When evaluating investment portfolios, a higher Sharpe ratio is typically better than a lower Sharpe ratio. Similarly, a higher Sortino ratio is better than a lower one. Finally, for portfolios with identical expected returns, the one with a lower standard deviation (sigma, σ) is better.
My best estimate is that less than 2% of portfolio assets are currently optimized for semivariance of any kind (mean-return semivariance, return semivariance, semivariance with respect to minimum acceptable return, etc.). Meanwhile at least 60% of portfolio assets take variance into account. According to the laws of supply and demand, the variance contribution (often related to beta) of an asset is strongly priced into its market value. Conversely, the asset’s semivariance is essentially not priced in.
If, as I believe, semivariance-based models continue to play an increasing roll in portfolio optimization strategies then asset-semivariance contributions will increasingly price in. If this prediction holds true, then early adopters of semivariance optimization will front-run asset pricing changes by buying assets with superior price-to-semivariance properties and shunning assets that detract from, say, Sortino ratios.
Sharpe and Sortino ratios differ only in the denominator (σp versus σd) . For portfolio-optimization, I prefer to modify σp and σd such that they would be identical for a normal distribution. In such a scenario, each sigma is the square root of its corresponding (return) variance. Because downside variance (σd ), in a normal distribution, is half of total variance I multiply downside variance by 2. For the same reason, I tend to avoid anything mathematically arbitrary such as minimum acceptable return (MAR), and use zero or mean-return instead. Empirically, I have found that zero works quite well.
My preliminary data shows is that for virtually any portfolio σp ≠ σd. While σp and σd are positively correlated, their ex-post correlation is as low as 0.5. In some cases, for optimized portfolios of the same return, increasing σp by one unit (say 0.01) reduces σd by a similar amount and vice versa. This is an astounding trade off — it means variance and semivariance compete head to head.
I don’t believe that the investment industry will switch from variance to semivariance models overnight. Similarly individual investment houses desire to shift gradually (each on their own timescale). Thus I propose the use of hybrid variance/semivariance ratios. With hybrid ratios, financial professionals can choose just how much they want semivariance to factor into their optimization… from zero to 100%, and everything in between.
The shifting portfolio-optimization market is large enough large enough for several players to make healthy profits. For those players that can and do make a shift to semivariance, I recommend a contiguous hybrid model.