1、23 oktober 2018,1,Alternative Investments and Risk Measurement,Paul de BeusAFIR2003 colloquium, Sep. 18th. 2003,23 oktober 2018,2,Contents,introduction the model application conclusions,23 oktober 2018,3,Alternative Investments,The benefits: lower risk higher returnThe disadvantages: risks that are
2、not captured by standard deviation (outliers, event risk etc),23 oktober 2018,4,Non-normality,Monthly data, period: January 1994 - March 2002* 95% confidence,23 oktober 2018,5,Implications of non-normality,portfolio optimization tools based on normally distributed asset returns (Markowitz) no longer
3、 give valid outcomes risk measurement tools may underestimate the true risk-characteristics of a portfolio,23 oktober 2018,6,The model,Two portfolios:traditional portfolio, consisting of equity and bondsalternative portfolio, consisting of alternative investmentsGiven the proportions of the traditio
4、nal and alternative portfolios in the resulting master portfolio, our model must be able to compute the financial risks of this master portfolio.,23 oktober 2018,7,Assumptions for our model,the returns on the traditional portfolio are normally distributed the distribution of the returns on the alter
5、native portfolio are skewed and fat tailed The returns on the two portfolios are dependent,23 oktober 2018,8,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 dev
6、iation, skewness and kurtosisRandom numbers can easily be generated,23 oktober 2018,9,The NIG distribution,Example of a Normal Inverse Gaussian distribution and a Normal distribution with equal mean and standard deviation,skewness: -1.6 kurtosis: 6.9,23 oktober 2018,10,Modeling the dependence struct
7、ure,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 depend
8、ence structures are possible (from normal to extreme dependence by adjusting the degrees of freedom) well suited for simulation,23 oktober 2018,11,Risk measures,To measure the risks associated with including alternatives in portfolio, our model will compute:Value at Risk(x%): with x% confidence, the
9、 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,23 oktober 2018,12,Monte Carlo Simulation,generate an alternative portfolio return from the NIG
10、 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,23 oktober 2018,13,Application,traditional portfolio: 50% equity, 50% bonds alternative portfo
11、lio: 100% hedge funds,Period: January 1990 - March 2002,23 oktober 2018,14,Computation,Computation of Value at Risk and Expected Shortfall:Method 1, our modelMethod 2, bivariate normal distributionObjective: minimize the risks,23 oktober 2018,15,Optimal variance,23 oktober 2018,16,Optimal Value at R
12、isk,23 oktober 2018,17,Optimal Expected Shortfall,23 oktober 2018,18,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 extremel
13、y 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,23 oktober 2018,19,Contacts,Paul de Beus Paul.de.BMarc Bressers Marc.BTony de Graaf Tony.de.GErnst & Young Actuaries Asset Risk Management Utrecht The Netherlands A,23 oktober 2018,20,Questions?,
