# Modigliani Squared (M2) and negative fund returns

I often see it quoted that the M2 measure offers an advantage over the sharpe, as sharpe is 'difficult to interpret' for negative returns. eg: https://en.wikipedia.org/wiki/Modigliani_risk-adjusted_performance#:~:text=The%20M2%20measure%20is,to%20the%20risk%2Dfree%20rate.

However, consider the following returns:

This has the following sharpe and M2 ratios:

Now Fund A has been more been more volatile and has eeked out a 1% return. Fund B has been less volatile and made a small loss. Both have beaten the benchmark.

Look at the M2 ratios. Fund A sees its M2 return reduced as it has been more volatile than the benchmark. Fund B's M2 shows a worse return, ie greater loss, despite having lower volatility than the benchmark.

Seems to me that Fund B should be showing a smaller loss if the M2 measure is meant to fix working with fund losses? Am I misunderstanding how M2 is meant to be applied?

Thanks

• The interpretation of negative Sharpe Ratios is indeed problematic. But M2 is basically a monotonic transformation or re-working of the Sharpe Ratio (which some people consider more intuitive than the SR), so I don't see how it could solve this inherent issue with the Sharpe Ratio. It is the same concept dressed in different clothing. Aug 26, 2020 at 19:29
• Devil's advocate, but any fund/strategy showing a negative Sharpe (return) is bad, so the fact comparing two negative Sharpes is problematic is moot Aug 27, 2020 at 2:20
• @noob2: it appears this is the case! I was thrown off by various internet sources stating M2 fixes this issue this sharpe. Obviously not. I had in my mind possibly I wasn't implementing the formula correctly. Aug 27, 2020 at 7:11
• @Chris. I see your point, but how would you assess funds where their benchmark has fallen for say 2-3 years? (I'd say alpha likely the better metric then.) Aug 27, 2020 at 7:15