Transcript Steve Greiner - Quaffers.org

Beta is not Sharpe Enough
….
September 2010
Steven P. Greiner, Ph.D.
[email protected]
0101.312.566.5109
Sharpe-r Risk Measures Agenda
•
•
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•
•
•
•
•
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Tracking Error Measures
FactSet’s Balanced Risk Module in PA
Tracking Error Forecasts
Introducing the “g-Factor”, a robust Volatility
Measure
Value-at-Risk
Stress Testing: Time & Event
Stress Testing: Black Swan Event
VAR Extreme Event Stress Testing
Fat-Tail VAR
Raising the IQ of the Intelligent Investor
Sharpe-r Risk Measures…
Ben Graham said:

In a Barron’s article, he said that what bothered him is that
authorities equate beta with the concept of risk. Price variability
yes, risk no
 Excerpt from Barron’s, Sept 23, 1974, Dow Jones and Company

Real risk he wrote, is measured not by price fluctuations but by a
loss of quality and earnings power through economic or
management changes

As for variance or standard deviation of return being a useful risk
measure, in the same Barron’s article he says that the idea of
measuring investment risks by price fluctuations is repugnant to
him, because it confuses what the stock market says with what
actually happens to the owner’s stake in the business
Tracking Error: What it isn’t!
•
Usually, TE is reported as meaning that the portfolio’s return is
“bounded” by being within +/- TE of the Benchmark 67% of the
time. Is this True?
3.5E-02
3.0E-02
2.5E-02
2.0E-02
1.5E-02
σ = sqrt[Σ{(x-μ)/(n-1)}^2]
1.0E-02
5.0E-03
0.0E+00
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
Avg(x) = μ = 2.0
4.0
5.0
6.0
7.0
Tracking Error: What it isn’t!
•
Using the math from the previous slide, substitute “P-BM” for “x” and re-plot
the graph…
0.04
•
This then implies TE is the stdev about the average value of the XS return,
0.04
not the BM return..
0.03
0.03
0.02
σ’ = sqrt[Σ{((P-BM)-μ’)/(n-1)}^2] = TE
0.02
0.01
0.01
-3.00
-2.00
-1.00
0.00
0.00
1.00
2.00
3.00
4.00
Avg(P-BM) = XS Ret = μ’ = 1.4
5.00
6.00
7.00
Tracking Error… What it is!!
+
Consider the impact this has on interpretation
+
There can be considerable asymmetry around bench returns
using Port = XS + Bench….
Annualized long term numbers..
Port Bench XS
TE
4.0
3.0
1.0
4.0
4.0
5.0
-1.0
4.0
so 68% of time XS is:
XS-TE
XS+TE
-3.0
5.0
-5.0
3.0
Port's Abs Ret Bounds
Lwr Bnd
Upr Bnd
0.0
8.0
0.0
8.0
Portfolio about Bench
Lwr Bnd Upr Bnd
-3.0
5.0
-5.0
3.0
6.0
6.0
5.0
7.0
1.0
-1.0
6.0
6.0
-5.0
-7.0
7.0
5.0
0.0
0.0
12.0
12.0
-5.0
-7.0
7.0
5.0
8.0
8.0
7.0
9.0
1.0
-1.0
9.0
9.0
-8.0
-10.0
10.0
8.0
-1.0
-1.0
17.0
17.0
-8.0
-10.0
10.0
8.0
Empirical Data for:
S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's
•
Weekly returns
downloaded from FactSet
from December 31st, 2006
to August 31st, 2010
Empirical FactSet Data for:
S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan,
Nikkei & 2 Hypothetical's
Data is Weekly Returns From 12/31/2006 to 8/31/2010…
S&P500
TE=>
XS=>
Mean Ret
Stdev Ret
True Defn =>
Usual Defn =>
-0.07
2.85
XLK
XLF
XO M
ISRG
LCV
1.42
0.09
0.04
2.89
3.92
-0.21
-0.34
5.59
2.61
0.02
-0.00
3.15
6.65
0.93
1.11
7.53
1.03
-0.11
-0.19
3.20
Magellan Nikkei
1.29
-0.05
-0.11
3.40
Normal t-Dist-12
2.67
-0.17
-0.24
3.43
5.46
0.06
-0.15
4.44
5.95
0.06
-0.18
4.61
68.8%
81.8%
% of time XS return is found within it's average value and +/- TE
76.0%
82.3%
77.1%
81.8%
87.5%
81.8%
68.8%
% of time Portfolio Return is found between S &P500 Ret and +/-TE
39.1%
64.1%
60.9%
74.5%
29.2%
32.3%
62.0%
78.6%
88.5%
Empirical Data for:
S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's
+
For smaller TE, the effect is more pronounced!
