Following a practice-based risk factor perspective, a conditional linear factor model can be used to uncover and analyze hedge fund strategy risk exposures.

A simple conditional linear factor model applied to a hedge fund strategy’s returns can be represented as:

(Return on HF* _{i}*)

*= α*

_{t}*+ β*

_{i}

_{i}_{,1}(Factor 1)

*+ β*

_{t}

_{i}_{,2}(Factor 2)

*+ … + β*

_{t}

_{i}_{,}

*(Factor*

_{K}*K*)

*+*

_{t}*D*β

_{t}

_{i}_{,1}(Factor 1)

*+ D*

_{t}*β*

_{t}

_{i}_{,2}(Factor 2)

*+ … +*

_{t}*D*β

_{t}

_{i}_{,}

*(Factor*

_{K}*K*)

*+ (error)*

_{t}

_{i}_{,}

*,where*

_{t}- (Return on HF
)_{i}is the return of hedge fund_{t}*i*in period*t*; - β
_{i}_{,1}(Factor 1)represents the exposure to risk factor 1 (up to risk factor_{t}*K*) for hedge fund*i*in period*t*during normal times; *D*β_{t}_{i}_{,1}(Factor 1)represents the_{t}*incremental*exposure to risk factor 1 (up to risk factor*K*) for hedge fund*i*in period*t*during financial crisis periods, where*D*is a dummy variable that equals 1 during financial crisis periods (i.e., June 2007 to February 2009) and 0 otherwise;_{t}- α
is the intercept for hedge fund_{i}*i*; and - (error)
_{i}_{,}is random error with zero mean and standard deviation of σ_{t}._{i}

Each factor beta represents the expected change in hedge fund returns for a one-unit increase in the specific risk factor, holding all other factors (independent variables) constant.

Any returns not explained by the model’s risk factors would be attributed to either omitted risk factors, alpha (i.e., hedge fund manager skill), or randomness (error).

A **stepwise regression** process is useful for creating linear conditional factor models that avoid multicollinearity problems, by avoiding the use of highly correlated risk factors.

- Equity risk (SNP500).
- Currency risk (USD).
- Credit risk (CREDIT).
- Volatility risk (VIX).