158 Optimizing Optimization
more severe extreme losses in the final part of the sample period. The results
of the Monte Carlo analysis show that this conclusion is not limited to the
particular set of alphas selected for the initial illustration. By averaging across
randomly simulated alphas, I obtained a consistent pattern.
6.5 Conclusion
In this chapter, I have argued that the need for a coherent risk measure, i.e.,
one that satisfies the most intuitive principles of risk measurement, is particu-
larly felt in a context where the risk characteristics of financial assets evolve
rapidly. I have shown how this can be achieved by adopting EVaR, a measure
recently proposed in the academic literature.
Furthermore , I have sketched a numerical algorithm that can be used for
asset allocation or low-dimensional portfolio construction problems. The
objective of the procedure is to minimize risk, possibly subject to a minimum
target expected return. Risk is measured by the predicted EVaR of the portfo-
lio, which adapts dynamically to the new information available from the time
series of asset returns.
The disadvantage of the proposed methodology, compared to the existing
approaches based on quantiles (VaR) or expected shortfall, is that its economic
interpretation is less straightforward. The 1% VaR, for example, can be viewed
as the best of the 1% worst cases.^7 No such intuitive characterization exists
for EVaR. However, an advantage of the EVaR approach is that it lends itself
naturally to a dynamic model of portfolio risk. In an environment where the
risk characteristics of a portfolio evolve rapidly, it is crucial to be able to pro-
cess the most recent information on downside events through a simple dynamic
weighting scheme. This is exactly what the spline smoothing expectile estima-
tor, which is at the heart of the methodology described in this chapter, achieves.
In my experience, the overall weighting pattern generated by a mean – EVaR
approach tends to be similar to the solution to a traditional mean – variance
problem. The main difference appears to be, as the empirical analysis in this
chapter illustrates, that EVaR tends to underweight assets that have experienced
extreme downside events, particularly if these have occurred in the recent past.
An attractive feature of the approach advocated in this chapter is its com-
putational simplicity. Because the objective function is convex (and piecewise
linear), the proposed optimizer is robust and reliable. Computation times are
modest for typical asset allocation applications. It is likely that by adopting a
more sophisticated optimization procedure, e.g., an interior point algorithm, it
would be possible to improve the computational efficiency further.
Several questions remain open for future research. It would be interesting
to backtest a simple trading strategy based on the mean – EVaR optimizer in
order to assess whether it improves on the traditional mean – variance approach
7 See Acerbi (2004).