Tracking Error Measures….
+
If the TE is large and the abs(XS) return is small, you can stick to the old
paradigm
+
If in 2008 one lowered TE hoping to lower relative risk while underperforming, one actually increased the likelihood of continued underperformance, hence risk actually increased.
+
This is because as TE goes down for a given XS return, one draws a narrower
range around (P-BM) where the portfolio spends the majority of time in. If
(P-BM) is negative, you lose the opportunity to out-perform as TE decreases.
+
If you have negative XS return, increase your TE to lower risk. E.g.
 XS Ret = -200 bps & TE = 4%; -6% < Port Ret < 2% (67% of the time)
 XS Ret = -200 bps & TE = 6%; -8% < Port Ret < 4% (67% of the time)
+
If you have positive XS return, decrease your TE to lower risk.
 XS Ret = 200 bps & TE = 6%; -4% < Port Ret < 8% (67% of the time)
 XS Ret = 200 bps & TE = 4%; -2% < Port Ret < 6% (67% of the time).
FactSet’s Balanced Risk Module…..
+
Components Uniting Equities, Fixed Income and Currencies..
 Monte Carlo Value-At-Risk
 Stress Testing 1: Time & Event Weighting (Equity Only)
 Stress Testing 2: Extreme Event (Equity Only)
 MC Extreme Event Risk
 Global Equities, Corp, Hi-Yld, Agencies, Tips, U.S.Treas, Sovereign, U.S. MBS, Exc-Trad Options
+
Four Equity Vendor Risk Models, Plus Factset’s Own..
 SUNGUARD – APT
 Axioma
 MSCI-Barra
 Northfield Inf. Services
 MAC-ST
+
(Country, Regional, & Global, MT & ST, Equity only)
(Global, EMG, Euro, U.S., Canada & Japan, Equity only)
(Country, Regional and Global, Equity only)
(Country, Regional, Global, MT and ST, Equity only)
(Included in Balanced Risk Product & Required for FI)
Fast Re-Pricing Algorithm for FI..
 Yield Curve (Int. Rate) Risk Specific to Underlying Currency of Security
 17 KR Dur specified by 4 PCA of 6 Libor & Govt Curves (U.S., Can, Aus, EUR, Jap, UK)
 Each Major Asset Class Has its Own Spread Model
 3 Base Currency (USD, EURO, GBP) Reporting Options w/ Exp. to 13 Currencies Available
+
Fully Integrated with Portfolio Attribution..
Example of Global Equity Portfolio…
+
Construct Global
Portfolio and
Compare VAR and
TE computed
through FactSet
Balanced Risk
Module
Percent of Total Holdings
GLOB_EQUITY vs. MSCI EAFE
MAC Global Multi-Asset Class Model (USD)
U.S. Dollar
12/31/2008
Asset Class
Port.
Weight
Bench.
Weight
Difference
MC %
Value at Risk
22 Day, 95%
Total
100.00
100.00
--
12.26
Equity
96.26
United States
26.14
Japan
15.57
France
11.82
Germany
8.66
Netherlands
6.02
Sw itzerland
4.59
Australia
4.12
Hong Kong
3.95
China Mobile Ltd.
3.73
Hutchison Whampoa Ltd.
0.20
Lenovo Group Ltd.
