Important paper:

SORTINO, Frank A. and Robert van der MEER, 1991. Downside Risk. *The Journal of Portfolio Management*, **17**(4), 27–31.

See also:
SORTINO, Frank A., 1998. http://www.sortino.com/htm/Sortino%20Ratio.htm.

‘As an alternative, the Sortino ratio has been advocated in order to capture the asymmetry of the return distribution. It replaces the standard deviation in the Sharpe ratio by the downside deviation which captures only the downside risk. However, higher moments are incorporated only implicitly.’

Bacmann and Scholz

‘The Sortino ratio also fails the lottery test.’

Keating and Semadeni (2004)

‘The Sortino ratio is the same as the Sharpe ratio except that the square root of the semi-variance replaces the volatility. That is, the risk is only measured with down moves (relative to some target value).

Naively it would seem that the Sortino ratio would always be preferred, but if the returns are symmetric, then the estimate of volatility is overly noisy because only half the data are used.’

pburns, Willmott Forum

‘The Sortino Ratio was introduced by Sortino and Price (1994), and Pedersen and Satchell (2002) proved that the risk/return frontier, when risk is defined by SSD (11), exhibits the same desirable convexity properties of the traditional mean-variance frontier, thus rendering it amenable for portfolio analytics."

Pedersen and Rudholm-Alfvin

‘Assuming portfolio returns are normally distributed, it is shown that both Sortino ratio (SR) and upside potential ratio (UPR) are monotonically increasing functions of the Sharpe ratio. As a result, all three risk-adjusted performance measures provide identical ranking among investment alternatives.’

‘Excessive kurtosis does not affect the monotonic relationship between Sortino and Sharpe ratios,...’

Lien (2002)

‘An important advantage of using the upside potential ratio rather than the Sortino ratio is the consistency in the use of the reference rate for evaluating both profits and losses.’

‘For higher levels of loss aversion, the Sortino ratio yields the best results with a correlation of approximately 60% with the preference function.’

Plantinga and de Groot (2001)

‘Other measures, such as the "Sortino ratio" or "Value at Risk", are ad hoc attempts to incorporate the importance of downside risk. But as they totally ignore upside risk, they are generally inaccurate as a appropriate risk and/or performance measures.’

Leland 1997 (revised 1998)

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