Sortino and asymmetric returns?

[sridhar]

From the reading on the various ratios, I see that the "Sortino ratio is a variation of the Sharpe ratios and is useful for a portfolio where the returns are not symmetric..."

Several questions:

1. David, what does "symmetric return" mean?

2. I understand that in the Sortino ratio, the SD in the denominator only takes into account portfolio returns that are below the min acceptable return....Is this related to symmetry?

3. More importantly, why are portfolio returns above the MAR rejected in the computation of the MSD(min)?

4. Finally, when is Sortino "more appropriate" than Sharpe? (Is Sharpe only restricted to comparisons of the portfolio return with the risk-free return?)

--sridhar

PS: thank you for your explanation on auto-correlation in another post. Clear and lucid explanation as usual!

 

[David Harper CFA FRM]

Hi sridhar,

1. Symmetric returns are not skewed (skew = 0). When we say, returns are normally distributed, this includes the idea that returns are "not skewed" or "are symmetrical;" e.g., if 10% is the mean return, then +15% is just as likely as +5%. +12% just as likely as +8%. Symmetry around the mean return.

2. Yes. The denominator in Sortino is called downside deviation (the square root of the downside variance). It is much like the standard devation except only returns below the MAR are included. If the returns are symmetrical, then downside deviation/Sortino is not necessary. But if they are skewed, then here is the concern: imagine a distribution with negative skew. It will have more extreme losses than extreme gains. (e.g., selling out of money puts gives a negative skew: mostly above average return collecting premiums, but very occassionally deep losses). A standard deviation will effectively "mix" the assymmetrry into a single number. But it will understate on the downside. So, the idea with downside deviation is to measure the "standard deviation but only on the downside" that we care about.

3. As to only include the downside deviations - because the returns above MAR are not "risk" and these measure try to better reflect risk

4. When the returns are skewed (not symmetrical). Although not everybody seems to think they are so great; I've seen many papers that showed the results (ordinal ranking) are about the same.

David