Portfolio Risk Surfaces

"Portfolio Risk Surfaces" is an initiative to explore the feasible set of a portfolio and to make risk and related measures visible across the feasible set. The resulting graphs can be considered as surfaces showing the diversification or concentration of risk for any feasible portfolio.

Have a look to such a risk surface showing the diversification of covariance risk budgets of a typical Swiss pension fund portfolio for the period November 2005 to April 2007.

We have computed the hull for this portfolio composed of swiss and foreign equities, bonds, and alternative instruments. We have rastered the feasible set on an equidistant grid of portfolios. Each portfolio on any grid point was optimized and the optimal weights are derived.

Covariance Risk Budgets Diversification:
Then we have calculated for each asset its covariance risk budgets. The resulting variance can be used as a mesure of goodness for risk diversification. The result is shown in the following figure.

Risk Surface:
The image plot and the contour lines visualize the structure of the risk surface. Like in topographhic maps, low risk is blue like "coast levels" and high risk is brown like "mountain levels". The black profile line marks a "kink" in the landscape where the considered risk is lowest. Along this line we have an investment which has a better "covariance risk budget" diversification compared to an investment on the efficient frontier. Now you can decide to take an investment for the same return but with a better covariance risk budget diversification on the cost of an increase in the total risk. Or if you like not to increase the total risk, you can improve your covariance risk budget diversification on the cost of a lower return.

We have attached some more portfolio risk surfaces. Currently Rmetrics has implemented a library with dozens of risk surface functions. This includes simple risk measures (standard deviation, variance, skewness, kurtosis, variability, volatility, test statistics, ...), measures from regression analysis (alphas, betas, correlations, Treynor ratio, selectivity, ...), relative risk measures (tracking error, information ratio, ...), drawdown risk measures (average and maximum drawdown, drawdown at risk, recovery times, Ulcer and Pain indices, Calman, Sterling, Burke, Martin ratios, ...), downside risk measures (Omega, d, Sortino ratios, kappa, ...), and value at risk and related measures (VaR, CVaR, Cornish-Fisher, ...) amongst others. We can also create risk surfaces from stability analysis and stress testing.

Any Questions? Do not hesitate to contact.

(c) Rmetrics association, 2010

KurtosisSurface.jpeg116.01 KB
PortfolioFrontier.jpeg101.9 KB
RasteredSet.jpeg139.82 KB
RiskBudgetsSurface.jpeg170.5 KB
ShortfallSurface.jpeg112.18 KB
ValueAtRiskSurface.jpeg133.55 KB
WeightsSurface.jpeg152.92 KB