let alone a path of years, is so large, it's for all intents and purposes infinite. Thus, try to construct a synthetic asset that pays off the same as gold, now and over time, and you're not going to come very close. And if you try buying it to sell gold, or vice versa, to get an "arbitrage", you're going to expose yourself to a lot of risk.

And this is a key. I think a lot of misunderstanding comes from loose use of the word "arbitrage". The textbook definition of arbitrage is a set of transactions that has zero risk, zero. It's 100% risk free. It's not low risk, as often things that are called arbitrage are. It's not 99% risk-free. It's riskless, zero. That's what makes it so powerful in models, at least one of the things.

Another one of the things that makes it so powerful in models is that it requires none of your own money. If there's an expert and informed enough investor anywhere, even just a single one, who sees it, it doesn't matter if he doesn't have two nickels to rub together, he can do it. He can borrow the money to buy the assets necessary, and at the market interest rate. Or, he can just sign the necessary contracts, for whatever amounts, no matter how big. His credit and credibility are always considered good enough.

So, if markets are incomplete, and your synthetic gold, or gold substitute, is significantly different from gold in its future payoffs, then your "arbitrage" is not an arbitrage. It's not risk free, and you – even with perfect expertise, perfect public information, perfect forsight, and perfect rationality – are going to, at most, put limited money into it. You certainly won't limitlessly put money into it for as long as it still exists, without a second thought, like you would with a real arbitrage.

Second, of course, people do have serious liquidity and credit constraints that prevent them from limitlessly jumping on an "arbitrage".

Third, in the Wallace model world, it's frictionless. There are no transactions and time costs and problems that could eat up a complicated, or ultra-complicated, arbitrage.

So, in the real world, unlike Wallace's, what you have when the government does a QE and starts pushing up the price of gold is not an arbitrage, but a good deal. You have an opportunity for an above average risk-adjusted return, an abnormal profit, if you will. And that's if you're one of the people expert and knowledgeable enough to see it, and to the extent that you have the money or credit to take advantage of it.

Well, let me say something that's fundamental here, but so often grossly not understood or appreciated:

A good deal is not an arbitrage.

It typically has nowhere near the power to move prices to their fundamental values.

Now, what you will often hear is that the market is efficient, or highly efficient. Suppose that the price of gold, or of IBM stock, is fundamentally worth some amount, and its price strays from there. It goes up by a few dollars due to the government doing a large, or vast, QE and buying it up. Well, so what if it's not a true arbitrage opportunity, it's still a good deal (to sell it, or sell it short); it's still an above average risk-adjusted return. It may be true that most investors have little finance expertise, little finance public knowledge, and little time and willingness to study and analyze individual financial assets even if they did have the expertise. But there are still a lot of big money investors and institutions that do have the expertise and knowledge, and the willingness to spend the time to use it to analyze. And those savvy investors will jump in and sell (or sell short) and sell until the price goes back down again, and it's no longer a good deal, just an average risk-adjusted deal.

Well, what are the problems with that? The usual one you hear is that savvy investors are only a small minority of all investors, and this is especially true of highly expert investors who are highly informed about a given individual asset, or even asset class. And they only have so much money. Eventually, if the government keeps buying in a QE it could exhaust their funds, their ability to counter, by, for example, selling gold they own, or selling gold they don't own short.

Even rich people and institutions only have so much money and liquidity, or credit. You can't outlast the Fed, if the Fed is truly determined. Your pockets may be very deep, but the Fed's pockets are infinite.

So, you usually hear that.

But there's another reason why the savvy marginal investor is limited in his ability and willingness to push prices back to their fundamentals that I never hear. It's a powerful and important reason: The more a savvy investor jumps on a mispriced individual asset, the more his portfolio gets undiversified, and that can quickly become dangerous and not worth it.

Gold may sell for $1,700/ounce and you think its fundamental price is $1,650, but it gets very risky, very fast, to put 10%, 20%, 30% of your wealth in gold, and the price is still only up to $1,651. What do you say then? It's still only $1,651, and it's fundamental value is $1,700, I'll put more in? What if you put 80% of your money into gold, and the price is still only up to $1,652? Put in 100%? What if the price is even then still only up to $1,653? What do you do next? Say, hey, it's still only $1,653, and it's fundamental value is $1,700, so I'll start borrowing money to buy gold?

Obviously not. Gold is a good price at $1,650, an above average risk-adjusted return, when put in a portfolio in the appropriate diversified proportion, which in the CAPM would be the market weight. But as you add more than that weight, your portfolio becomes unbalanced, and any additional gold becomes worth less to you, and very quickly.

Let me be very clear on this powerful idea. It got me a letter published in The Economists' Voice, an outstanding economics and policy journal, whose chief editor is Joseph Stiglitz. The key quote from that letter is here:
...One reason which was missing, at least explicitly, and which I have not seen yet in the literature, at least explicitly, is that a smart rational investor is limited in how much of a mispriced stock he will purchase or sell by how undiversified his portfolio will become. For example, suppose IBM is currently selling for $100, but its efficient, or rational informed, price is $110. It must be remembered that the rational informed price is what the stock is worth to the investor when added in the appropriate proportion to his properly diversified portfolio of other assets. Such a savvy investor will purchase more IBM as it only costs $100, but as soon as he purchases more IBM, IBM becomes worth less to him per share, because it becomes increasingly risky to put so much of his money in the IBM basket. By the time this investor has purchased enough IBM that it constitutes 20 percent of his portfolio, the stock may have become so risky that it’s worth less than $100 to him for an additional share. At that point he may have only purchased enough IBM stock to push the price to $100.02, far short of its efficient market price of $110. Thus, if the rational and informed investors do not hold or control enough—a large enough proportion of the wealth invested in the market—they may not be able to come close to pushing prices to the efficient level.
So, taking the gold example, suppose the government goes in and starts buying up gold big time and pushing its price up. As you can imagine, lots of gold owners are of the Fox News, and, shall we say, not so expert, variety, and aren't even going to think of selling their precious gold if it goes up by 10, 20, 30%. In fact, that will probably make them want to buy more! But, a lot of savvy expert investors will sell what they have, and even sell some short, but they will start taking on a lot of unbalanced risk as they start doing this in earnest, and the government can outlast them and keep the price up.

And likewise with any asset, or asset class, that the Fed decides to attack in earnest with a QE.

The bottom line is that unlike in Wallace's model, an arbitrage will not be created, only a good deal, something very different. And while the government can't overwhelm even a single savvy investor, without even two nickels to rub together, with an arbitrage, the government can overwhelm all of the savvy marginal investors when there's just a good deal created.

I don't think this (multipart) reason is the only reason why Wallace neutrality won't hold, and QE can work, in the real world, but it's a big whopping one. So I think at some point, at least, QE would have a large effect, albeit the QE might have to be much larger than anything ever attempted.

One last note: Individual assets that the fed may buy in a QE may sometimes have pretty close substitutes, but with the unlimited buying power of the Fed, they can buy up large percentages of not just the individual assets, but of the close substitutes to the individual assets too! So, in another words, they can buy up and move the demand curve for whole classes of assets, close substitutes and all.