Alternative Investments and Risk Measurement Paul de Beus AFIR2003 colloquium, Sep. 18th. 2003 20 november 2018

Contents introduction the model application conclusions 20 november 2018

Alternative Investments The benefits: lower risk higher return The disadvantages: risks that are not captured by standard deviation (outliers, event risk etc) 20 november 2018

Non-normality skewness kurtosis Jarque-Bera statistic   skewness kurtosis Jarque-Bera statistic reject normality* equity -0.62 0.67 8.19 yes bonds 0.41 4.61 no hedge funds -0.55 2.81 37.54 commodities 0.38 0.44 3.15 high yield -0.76 3.35 55.88 convertibles 0.05 real estate -0.50 0.70 6.11 em. markets -2.04 9.27 422.85 Monthly data, period: January 1994 - March 2002 * 95% confidence 20 november 2018

Implications of non-normality portfolio optimization tools based on normally distributed asset returns (Markowitz) no longer give valid outcomes risk measurement tools may underestimate the true risk-characteristics of a portfolio 20 november 2018

The model Two portfolios: traditional portfolio, consisting of equity and bonds alternative portfolio, consisting of alternative investments Given the proportions of the traditional and alternative portfolios in the resulting ‘master portfolio’, our model must be able to compute the financial risks of this master portfolio. 20 november 2018

Assumptions for our model the returns on the traditional portfolio are normally distributed the distribution of the returns on the alternative portfolio are skewed and fat tailed The returns on the two portfolios are dependent 20 november 2018

Modeling the alternative returns We model the distribution of the returns on the alternative portfolio with a Normal Inverse Gaussian (NIG) distribution Benefits: adjustable mean, standard deviation, skewness and kurtosis Random numbers can easily be generated 20 november 2018

The NIG distribution skewness: -1.6 kurtosis: 6.9 Example of a Normal Inverse Gaussian distribution and a Normal distribution with equal mean and standard deviation 20 november 2018

Modeling the dependence structure We model the dependence structure between the two portfolios using a Student copulas, which has been derived form the multivariate Student distribution Benefits of the Student copula: the dependence structure can be modeled independent from the modeling of the asset returns many different dependence structures are possible (from normal to extreme dependence by adjusting the degrees of freedom) well suited for simulation 20 november 2018

Risk measures To measure the risks associated with including alternatives in portfolio, our model will compute: Value at Risk(x%): with x% confidence, the return on the portfolio will fall above the Value at Risk Expected Shortfall(x%): the average of the returns below the Value at Risk (x%) Together they give insight into the risk of large negative returns 20 november 2018

Monte Carlo Simulation generate an alternative portfolio return from the NIG distribution using the bivariate Student distribution and a correlation estimate, generate a traditional portfolio return repeat the steps 10.000 times and compute the Value at Risk and Expected Shortfall 20 november 2018

Period: January 1990 - March 2002 Application traditional portfolio: 50% equity, 50% bonds alternative portfolio: 100% hedge funds portfolio mean volatility skewnes kurtosis traditional 0.51% 2.52% -0.10 -0.11 alternative 0.57% 2.10% -0.71 2.90 correlation 0.54 Period: January 1990 - March 2002 20 november 2018

Computation Computation of Value at Risk and Expected Shortfall: Method 1, our model Method 2, bivariate normal distribution Objective: minimize the risks 20 november 2018

Optimal variance 20 november 2018

Optimal Value at Risk 20 november 2018

Optimal Expected Shortfall 20 november 2018

Conclusions returns on many alternative investments are skewed and have fat tails using traditional risk measuring tools based on the normal distribution, risk will be underestimated based on mean-variance optimization, an extremely large allocation to alternatives such as hedge funds is optimal using Value at Risk or Expected Shortfall, taking skewness and kurtosis into account, the optimal allocation to hedge funds is much lower but still substantial 20 november 2018

Contacts Paul de Beus Marc Bressers Tony de Graaf Paul.de.Beus@nl.ey.com Marc Bressers Marc.Bressers@nl.ey.com Tony de Graaf Tony.de.Graaf@nl.ey.com Ernst & Young Actuaries Asset Risk Management Utrecht The Netherlands Actuarissen@nl.ey.com 20 november 2018

Questions? 20 november 2018