0.02
United Kingdom
2.86
Canada
2.45
Sw eden
2.07
Spain
1.72
Finland
1.46
Denmark
1.26
Brazil
1.01
Portugal
0.77
Israel
0.59
Peru
0.55
Italy
0.51
Singapore
0.14
Singapore Telecommunications Ltd.0.14
[Cash]
3.74
Euro
1.32
British Pounds
1.17
U.S. Dollar
1.14
Japanese Yen
0.10
100.00
-25.25
10.50
8.74
2.52
8.41
5.94
2.01
-0.14
-19.88
-1.97
4.53
1.39
0.84
-0.33
--3.62
1.06
0.18
------
-3.74
26.14
-9.68
1.33
-0.09
3.50
-3.82
-1.82
1.93
3.73
0.06
0.02
-17.01
2.45
0.10
-2.82
0.07
0.42
1.01
0.44
0.59
0.55
-3.11
-0.92
-0.04
3.74
1.32
1.17
1.14
0.10
12.18
2.85
1.09
1.95
1.06
0.89
0.51
0.61
0.54
0.51
0.02
0.00
0.38
0.67
0.37
0.26
0.23
0.21
0.11
0.10
0.10
0.13
0.10
0.02
0.02
0.10
0.05
0.04
-0.00
-0.00
MC %
Marginal
Value at Risk
22 Day, 95%
0.13
0.11
0.07
0.17
0.12
0.15
0.11
0.15
0.14
0.14
0.10
0.05
0.13
0.27
0.18
0.15
0.15
0.17
0.10
0.14
0.17
0.24
0.19
0.11
0.11
0.03
0.04
0.04
-0.00
-0.02
MC %
MC %
Standalone
Relative
Value at Risk
Tracking Error (StDev)
22 Day, 95%
22 Day
12.26
3.55
12.65
16.71
17.75
18.90
19.84
18.04
15.77
21.84
22.03
22.31
21.55
35.61
18.13
36.72
23.70
19.61
20.66
23.59
40.18
21.61
35.90
46.63
30.37
20.29
20.29
3.77
6.01
6.23
-0.00
5.95
-------------------------------
Tracking Error Forecasts….
+
Computed TE using VAR and Historical (black) for Global Portfolio Measured
with various risk models………Which is right?
Tracking Error Forecasts with CI’s….
+
Which is right? Most are, whence you compute the 95% Confidence Interval
on the Historical….Note Asymmetry…
Tracking Error… Bias
A cross-section of the TE at a point in time has the following form..
bootstrap : test : var
0.2
0.4
0.6
0.8
1.0
Observ ed
Mean
0.0
Density
+
1
2
v ar1.1
3
Using Betas for measures of Volatility…
+
What is the impact of the
correlation on one’s
interpretation of how
volatile a stock or
portfolio is?
+
Beta’s ~
ISRG: 1.2
XLK: 0.9,
XOM: 0.7
Using Betas for measures of Volatility…
+
So a portfolio that has
next to no correlation
with it’s bench then, has
essentially no volatility?
+
Beta’s ~ Norm: 0.08 &
t-Dist-12: 0.01
The Way to a Better Volatility Measure…g-Factor
A question we might ask is, what’s the amount of time the bench & portfolio spend in a
constant vicinity of their mean return?
Stdev of Bench = SD
+
Form the distribution of returns for a time period
+
Measure the area under curve between Mean +/- SD for both Bench and Portfolio…..
Use the Bench’s SD for each…
+
Ratio of Bench area to Portfolio area is g-Factor
The “g-Factor”…
+
The g-Factor is independent of the correlation and just compares the amount
of time the benchmark and portfolio “spend” within an identical distance of
their mean values
g-Factor: (% of time Bench within +/- SD) / (% of time Port within +/-SD)
SP50
XLK
XLF
XOM
ISRG
LCV
11.752
11.752
11.455
10.535
42.698
19.429
12.160
8.515
62.615
14.982
14.132
12.342
16.049
12.999
14.653
9.582
20.003
0.974
24.018
0.164
76.6%
g-Factor 1.000
Beta 1.000
76.0%
1.007
0.896
0.83
58.9%
1.301
1.653
0.76
69.8%
1.097
0.725
0.51
50.0%
1.531
1.275
0.31
74.5%
1.028
1.050
0.93
71.4%
1.073
1.106
0.91
72.4%
1.058
0.815
0.54
56.3%
1.361
0.083
0.00
80.7%
0.948
0.014
0.00
Variance
Covariance
Magellan Nikkei
Normal t-Dist-12
% of Time Ret is Spent
within +/- SD of its Mean
R^2 on Beta
Issues for Value-at-Risk..
