Using @RISK to Develop Financial
Products
Christian R. Gärtner
Union Asset Management Holding AG
London
24 April 2007
1 24 April 2007
C.R. Gärtner
Historical Simulation vs. Monte Carlo Simulation
„Equities are better than bonds“
Comparison of a 100$ investment into equities or government bonds* (13 years)
350,00
Equity
investment is
worth 324.49$
300,00
250,00
Bond
investment is
worth 216.11$
Value
200,00
150,00
100,00
50,00
Time
Equity Index
Bond Index
*Equities represented by MSCI World index and bonds by the ML Global Government Bond Index II
2 24 April 2007
C.R. Gärtner
Apr 07
Okt 06
Apr 06
Okt 05
Apr 05
Okt 04
Apr 04
Okt 03
Apr 03
Okt 02
Apr 02
Okt 01
Apr 01
Okt 00
Apr 00
Okt 99
Apr 99
Okt 98
Apr 98
Okt 97
Apr 97
Okt 96
Apr 96
Okt 95
Apr 95
Okt 94
Apr 94
0,00
Historical Simulation vs. Monte Carlo Simulation
„Nonsense, bonds are better than equities“
Comparison of a 100$ investment into equities or government bonds* (7 years)
180,00
Bond
investment is
worth 154.84$
160,00
140,00
Equity
investment is
worth 121.79$
Value
120,00
100,00
80,00
60,00
40,00
20,00
Ap
r0
Au 0
g
0
De 0
z
00
Ap
r0
Au 1
g
0
De 1
z
01
Ap
r0
Au 2
g
0
De 2
z
02
Ap
r0
Au 3
g
0
De 3
z
03
Ap
r0
Au 4
g
0
De 4
z
04
Ap
r0
Au 5
g
0
De 5
z
05
Ap
r0
Au 6
g
0
De 6
z
06
Ap
r0
7
0,00
Time
Equity Index
Bond Index
*Equities represented by MSCI World index and bonds by the ML Global Government Bond Index II
3 24 April 2007
C.R. Gärtner
Historical Simualtion vs. Monte Carlo Simulation
Advantages and Disadvantages of both Methods
Historical Simulation
Monte Carlo Simulation
&Based on “hard facts“
&Distribution of results gives
much more information
&Easy to explain
&Easy to perform
&Less dependent on historical
data (but still: garbage in –
garbage out)
'“Tell me which result you want to 'More difficult to explain
see and I‘ll find an appropriate
'More time and effort
period“
'Result is only one figure
'Assumption: history will repeat
itself
4 24 April 2007
C.R. Gärtner
Product Requirements and Assumptions
Product Requirements
„ Investment for 10 years
„ Invested capital guaranteed at maturity
„ Own capital needed not more than 1% on a 99.9% confidence level
„ Yield at least 6%
Assumptions
„ Equities earn 9% p.a. with a volatility (stddev) of 17%
„ Money Market earns 3% p.a. with a volatility (stddev) of 0,5%
„ Both yields follow a normal distribution
5 24 April 2007
C.R. Gärtner
Product Development
1st Approach with different static Asset Allocations
Description
„ A certain and static percentage of the money will be invested into
equities
„ The remainder will be invested into a “safe” asset class, e.g. into
money market papers
„ In order to find the optimal mix between risky assets (equities) and
“safe“ assets several combinations will be evaluated using Monte
Carlo Simulation:
„ 100% equities, 0% money market
„ 75% equities, 25% money market
„ 50% equities, 50% money market
„ 25% equities, 75% money market
„ 0% equities, 100% money market
6 24 April 2007
C.R. Gärtner
Product Development
Evaluation of different static Asset Allocations
Simulation model
fundt+1=fundt*(1+ep*eyt+1+mmp*mmyt+1)
equityt+1=equityt*(1+equity_yieldt+1)
equity_yield=μE+Z1*σE
Z1, Z2 ∼Ν(0,1)
bond_yield=μB+Z1*σB*ρ+Z2*σB* √(1-ρ2)
7 24 April 2007
C.R. Gärtner
Product Development
Evaluation of different static Asset Allocations
Using a VBA macro different combinations of input parameters can be run in
batch
8 24 April 2007
C.R. Gärtner
Product Development
Static Asset Allocations don‘t help us
Own capital for guarantee to high
(VaR 99% >1%=1€)
Yield to low (< 6%)
9 24 April 2007
C.R. Gärtner
Product Development
Properties of different static Asset Allocations
Final value and yield are quite symmetric when using a static asset allocation
Verteilung für final value:/I4
9
Werte in 10^-3
8
95
Mittelwert=178,4579
7
6
5
4
3
Verteilung für yield:/I5
2
16
1
0
50
200
1%
90,8197
350
94%
5%
268,562
Mittelwert=5,618007E-02
14
500
12
10
8
6
4
2
0
-0,1
-0,025
0,05
5%
90%
,0103
10 24 April 2007
0,125
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0,2
5%
,1038
CPPI – Definition and Example
What is Constant Proportion Portfolio Insurance (CPPI)?
