Measuring the performance of an investment is essential in evaluation. The Sharpe ratio (Sharpe 1966), which measures the excess return over the risk-free rate in relation to total risk, is the most widely known performance measure. It is used by Ackermann et al. (1999), Liang and Kat (2001) and others, to measure hedge fund performance. However, since it assumes normally distributed returns and does not account for hedge funds' special characteristics, it is criticised as an inadequate measurement for hedge fund performance. This is also stated by Brooks and Kat (2002), Amin and Kat (2003), Mahdavi (2004) and Murguia and Umemoto (2004), on the basis that Hedge fund returns typically have asymmetric distributions.

To solve this issue, Sortino and Price (1994) developed the Sortino ratio, which divides the excess return on a portfolio, with respect to a minimum acceptable return (MAR), by a term called the downside deviation (deviation of returns below the MAR). Later on, Sortino, Sortino et al. (1999) developed the Upside Potential ratio, which divides the positive excess returns of the portfolio by the downside deviation. Sortino et al. (2001) claimed that the downside risk framework was able to overcome the problems in ranking skewed return distributions, and found that the Upside Potential ratio was a more accurate evaluator than the Sharpe ratio, particularly when the strategies included the use of options. Studies by Rosenberg et al. (2004), and Scherer (2004), found the Sortino ratio to be a superior performance ratio compared to the Sharpe ratio. Chaudhary and Johnson (2008) in a simulation study of skewed distributions, also found that the Sortino ratio is a superior performance measure to the Sharpe ratio.

To analyse fund performance, in terms of various attributes, factor models were created over time. The models can broadly be divided into two categories – linear multi factor models and non-linear multi factor models.

Linear multi factor models were created by Sharpe (1992), Fama and French (1993) and Carhart (1997). They identified several factors to explain performance and returns. Sharpe (1992) implemented the asset class factor model that allows for style analysis. The model includes twelve asset classes and the degree of exposure to each asset class is used to explain the variation of returns in the specific period. Unfortunately, Sharpe's model can only be applied to funds pursuing a long-only strategy, while many hedge fund strategies use short selling and leverage. In 1993, Fama and French built their three-factor model. It expanded the Capital Asset Pricing Model (CAPM) by considering size (small and large cap) and value (book to market ratio) factors. Kothari and Warner (2001) consented to the improvement of the CAPM, by including the new factors, however, they criticised the Fama and French model by pointing out that it detects abnormal results that do not exist. Building up on this, Carhart (1997) came up with a four-factor model. He included momentum, which made his model superior to the CAPM, as well as the Fama and French. Linear multi factor models are used to measure hedge fund performance in several studies, like Schneeweis and Spurgin (1999), Capocci (2002) or Jordao and De Moura (2011). Despite the application to hedge fund performance, the linear models are more suitable to evaluate traditional funds because they fail to capture hedge fund characteristics like time variation. Furthermore, Slavutskaya (2013) concluded that linear factor models are not suitable for hedge funds as they lead to over-parameterisation, because many hedge funds have a life of three years.

Non-linear multi factor models include the asset factor model by Fung and Hsieh (1997, 2001) and models by Agarwal and Naik (2000) or Huber and Kaiser (2004). Fung and Hsieh (1997) extend the asset class factor model by Sharpe (1992) to make up for major hedge fund investment styles and consider hedge funds as option portfolios. In 2001, they used the trend-following strategy, to model hedge fund returns and demonstrated that the returns resemble lookback straddle returns. Huber and Kaiser (2004) arrived at the same conclusion. Agarwal and Naik (2000) introduced a general asset class factor model that is optimised for passive option-based strategies and buy-and-hold strategies. Agarwal and Naik (2004) later focussed on hedge funds that use these strategies and their risk exposure. Their findings suggest that hedge funds have a significant exposure to the Fama and French three-factor model and Carhart's four-factor model. More recently, Gregoriou et al. (2016) analysed hedge funds' returns and cross-sectional dispersion, using the Fama and French (1993) model, as well as Fung and Hsieh (1997, 2001) factors.

Although non-linear multifactor models can explain hedge fund returns in a more detailed way and account for special characteristics of hedge funds, they might not be best for investors' performance evaluation. This is mainly due to the fact that exposures are not static and, therefore, need to be adjusted and that the models and factors are complicated to replicate.

In another study, Fung and Hsieh (2004) attempted to model hedge fund returns in terms of seven asset-based style (ABS) factors – two equity ABS factors (market risk and the spread between small-cap stock returns and large-cap stock returns), two fixed income ABS factors (10-year treasury yields, change in the yield spread between 10-year T-bonds and Moody's Baa bonds), and three trend-following ABS factors (portfolios of lookback straddles on bonds, on currencies and on commodities), as an alternative to other models. Although they report success with high R-squares, it could be argued that introduction of too many factors introduces an arbitrariness in the analysis, which might not be robust when market conditions change. Moreover, there may be other factors which have a higher explanatory power over short horizons and such factors can change with time, making it burdensome to identify them.