+
Trading or portfolio positions change over time, thus the longer horizon VAR calculated,
the less realistic it’s going to be, which is why we use daily VAR
+
VAR techniques are subject to model risk. In particular, the parametric model used for
the drawing in Monte Carlo influences the value of the VAR calculated, hence there’s no
“correct” VAR, it’s just an estimate
+
VAR isn’t effective when macro-risks, extreme events (Black Swans or ELE) are
occurring. The returns distribution obtained from either a covariance based method or a
copula, predicated on modeling the past years dependencies, isn’t representative of how
the returns will behave in extreme events.
 Even in a copula fitting of the factor returns with an attempt to garner non-linear dependencies in the tail, VAR
will not show how the dependency really behaves during a Black Swan event
 Existing VAR models reflect risks that are not useful during transition periods or when “broken” correlation
structures occurs across assets
+
For a given covariance matrix, there are many, many datasets whose variance or
covariance will satisfy it. There is no unique set of factor returns for a given covariance
matrix (or copula)
Value-at-Risk Example_1
Stress Testing One: Time & Event Weighting..
+
Pick a “shock”, any risk model factor or exogenous factor that has a timeseries (obviously, cause & effect economic variables, not weather forecasts)
+
Determine covariance/correlation of this “shock” to all risk model factors
+
Compute “Beta” between shocked factor “K” and all risk model factors from
the covariance measurements
+
New Factor Return = Beta * Shock
Earnings/Price
Book/Price
Trading Activity
Log of Market Cap
Earnings Variability
EPS Growth Rate
Revenue/Price
Debt/Equity
Industry
Current Factor Exposures
Current Factor Returns
Return Forecast
2.62
Factor Contribution to Return Forecast
Oil Shock Magnitude
-30%
Beta between Oil Shock and Factor Return
New Factor Return w/Oil Shock
Shock Return Forecast
-0.08
Factor Contribution to Shock Return Forecast
Beta
Table 1.1 EXAMPLE OF STRESS TEST
0.103
0.802
0.082
3.2%
0.658
0.848
0.558
21.3%
0.085
0.851
0.072
2.8%
0.587
1.153
0.677
25.9%
0.720
0.557
0.401
15.3%
0.711
1.033
0.734
28.1%
0.022
1.066
0.024
0.9%
0.132
0.822
0.108
4.1%
-0.158
0.687
-0.109
-4.2%
0.049
1.390
0.069
2.6%
0.185
-0.056
-0.006
7.5%
0.139
-0.042
-0.027
36.3%
-0.038
0.011
0.001
-1.3%
-0.015
0.005
0.003
-3.5%
0.208
-0.062
-0.045
59.3%
0.032
-0.010
-0.007
8.9%
0.014
-0.004
0.000
0.1%
0.000
0.000
0.000
0.0%
0.106
-0.032
0.005
-6.6%
-0.037
0.011
0.001
-0.7%
Stress Testing One: Time vs. Event Weighting..
