3. Risk-adjusted return: the Sharpe ratio without heavy formulas

Theory 4: Risk, return and diversification

Two strategies end the year making exactly the same amount: fifteen percent. One of them is clearly worse than the other, and the return figure does not say so.

With volatility and correlation now in the toolbox, we can tackle a question that has been implicitly hovering since the beginning of this course. How do we fairly compare two investments or two strategies that delivered different returns, when one of them took on far more risk to get there?

Two roads to the same return

Picture those two strategies in a little more detail:

• Strategy A gains 15% in a year, with smooth, predictable month-to-month moves.
• Strategy B also gains 15% that same year, but with months of +12% followed by months of -8%. Far more erratic.

On gross return, they tie. Yet almost any reasonable investor would prefer Strategy A, because it delivered the same result while taking on much less risk along the way:

• A lower chance of being forced to sell at the worst possible moment out of panic.
• Less volatility for the capital, and for the nerves of whoever is following it.

Comparing only the final return, without accounting for the path taken to get there, is one of the most common ways to reach mistaken conclusions when evaluating investments.

The Sharpe ratio: return per unit of risk

The Sharpe ratio, developed by the economist William Sharpe (also a Nobel laureate), formalizes exactly this intuition.

Without going into the exact formula, the idea comes in two steps:

• Take the return earned above what you would have made with no risk at all, that is, above the return of a risk-free asset such as short-term government debt.
• Divide it by the volatility — the standard deviation — taken on to achieve it.

The result is a single number answering one very specific question: how much extra return did I get per unit of risk taken?

How to read the figure

• A Sharpe of 1 is considered reasonable.
• A Sharpe above 2 is, in most contexts, exceptionally good. And it deserves some suspicion as to whether it is sustainable or the product of a particularly favorable period.
• A Sharpe close to zero or negative indicates that the return obtained did not adequately compensate for the risk taken. Even if the gross return figure looked attractive on its own.

What Sharpe reveals about leverage

The Sharpe ratio makes it far fairer to compare strategies with very different risk profiles. And even to compare the same strategy run at different levels of leverage.

If you double a strategy's leverage, you normally double both its expected return and its volatility. The Sharpe ratio is left practically unchanged.

That detail reveals something well worth keeping in mind. Leverage, on its own, does not improve the quality of a strategy: it merely amplifies its outcome, good or bad, in both directions.

The inherited limitation, and Sortino

Like any measure built on standard deviation, the Sharpe ratio inherits the same limitation we saw in the first module of this level. It penalizes upside volatility exactly as much as downside volatility, even though no investor is actually 'bothered' by the volatility that comes from unexpectedly large gains.

That is why variants exist, such as the Sortino ratio, which penalizes only downside volatility, the kind that genuinely worries investors. It ignores the part of the dispersion that comes from positive surprises.

None of these metrics is perfect or definitive on its own. Not even Sortino fully escapes the fat-tail problem mentioned earlier.

But they all share the same underlying purpose: to force any serious evaluation of an investment or strategy to ask the same uncomfortable question every time. At what price in risk was this return achieved? Instead of stopping at whichever final number shines brightest in a headline.

The mistake of comparing Sharpes without looking at the period

There is a common mistake when using the Sharpe ratio, even among those who know its definition well: comparing it across strategies computed over very different time periods, without adjusting anything else.

A Sharpe of 0.8 computed over ten years of data, spanning several complete economic cycles, is a far more reliable figure than a Sharpe of 1.5 computed over six exceptionally favorable months.

The reason is that the number itself carries no information about how many different market conditions the strategy has proven it can withstand.

So comparing two Sharpe ratios without also looking at the period and the context in which they were computed is, once again, a comparison out of context. Much like the one we saw with valuation multiples in the previous level.