The Sharpe-less-ness: Why Fund Rankings Invert in a Down Market

In a falling market, ranking funds by Sharpe ratio can quietly invert the answer and mark down the more careful fund. Here is why it happens, and the one-line adjustment that fixes it.

The Sharpe ratio is the closest thing fund analysis has to a universal yardstick. It takes return, divides by risk, and gives one number that lets a cautious fund and an aggressive one be compared on the same footing. That convenience is why it sits on almost every factsheet and screening tool.

But it hides a flaw that surfaces at the worst possible moment. When markets fall, the ratio can rank the more sensible fund as the worse one, and do it so quietly that the error rarely gets noticed.

What the Sharpe ratio is meant to do

The Sharpe ratio is excess return per unit of risk:

Sharpe ratio = (Rp − Rf) / σp

where Rp is the portfolio return, Rf is the risk-free rate, and σp is the volatility of the portfolio. The intuition is clean. For two funds with the same return, the one that took less risk to get there is better, and a smaller σp in the denominator gives it a higher ratio. For the same risk, the fund with the higher return is better. Read this way, a higher Sharpe is a better fund, and the measure does exactly what a risk-aware reader wants.

That reasoning holds as long as the numerator is positive. The moment excess return turns negative, it breaks.

Where the Sharpe ratio inverts: negative returns

When a fund loses money relative to the risk-free rate, the numerator (Rp − Rf) is negative. Dividing a negative number by a smaller denominator makes it more negative, not less. So for two funds with the same negative excess return, the one with lower volatility gets the more negative Sharpe ratio. A negative Sharpe ratio no longer behaves like its positive counterpart: more risk now improves the score instead of hurting it. The careful fund is marked down for being careful.

Consider two funds over the same falling quarter, with a 6% risk-free rate:

Both lost the same amount. Fund B did it with less volatility, so by any reasonable standard Fund B is the better of the two. The Sharpe ratio says the opposite: Fund A, at −2.25, outranks Fund B at −3.00. Here the right answer is not a matter of taste. Same return, lower risk, is simply better, and the ratio gets it backwards. This is the case worth keeping in mind, because it is provably wrong rather than debatable.

The distortion is not always this visible. Take a second pair:

Now Fund A lost less but was more volatile, and Fund B lost more but was steadier. Neither clearly beats the other; the right ranking genuinely depends on what an investor values. Sharpe ranks Fund A first. That may or may not be the answer you would defend, and the point is precisely that the ratio hands you a confident ordering in a situation where confidence is not warranted. In a down market, the measure stops distinguishing between the cases where it is reliable and the cases where it is not.

A simple adjustment for negative Sharpe ratios

The cause of the inversion is structural: in the negative region, volatility belongs on the other side of the operation. The fix follows directly. When excess return is negative, multiply by volatility instead of dividing by it:

When (Rp − Rf) is positive: Adjusted = (Rp − Rf) / σp

When (Rp − Rf) is negative: Adjusted = (Rp − Rf) × σp

Applied to the first pair, Fund A scores −18 × 8 and Fund B scores −18 × 6, so Fund B now correctly ranks ahead. The careful fund stops being punished for its caution. In the negative region, higher volatility now makes a loss look worse, which is what a risk-aware reader expects.

The two halves live on different scales, since the positive side is a ratio and the negative side is a product. That makes the adjusted figure useful for ordering funds within a peer set over the same period, not as a number to be read on its own or compared across the zero boundary. A constant can be applied to bring the negative-region values onto a more familiar scale for display, but it is cosmetic: multiplying every fund by the same constant does not change their order, so it should be treated as presentation, not as part of the measure.

Prior art: Israelsen's modified Sharpe ratio

The adjustment above is not new, and the published record matters here. Craig Israelsen set out the same correction, sometimes called the modified Sharpe ratio, in the Journal of Asset Management in 2005, expressed as a single closed form rather than two cases. He raised the standard deviation to the power of the excess return divided by its absolute value:

Sharpe* = (Rp − Rf) / σp^(ER/|ER|)

The exponent is +1 when excess return is positive and −1 when it is negative, so the expression divides by volatility in the first case and multiplies by it in the second. It is the same fix written as one line. Israelsen also carried the correction over to the Information Ratio, where excess return over a benchmark is divided by tracking error and the same sign problem appears.

The version laid out here was first developed in an internal Valuefy note in 2012, arrived at independently from the practical problem of ranking funds in falling markets. We treat Israelsen's paper as the formal precedent and the source worth citing; the contribution of restating it here is to make the failure mode legible to a practitioner and to be precise about where the adjusted number can and cannot be used.

Beyond Sharpe: Treynor, Sortino and the Information Ratio

The Sharpe ratio is not alone in this. Any measure that divides a possibly-negative excess return by a risk term inherits the same inversion. The Treynor ratio divides by beta, the Sortino ratio by downside deviation, and the Information Ratio by tracking error, and all three flip in the same way when the numerator goes negative. The M-squared measure inherits it too, because it is a monotonic transformation of the Sharpe ratio and therefore preserves whatever ranking Sharpe produces.

One common measure does not have the problem. Jensen's alpha is a difference, not a ratio: it subtracts the return predicted by the market model from the fund's actual return, with no division by the fund's own risk. There is no denominator to invert, so alpha stays well-behaved when returns turn negative. The distinction is the lesson. The vulnerability comes from dividing by risk, so the measures to watch are the ratios, and the measures to reach for when in doubt are the ones built on differences.

What to take from it

None of this makes the Sharpe ratio a bad measure. In rising markets it does its job. The caution is narrow and specific: in a falling market, a negative numerator turns the ratio against the risk-aware reader, and the fund that lost the least with the least volatility can show up at the bottom of the table exactly when its discipline mattered most. The remedy is to recognise the regime, switch the role of volatility when excess return is negative, and read the result as an ordering rather than a score. Risk-adjusted measures are only as useful as the conditions they are read in, and the down market is the condition where most of them need a second look.

Common questions

What does a negative Sharpe ratio mean?

A negative Sharpe ratio means the investment returned less than the risk-free rate over the period, so its excess return is below zero. It signals underperformance against a cash benchmark. It is not, on its own, a statement about how much risk the fund took.

Can you compare two funds using negative Sharpe ratios?

Carefully, and not at face value. When excess returns are negative, the ranking inverts: for the same loss, the lower-volatility fund gets the more negative Sharpe ratio and looks worse, even though it took less risk. Compare only over the same period against the same risk-free rate, and apply the adjustment described above before reading the order.

Is a higher or lower Sharpe ratio better when it is negative?

A less negative Sharpe ratio is nominally higher, but in the negative region a higher reading can simply reflect more volatility rather than better performance. The raw ranking should not be trusted on its own here. Moving volatility to the numerator side, multiplying rather than dividing, recovers a sensible order.

About Valuefy

Valuefy builds quantitative wealth and asset management technology used by leading institutions, with roots in the math-first analytics tradition its founders brought from Fractal Analytics. Performance measurement that behaves correctly in every market regime is part of how a well-built platform earns trust.

References

• Israelsen, C. L. (2005). A refinement to the Sharpe ratio and information ratio. Journal of Asset Management, 5(6), 423–427.
• Sharpe, W. F. (1966). Mutual fund performance. Journal of Business, 39(1), 119–138.
• The Sharpe-less-ness (Valuefy, internal note, 2012), where the adjustment used here was first developed.