Test Name:
Report Date:
Report Currency:
Risk Model:
Time Decay:
Event Decay:
Factor:
S&P 500 30% Decline
8/23/2010
U.S. Dollar
NIS US Fundamental Model
0.98
0.94
Shock %
-30.00%
Date
Factor Chg (%)
Tim e Weight (%)
#
Date
Factor Chg (%)
Event Weight (%)
7/30/2010
6/30/2010
5/28/2010
4/30/2010
3/31/2010
2/26/2010
1/29/2010
12/31/2009
11/30/2009
10/30/2009
""
""
""
""
7/31/2006
6/30/2006
5/31/2006
4/28/2006
3/31/2006
2/28/2006
1/31/2006
12/30/2005
11/30/2005
10/31/2005
9/30/2005
8/31/2005
7.01
-5.24
-7.98
1.58
6.03
3.10
-3.60
1.93
6.00
-1.86
""
""
""
""
0.62
0.14
-2.88
1.34
1.25
0.27
2.65
0.04
3.78
-1.67
0.81
-0.91
2.01
1.97
1.93
1.89
1.85
1.82
1.78
1.75
1.71
1.68
""
""
""
""
0.76
0.75
0.73
0.72
0.70
0.69
0.68
0.66
0.65
0.64
0.62
0.61
1
2
3
4
5
6
7
8
9
10
""
""
""
""
49
50
51
52
53
54
55
56
57
58
59
60
10/31/2008
8/31/1998
9/30/2002
2/27/2009
2/28/2001
8/31/1990
9/30/2008
6/30/2008
1/30/2009
9/28/2001
""
""
""
""
1/31/2005
6/29/2001
4/30/1993
5/28/1999
5/31/2000
8/31/1992
12/31/1996
2/28/2007
3/31/1992
2/28/2002
4/29/2005
2/29/2000
-16.79
-14.46
-10.87
-10.65
-9.12
-9.11
-8.91
-8.43
-8.43
-8.08
""
""
""
""
-2.44
-2.43
-2.42
-2.36
-2.05
-2.05
-1.98
-1.96
-1.95
-1.93
-1.90
-1.89
6.00
5.64
5.30
4.98
4.68
4.40
4.14
3.89
3.66
3.44
""
""
""
""
0.31
0.29
0.27
0.26
0.24
0.23
0.21
0.20
0.19
0.18
0.17
0.16
Stress Testing One: Example
Percent of Total Holdings
50 notsonifty and 50 sp100 eq.wgt vs. Russell 1000
9/07/2010
R-Squared Daily Global Equity Model (USD)
U.S. Dollar
FX Rate - US$ per E uro (!XRE UR)
D aily from 31-Aug-2007 to 23-Aug-2010
U.S. D olla r (Spli t / Spinoff - Adjusted)
USD/EUR FX Rate 30% Decline
High: 1.60
Low: 1. 19
BenchmarkLast: 1.27
Benchmark
Percent
Standalone
Return
(Time Wght)
Percent
Return
(Event Wght)
Percent
Standalone
Return
(Event Wght)
Percent
Return
(Time Wght)
Percent
1.60
Return
(Event Wght)
Economic Sector
Port.
Weight
Bench.
Weight
Difference
Percent
Return
(Time Wght)
Total
100.00
100.00
--
-21.19
-21.19
-18.62
-18.62
-19.17
-16.34
6.19
5.99
13.03
10.27
14.37
4.75
8.93
1.86
19.54
15.07
4.07
10.42
10.96
10.55
18.01
3.93
11.66
3.09
10.95
16.36
2.12
-4.43
2.08
-0.28
-3.64
0.82
-2.74
-1.22
8.59
-1.29
-1.29
-0.61
-2.97
-2.60
-3.22
-0.76
-1.25
-0.03
-4.32
-4.15
-20.80
-10.22
-22.80
-25.33
-22.38
-15.99
-13.96
-1.50
-22.12
-27.53
-1.00
-0.48
-2.64
-2.00
-2.97
-0.61
-0.89
-0.11
-4.00
-3.91
-16.20
-8.06
-20.22
-19.48
-20.69
-12.88
-9.98
-6.14
-20.48
-25.95
-0.85
-1.12
-2.66
-2.40
-3.38
-0.53
-1.68
-0.39
-2.30
-3.85
-0.67
1.45
-1.00
-2.42
1.40
-1.93
-2.84
1.35
-0.46
-1.24
1.30
-0.36
-2.08
1.25
-3.32
Materials
Consumer Staples
Industrials
Energy
Information Technology
Utilities
Health Care
Telecommunication Services
Consumer Discretionary
Financials
1.55
1.50
1.20
Holdings Data As Of
50 notsonifty and 50 sp100 eq.wgt 12/31/2008
Russell 1000 9/07/2010
Risk Model As Of
R-Squared Daily Global Equity Model (USD) 9/06/2010
Market Portfolio: Russell 1000
Volume in Thousands (max/avg)
0
08
Data Source: IDC / Exshare
09
10
Stress Testing One: Example
…same data, but perspective has changed…
Stress Testing Two: Extreme Event Stress..
