Alternative Investments and
Risk Measurement
Alternative Investments and
Risk Measurement
Paul de Beus
26 juli 2016
AFIR2003
colloquium, Sep. 18th. 2003
1
Contents




introduction
the model
application
conclusions
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Alternative Investments
The benefits:

lower risk

higher return
The disadvantages:

risks that are not captured by standard deviation
(outliers, event risk etc)
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Non-normality
skewness
kurtosis
0.67
Jarque-Bera
statistic
8.19
reject
normality*
yes
equity
-0.62
bonds
0.41
0.67
4.61
no
hedge funds
-0.55
2.81
37.54
yes
commodities
0.38
0.44
3.15
no
high yield
-0.76
3.35
55.88
yes
convertibles
0.05
0.05
0.05
no
real estate
-0.50
0.70
6.11
yes
em. markets
-2.04
9.27
422.85
yes
Monthly data, period: January 1994 - March 2002
* 95% confidence
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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
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The model
Two portfolios:
1.
traditional portfolio, consisting of equity and
bonds
2.
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.
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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
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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
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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
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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
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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
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Monte Carlo Simulation
1.
2.
3.
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
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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
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Computation
Computation of Value at Risk and Expected Shortfall:

Method 1, our model

Method 2, bivariate normal distribution
Objective: minimize the risks
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Optimal variance
Expected return and volatility
3,0%
2,5%
2,0%
expected
return
1,5%
volatility
1,0%
0,5%
10
0%
90
%
80
%
70
%
60
%
50
%
40
%
30
%
20
%
10
%
0%
0,0%
percentage alternatives
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Optimal Value at Risk
Value at Risk
0,0%
VaR 5%
model 1
-1,0%
-2,0%
VaR 5%
model 2
-3,0%
-4,0%
VaR 0.5%
model 1
-5,0%
-6,0%
VaR 0.5%
model 2
-7,0%
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90
%
10
0%
percentage alternatives
80
%
70
%
60
%
50
%
40
%
30
%
20
%
10
%
0%
-8,0%
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Optimal Expected Shortfall
Expected Shortfall
0,0%
-2,0%
ES 5%
model 1
-4,0%
ES 5%
model 2
-6,0%
ES 0.5%
model 1
-8,0%
ES 0.5%
model 2
10
0%
90
%
80
%
70
%
60
%
50
%
40
%
30
%
20
%
10
%
0%
-10,0%
percentage alternatives
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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
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Contacts
Paul de Beus
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
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Questions?
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