Asymmetry


Asymmetry is at the heart of an Asset Manager’s preoccupations: any investor wants to be positively exposed to bullish markets while controlling the impact of bearish market conditions.

This keen interest of investors explains the growing success of complex financial instruments such as structured derivatives, capital-guaranteed products... These products have a non Gaussian behavior, meaning that their returns are not distributed according to a Normal model. The shape of the distribution might be radically different on the left side and on the right side of the distribution, with fatter tails for instance.


Measuring the asymmetry

Standard statistics (mean return and volatility, the first and second-order moments of the distribution) do not capture the whole shape of a distribution. To evaluate the asymmetric properties of a financial instrument, one can use the following measures:

• - Semi-volatility (or downside volatility), which measures the “bad” volatility, i.e. the volatility of the returns which are lower than the mean return.
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• - Sortino ratio, which measures the excess return to downside volatility.
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• - Skewness: this 3rd-order moment of the distribution evaluates the degree of asymmetry of a financial instrument. The higher the skewness, the fatter the tail at the right of the distribution, which is why investors favor a positive skewness.

Shaping the asymmetry through active risk management

It is one thing to measure the asymmetry, but the real challenge is to control this asymmetry in the allocation process itself (ex-ante). Adding asymmetry constraints (such as a skewness constraint) in the portfolio optimization problem allows investment managers to shape their distribution of returns according to their risk/return profile. These tailored quantitative approaches help investors design asymmetric funds (even based on classical underlying components).

But a straightforward formulation of such advanced allocation strategies leads to ill-posed optimization problems which are not only difficult to solve but may also lead to unstable portfolios. It is crucial to formulate strongly convex counterparts of such optimization problems in order to ensure the robustness and consistency of the optimal portfolios.

See also : Downside Volatility, Skewness, Sortino Ratio,