+
Extreme Event Stress let’s us go back in time and measure the current
portfolio’s response to factor returns garnered from the past
+
It’s like using the cross-security relationships, the dependence structure from
the past, because the factor returns used from a chosen historical stressed
market environment, were those used to construct the covariance matrix at
that time
+
In this module, we use past factor returns, multiplied by current exposures to
allow us to examine how a portfolio today might behave should history
“almost” repeat itself
Stress Testing Two: Example
Percent of Total Holdings
+
+
GLOB_EQUITY vs. MSCI EAFE
9/23/2010
NIS Global Model
U.S. Dollar
What’s the Internet
Bubble’s impact on
Global Equity
Portfolio, “Today”?
Borrow factor returns
from April 2000
Ru ssell 1000 (R.1000)
D a il y fro m 3 1 -D e c- 1 9 96 to 3 1 -D e c- 2 0 09
To ta l R e tu rn
Internet Bubble (4/2000)
Bench.
Weight
Difference
Total
100.00
100.00
--
-6.71
-6.71
-7.03
0.32
Equity
United States
Japan
France
Netherlands
Germany
Switzerland
Australia
United Kingdom
Sweden
Canada
Hong Kong
Denmark
Spain
Finland
Israel
Italy
Portugal
Peru
Brazil
Singapore
[Cash]
97.06
25.36
12.51
11.80
6.29
6.25
5.40
4.54
4.51
3.59
3.46
3.24
1.84
1.80
1.78
0.94
0.91
0.91
0.89
0.89
0.14
2.94
40.99
000
100.00
-21.62
9.52
2.75
7.75
7.85
8.59
21.72
3.02
-2.66
1.00
3.72
1.08
0.84
2.70
0.27
--1.64
--
-2.94
25.36
-9.11
2.28
3.54
-1.50
-2.45
-4.05
-17.22
0.57
3.46
0.58
0.84
-1.91
0.70
0.10
-1.79
0.63
0.89
0.89
-1.49
2.94
-6.64
-1.38
-1.23
-0.74
-0.42
-0.35
-0.32
-0.11
-0.24
-0.31
-0.21
-0.36
-0.27
-0.19
-0.14
-0.07
-0.08
-0.05
-0.11
-0.05
-0.01
-0.07
-6.84
-5.42
-9.87
-6.31
-6.60
-5.64
-5.86
-2.44
-5.42
-8.62
-5.97
-11.11
-14.70
-10.38
-7.95
-7.73
-8.45
-5.78
-12.55
-5.26
-5.81
-2.37
0.39
-1.38
0.81
-0.09
-0.21
0.29
0.03
0.27
0.64
-0.08
-0.21
-0.09
-0.19
0.21
-0.04
-0.03
0.15
-0.03
-0.11
-0.05
0.14
-0.07
-----
0.99
0.98
0.88
0.08
-0.02
-0.05
0.00
-0.00
-1.91
-4.74
0.01
-5.09
-7.03
--2.04
-0.66
-0.21
-0.65
-0.35
-0.39
-0.89
-0.23
--0.27
-0.08
-0.39
-0.10
-0.04
-0.22
-0.02
---0.15
------
H ig h : 3 8 5 0 .8 6
L o w : 1 4 8 7.2 9
L a st: 2 9 0 9 .1 8
0.98
0.88
3500
0.08
2500
2000
1500
99
00
01
02
03
Port vs Bench
Percent
Difference
(Event)
Port.
Weight
3000
98
Benchmark
Percent
Return
(Event)
Asset Class
British Pounds
Euro
U.S. Dollar
Japanese Yen
97
Data Source: Russell
Percent
Standalone
Return
(Event)
Percent
Return
(Event)
04
05
06
07
08
09
-0.02
-0.05
0.00
-0.00
Stress Testing Two: Example
+
Internet Bubble’s impact on Global Equity Portfolio is…
+
Wouldn’t be the worst since 1997!!
