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

2. Contents introduction the model application conclusions
20 november 2018

3. 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

4. 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 March 2002
* 95% confidence
20 november 2018

5. 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

6. 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

7. 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

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 deviation, skewness and kurtosis
Random numbers can easily be generated
20 november 2018

9. 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

10. 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

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 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

12. 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 times and compute the Value at Risk and Expected Shortfall
20 november 2018

13. 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 March 2002
20 november 2018

14. 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

15. Optimal variance
20 november 2018

16. Optimal Value at Risk
20 november 2018

17. Optimal Expected Shortfall
20 november 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 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

19. Contacts Paul de Beus Marc Bressers Tony de Graaf
Marc Bressers
Tony de Graaf
Ernst & Young Actuaries
Asset Risk Management
Utrecht The Netherlands
20 november 2018

20. Questions?
20 november 2018