The Other Father of the CAPM: Lintner's Version of Risk and Return

Everyone learns the CAPM as "Sharpe's model." That is a little unfair. In 1965, one year after Sharpe's paper, a Harvard economist named John Lintner published a long, dense, and remarkably complete derivation of essentially the same result, arrived at independently and from a different starting point. This is why careful textbooks call it the Sharpe-Lintner CAPM, and why the version of the model with a genuine risk-free rate in it usually carries Lintner's name attached.

What makes Lintner's paper worth its own explainer is not just that he got there too. It is why he was looking. Sharpe was asking a market question: what should assets be priced at in equilibrium? Lintner was asking a boardroom question: when a company is deciding whether to build a factory, what return should it demand from that factory before saying yes?

The problem: nobody knew what "required return" meant

Before this paper, corporate finance had a gaping hole in the middle of it. Textbooks said a firm should accept a project if its expected return exceeded the firm's "cost of capital." Fine. But what is the cost of capital for a risky project? The going answer was some hand-waving mixture of the firm's borrowing rate plus a fudge factor for risk, with the fudge factor essentially made up.

Worse, the fudge factor was usually applied to the wrong kind of risk. The intuitive move is to say "this project is very uncertain, so demand a high return." Lintner realized that this intuition, applied naively, gives the wrong answer, and he was able to say precisely why.

The key idea, via analogy

Imagine you already own a large, diversified vegetable garden, and someone offers to sell you one more plant. You want to know how much that plant is worth to you.

The tempting way to judge it is on its own: is this a fragile plant or a hardy one? But that is not what actually matters to your garden. What matters is whether the plant thrives and fails at the same times as everything else you already own. A plant that wilts in exactly the droughts that wilt your whole garden makes your bad years worse, so you want a discount to take it. A plant that happens to thrive in droughts is a form of insurance, and you would happily pay up for it, even if that plant is individually fragile and erratic.

That is Lintner's central point, translated into portfolio language. An asset's own volatility is nearly irrelevant to a diversified investor. What is priced is the part of its risk that moves with everything else, because that is the part diversification cannot remove. Everything else washes out across a large portfolio.

From this he derives the familiar result: an asset's expected return equals the risk-free rate plus a premium proportional to how much it co-moves with the market as a whole. Individual, idiosyncratic wobble earns you nothing, because you could have diversified it away for free and the market will not pay you for a risk you chose to keep.

Lintner then turns this back on his original question. A corporation evaluating a project should not ask "how uncertain are this project's cash flows?" It should ask "how do this project's cash flows co-move with the broad economy?" A project with wild but idiosyncratic swings, say the outcome of a single drug trial, deserves a low required return, because a diversified shareholder barely feels it. A project whose profits swing hard with the business cycle deserves a high one. This was a genuinely counterintuitive conclusion in 1965, and it is now standard corporate practice.

Why it mattered

• It gave companies a defensible hurdle rate. Instead of inventing a risk premium out of thin air, a firm could estimate the project's sensitivity to the economy and read the required return off a formula. Every discounted cash flow model taught today inherits this logic.
• It confirmed the CAPM by independent discovery. Two people reaching the same law from different directions, in different journals, within a year, is exactly the kind of evidence that turns a conjecture into a cornerstone. Mossin would make it three the following year.
• It killed the "risky project, high hurdle rate" reflex. Separating diversifiable risk from market risk is arguably Lintner's most useful practical legacy, and it is still the single most common mistake in amateur capital budgeting.
• It was unusually complete. Lintner worked through short selling, borrowing, and the aggregation of many investors' portfolios in more detail than Sharpe did, which is why his version of the derivation is the one many graduate courses actually follow.

The honest limitations

• The assumptions are heroic. Everyone agrees on the same forecasts of returns and covariances, everyone cares only about mean and variance, everyone can borrow and lend freely at one risk-free rate, and there are no taxes or trading costs. Lintner was explicit that these were simplifications, but the whole edifice rests on them.
• One period only. The model imagines investors making a single decision and then the world ending. Real investors face a long, rolling sequence of decisions with changing opportunities, which is exactly the gap Merton would later fill.
• The empirical record is mixed at best. The prediction that expected return rises in a straight line with market sensitivity has been tested to death, and the line is persistently flatter than the theory says. Low-sensitivity stocks do better than predicted and high-sensitivity ones do worse, an anomaly that Black would soon try to explain and that low-volatility funds now try to harvest.
• You need inputs you cannot really get. The formula demands expected returns and covariances that must be estimated from noisy history. The theory is exact; the numbers you feed it are not.

The one-line takeaway

Lintner independently derived the CAPM while trying to solve a corporate problem, and his enduring lesson is that an investment should be priced on how it moves with everything else, not on how wild it looks by itself, which means the scary-looking project may deserve a lower hurdle rate than the boring one.