EAFE
-18.224
-14.397
-13.050
-11.580
-11.116
-9.936
-9.670
-9.208
-9.182
-8.498
-8.424
-8.381
-7.570
-7.340
-7.329
-55.591
-50.777
-38.937
-32.961
-31.239
-27.722
-27.132
-26.812
-24.273
-22.718
-20.163
-17.746
-16.541
-14.758
-14.715
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
-6.708
-14.467
-13.900
-13.750
-13.077
-11.255
-11.179
-10.883
-10.370
-10.235
-9.749
-9.663
-9.494
-9.382
-9.199
-8.093
-7.492
32
33
34
35
-2.957
-2.909
-2.636
-2.602
-6.470
-6.364
-5.572
-4.903
-4.153
-4.128
-3.902
-3.798
-3.630
-3.497
-3.207
-3.189
-3.162
-3.150
-3.107
-7.030
-5.315
-5.281
-4.397
45.0
40.0
Monthly Returns: 3/1997 to 8/2010
35.0
30.0
25.0
20.0
15.0
10.0
5.0
0.0
-5.0
-10.0
-15.0
-20.0
-25.0
-30.0
-35.0
-40.0
-45.0
-50.0
-55.0
-60.0
1
6
11
16
21
26
31
36
41
46
51
56
61
66
71
76
81
86
91
96
101
106
111
116
121
126
131
136
141
146
151
156
161
Global Equity
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Global Equity
EAFE
Monte-Carlo Extreme Event Risk..
+
Monte-Carlo Extreme Event Risk is enabling and is a unique combination of
FactSet’s stress testing platform combined with Value-at-Risk methodologies
+
Go back in time and literally take the covariance matrix from the past,
decompose it via “Cholesky”, while separately and simultaneously, Monte
Carlo-generated scenarios are made, and multiplied by this historically
fashioned Cholesky matrix to compute “factor returns”
+
The Monte Carlo VaR is computed by multiplying each set of Monte-Carlo
generated factor returns by the current exposure matrix
In this way, we use the dependence structure from a “Black Swan” event and
past co-variances to see what a current portfolio’s VaR would look like under
that past stressed situation
Monte-Carlo Extreme Event Risk Example..
+
LTCM occurred August of 1998
+
Retns ~ -10% to -20%
Monte-Carlo Extreme Event Example..
Percent of Total Holdings
50 notsonifty and 50 sp100 eq.w gt vs. Russell 1000
9/07/2010
NIS US Fundam ental Model
U.S. Dollar
Current Sim
Economic Sector
Port.
Weight
Bench.
Weight
Difference
MC %
Value at Risk
1 Day, 95%
Total
Consum er Discretionary
Consum er Staples
Energy
Financials
Health Care
Industrials
Inform ation Technology
Materials
Telecom m unication Services
Utilities
100.00
19.51
5.99
10.26
15.02
8.94
13.05
14.40
6.19
1.88
4.76
100.00
10.94
10.43
10.53
16.32
11.69
10.97
18.03
4.07
3.09
3.93
-8.57
-4.43
-0.27
-1.31
-2.75
2.08
-3.63
2.12
-1.21
0.83
2.65
0.58
0.08
0.25
0.51
0.11
0.29
0.49
0.18
0.07
0.09
Holdings Data As Of
50 notsonifty and 50 sp100 eq.w gt 12/31/2008
Russell 1000 9/07/2010
Risk Model As Of
NIS US Fundamental Model 8/31/2010
Market Portfolio: Russell 1000
+
When LTCM happened,
the covariance matrix
defined more lepokurtic
return distributions
+
Whereas now, it shows a
much broader
distribution of returns
+
So today’s VAR is
greater than that of this
past extreme event
LTCM (8/1998) - Sim
MC %
Expected
Tail Loss
1 Day, 95%
MC %
Standalone
Value at Risk
1 Day, 95%
ST %
Value at Risk
1 Day, 95%
ST %
Expected
Tail Loss
1 Day, 95%
ST %
Standalone
Value at Risk
1 Day, 95%
3.27
-----------
2.65
3.08
1.59
2.57
3.47
1.62
2.31
3.81
3.27
4.95
2.30
1.95
0.44
0.06
0.16
0.36
0.08
0.22
0.39
0.13
0.04
0.07
2.45
-----------
1.95
2.34
1.41
2.21
2.58
1.42
1.80
3.14
2.52
4.30
1.81
Monte-Carlo Extreme Event Risk Example Two
+ Credit
Crisis of November 2008
Monte-Carlo Extreme
Event Risk Example Two..
