Equilibrium and the price of risk

The second chapter ended with three men, in three different ways, telling you how to build a portfolio for yourself. This chapter asks a bigger question: what happens to prices if everyone does that? Four papers answer it, and between them they invented the language every professional still speaks, alpha, beta, benchmark, factor, even the ones who claim not to believe a word of it.

Sharpe, 1964

William Sharpe was a young economist who had worked with Markowitz and asked the obvious next question. If every investor builds a Markowitz portfolio, with the same information and the ability to borrow freely, what does the market look like when they are all done? The answer was elegant enough to win a Nobel Prize: everyone ends up holding the same portfolio, the whole market, and the only thing that varies is how much of it they hold. The cautious hold some of it and keep cash. The bold hold it and borrow to hold more.

From that came the result that matters. If everyone holds the market, then the only risk that gets paid is the risk of the market itself, the part you cannot diversify away. The risk of any single company, any single bet, earns you nothing, because anyone could have gotten rid of it for free by spreading out. Sharpe wrote it as a line: an asset’s expected return rises with its beta, its sensitivity to the market, and with nothing else.

The Journal of Finance rejected the paper the first time. It went on to become the framework everything else is stated against, and it has a practical consequence that arrived before the product existed to deliver it: if the market portfolio is the best portfolio, the sensible thing is to hold it. Index funds are Sharpe’s theorem made cheap.

Here is what I take from it. The model is wrong in its details, and everyone has known that since the seventies; the line that relates beta to return is too flat in real data, and beta alone does not explain who earns what. But the accounting survived the model. Every return you earn can be split into two parts: the part that came from being exposed to the market, which is cheap to obtain, and the part that came from something else, which is expensive and usually not there. Once you learn to see returns that way, most bank proposals turn out to be beta at an alpha price.

Jensen, 1968

Michael Jensen took Sharpe’s line and turned it into a ruler. If the market pays you according to your beta, then a manager’s contribution is whatever is left over after you subtract what the market would have given anyone with the same beta. He called that leftover alpha, and he measured it for 115 mutual funds over nineteen years.

The average was negative, roughly one percent a year, and even before subtracting their fees the funds as a group could not cover their own trading costs. Nor could Jensen find funds whose good years predicted their next good years; the winners looked like what chance would produce. The presumption that professionals add value reversed in a single paper, and the case for simply holding the market had its evidence five years before the first index fund was launched.

This result has been repeated in every decade since, with better data and better benchmarks, and the corrections have generally made managers look worse. The way I use it is as a starting assumption. Any manager I am shown starts, in my mind, at minus their fee. They have to earn their way up from there with evidence, and the evidence has to cover the fee before it counts as skill. Most never get there. The concrete exercise from my own reading is worth doing once: take your three largest funds, get thirty-six months of returns, and measure them against the market the way Jensen did. Then put the alpha next to the fee. In most cases the fee will be bigger than the alpha, and then you know what to do.

Merton, 1973

Robert Merton noticed something Sharpe’s world left out: people live for more than one period. A real investor is not only afraid of the market falling this year. She is afraid of interest rates collapsing when she needs income, of her industry shrinking, of the currency she spends in losing value. Merton showed that a long-lived investor will pay to hold assets that do well in those bad states, and that the market will therefore price more than one risk.

Why does that matter? Because it explains when an investment deserves to pay more than the market, and when it does not. Think of it as insurance in reverse. An insurance company pays you when your house burns down, and you pay it a premium every year for that protection. In markets it works the other way: an asset that loses money exactly when you are already in trouble, when jobs disappear or rates spike or your business slows, is an asset nobody wants to hold in a crisis, so it has to pay a higher return in normal times to find an owner. That extra return is the premium, and it is real because the pain it compensates for is real.

So here is the test, and it is the most useful sentence in this chapter. When someone offers you an investment that supposedly pays more than the market, ask them: in what kind of bad year does this thing lose money, and why would I be paid for accepting that? If they can give you a clear answer, the premium may be real. If they cannot, if the only answer is “look at the chart,” then somebody found a pattern in old data and gave it a name, and the pattern will probably not be there when you need it.

For a family this cuts the other way too. Your bad states are specific: the local economy, the business you depend on, the currency your life is priced in. Merton is the permission to deviate from the world market portfolio in order to hedge those, and to do it on purpose rather than by accident.

Ross, 1976

Stephen Ross arrived at a similar place from the opposite direction. Merton had to build a whole world of investors to get there. Ross needed only one assumption: nobody leaves free money on the table for long.

Here is his argument in plain terms. Suppose two large, well-spread portfolios react the same way to the same things, both fall the same amount when the economy slows, both gain the same amount when rates drop, and so on. Then they are, for practical purposes, the same investment, and they have to offer the same return. If one paid more, people would buy it, sell the other, and pocket the difference with no risk, and that would push the prices back in line within days. What follows is that the return you can expect from a portfolio is set by a few things it is exposed to, the economy, rates, credit, and so on, and not by the particular names in it. Ross got there without needing to assume anything about how investors think or what the market as a whole looks like.

What changed because of this paper is how risk is managed everywhere. A portfolio’s behavior is determined by a few exposures, to the market, to rates, to credit, to currencies, to value, to momentum, to illiquidity, and not by the list of names inside it. Manage the exposures and the names take care of themselves. The single most useful document a family can own is one page that shows all of its holdings, across every bank and every wrapper, as a set of factor exposures. Ross is the reason that page is worth more than any account statement.

One thing Ross does not do, and people forget it: he does not tell you which factors are priced. That took the next twenty years of data, and it is a story for later.

Three habits

Benchmark everything. If you cannot say what the market would have paid you for the same risk, you cannot say whether anyone added anything.

Buy the market cheaply, and price every fee against the passive cost of the exposure it delivers.

Demand a named risk behind every premium. If nobody can tell you when it loses money, nobody can tell you why it should make money either.

Gala: when someone shows you a return, ask two questions in this order. How much of it was the tide, and what did you pay for the rest?