Definition
Constant proportion portfolio insurance
From Wikipedia, the free encyclopaedia
(Redirected from CPPI)
Constant proportion portfolio insurance (CPPI) is a capital guarantee derivative
security that embeds a dynamic trading strategy in order to provide
participation to the performance of a certain underlying. See also dynamic
asset allocation. Note that the intuition behind CPPI was adopted from the
interest rate universe.
11 24 April 2007
C.R. Gärtner
CPPI – Definition and Example
How does CPPI work?
Explanation
„ Investment strategy based on two assets (asset classes), one risky, one “safe”
„ Calculation of a risk budget based on the difference between the current
portfolio value and the discounted value of the guarantee (using the yield of a
“safe” asset). This risk budget is multiplied with a factor reflecting the risk of
the “risky” asset (the riskier the asset the lower the factor).
„ The result is invested into the risky asset, the rest into the safe asset
„ Changes of the portfolio value and the discounted value of the guarantee will
change the exposure of the risky asset
„ Formula:
exposureRISK
⎛
guarantee
= ⎜⎜ value portfolio −
(1 + yield SAFE )maturity
⎝
12 24 April 2007
⎞
⎟ × factorRISK
⎟
⎠
C.R. Gärtner
CPPI – Definition and Example
How does CPPI work?
in-/decreases
value
risk budget increases
withwith
fundfund
value
Example
120,00 €
100,00 €
value (€)
80,00 €
60,00 €
„lock-in“
40,00 €
20,00 €
-
€
1
2
3
4
5
6
7
8
9
time(years)
fund
disc. guar.
risk budget
risk budget decreases with time
13 24 April 2007
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10
Product Development
Simulation of a CPPI model
Simulation model
risk budget according to formula
DF: discounted guarantee value
CPPI-fundt+1=fundt*(1+ept*eyt+1+mmpt*mmyt+1)
14 24 April 2007
C.R. Gärtner
Product Development
Our CPPI Product fulfils the Requirements
Own capital for guarantee ok
(VaR 99% <1%=1€)
Yield above 6%
(even median is ok)
15 24 April 2007
C.R. Gärtner
Product Development
A CPPI produces right skewed Results for the Final Value
For the final value the skewness is 1,96, and there is only a approx. 38% chance
to reach the mean value
16 24 April 2007
C.R. Gärtner
Product Development
The yield of a CPPI Product is rather asymmetric
The chance to earn the mean yield is only 46%
17 24 April 2007
C.R. Gärtner
Summary
What did we learn?
„ Historical simulation is not as objective as it seems
„ It is easy to apply “Trial-and-Error” development methodes using
Excel and @Risk, esp. with VBA batches
„ Static Asset Allocations produce usually symmetric results (when
assets are distributed symmetrically)
„ Constant proportion portfolio insurance (CPPI) is a mechanism to
reach a given value with a high confidence
„ CPPI produces rather asymmetric results for final value and yield
with the mean higher than the median
18 24 April 2007
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