The document discusses different types of market neutrality for hedge funds: 1) Correlation neutrality means a fund's returns only depend linearly on market returns. 2) Mean neutrality means a fund's expected return is independent of market returns. 3) Variance neutrality means a fund's risk does not increase as market risk increases. 4) Value-at-risk neutrality means all quantiles of a fund's return distribution are neutral to the market. 5) Tail neutrality means extremely low fund returns do not depend on extremely low market returns. 6) Complete neutrality requires a fund's return distribution to be completely independent of the market return.
3. 1. Definitions
Market neutrality:
Depth: reproduces the completeness of the neutrality of
the fund to market risks;
breadth: reveals the number of market risks to which
the hedge fund is neutral.
(Patton, 2004)
4. 2. Correlation neutrality
Correlation neutrality:
An investor facing returns that are multivariate normally
distributed or one with quadratic utility, will only
require linear correlation as the measure of
dependence.
(Patton, 2008)
5. 3. Mean neutrality
Mean neutrality:
Is the expected return on the fund being independent of the
return on the market. Requires not only that there are no
nonlinear relationships, but also that there is no linear
relationship between the market return and the fund return.
(Patton, 2008)
6. 4. Variance neutrality
Variance neutrality:
Considering risk as measured by variance, while not constant,
is expected that the risk of the fund does not increase at the
same time as the risk of the market index. That means the
risk of the fund is neutral to market risk.
(Patton, 2008)
7. 5. Value-at-risk neutrality
Value-at-risk neutrality:
Given that the VaR of a fund is simply a quantile of its
distribution of returns, value-at-risk neutrality implies
that all quantiles of the fund are neutral to the market.
(Patton, 2008)
8. 6. Tail neutrality
Tail neutrality:
Implies that conditioning on the fact that an extremely
low return on the market is observed do not affect the
probability of an extremely low return on the fund.
(Patton, 2008)
9. 7. Complete neutrality
Complete neutrality:
Requires completely indenpence on the market return
by the distribution of fund returns.
(Patton, 2008)
10. References
Patton, A. J., 2004, Are Market Neutral Hedge
Funds Really Market Neutral? London School of
Economics
Patton, A. J., 2008, Are Market Neutral Hedge
Funds Really Market Neutral? Oxford University Press