+
Using Global Portfolio of
Equities, FI, Options and
Currencies (Balanced..)
+
Examine impact of Credit
Crisis (11/30/2008) on VaR
Percent of Total Holdings
GLOB_BAL_MAND vs. MSCI EAFE
9/23/2010
U.S. Dollar Report
Asset Class
Port.
Weight
Bench.
Weight
Difference
Total
Equity
United States
Japan
France
100.00
73.60
25.15
13.10
9.34
100.00
100.00
-21.62
9.52
--26.40
25.15
-8.52
-0.18
Germany
Australia
Canada
United Kingdom
Sweden
Hong Kong
Hutchison Whampoa Ltd.
Sun Hung Kai Properties Ltd.
Hang Seng Bank Ltd.
Swire Pacific Ltd.
China Mobile Ltd.
Lenovo Group Ltd.
Netherlands
Finland
Switzerland
Italy
Singapore
United Overseas Bank Ltd.
Singapore Telecommunications Ltd.
Ireland
Israel
Fixed Income
Corporate
Canada
South Korea
Australia
France
United States
United Kingdom
Italy
Spain
Hungary
Japan
Honda Bank Gmbh 0.0% 12-oct-2010
Toyota Motor Credit Corp. 0.0% 04-jan-2011
Toyota Finance Australia Ltd. 4.12% 31-jul-2017
Toyota Capital Malaysia Sdn. Bhd. 4.2% 02-jul-2014
Government Related
United States
Sovereign
United States
Derivatives
Metlife Inc Call DEC10 36
Factset Research S Call DEC10 80
State Street Corp Put JAN11 32
Bank Of Ny Mellon Put DEC10 22.5
Costco Whsl Corp N Put JAN11 65
Kraft Foods Inc Put DEC10 28
Bristol-Myers Squi Put DEC10 23
Astrazeneca Plc Put OCT10 28
Standard Chartered Plc Put OCT10 14
[Cash]
U.S. Dollar
British Pounds
Euro
Japanese Yen
7.34
4.38
3.48
2.81
1.60
1.59
0.48
0.31
0.28
0.26
0.20
0.06
1.32
0.95
0.84
0.73
0.38
0.26
0.11
0.32
0.28
20.69
14.05
4.60
2.18
2.12
2.01
1.95
1.04
0.12
0.02
0.02
0.02
0.01
0.01
0.01
0.01
5.08
1.07
0.48
0.48
5.39
1.71
1.57
1.02
0.40
0.25
0.25
0.15
0.02
0.01
0.32
0.10
0.09
0.08
0.06
7.75
8.59
-21.72
3.02
2.66
0.18
0.22
0.11
0.10
--2.75
1.08
7.85
2.70
1.64
0.16
0.18
0.23
0.84
------------------------------------
-0.41
-4.21
3.48
-18.91
-1.42
-1.07
0.31
0.09
0.17
0.16
0.20
0.06
-1.43
-0.14
-7.01
-1.97
-1.26
0.10
-0.07
0.09
-0.56
20.69
14.05
4.60
2.18
2.12
2.01
1.95
1.04
0.12
0.02
0.02
0.02
0.01
0.01
0.01
0.01
5.08
1.07
0.48
0.48
5.39
1.71
1.57
1.02
0.40
0.25
0.25
0.15
0.02
0.01
0.32
0.10
0.09
0.08
0.06
Holdings Data As Of
GLOB_BAL_MAND 12/31/2009
MSCI EAFE 9/23/2010
Hidden: Benchm ark Only Securities and Groups
Monte-Carlo Extreme Event Risk Example Two..
+
It’s clear that if the crisis of 2008 were to occur again, the addition of
derivatives in the portfolio would offer a strong hedge against losses
Percent of Total Holdings
GLOB_BAL_MAND vs. MSCI EAFE
9/23/2010
Factset/R-Squared Daily Global Multi-Asset Class Model (USD)
U.S. Dollar
Credit Crisis
ST %
Value at Risk
Difference 22 Day, 95%
ST %
Standalone
Value at Risk
22 Day, 95%
MC %
Value at Risk
22 Day, 95%
MC %
Marginal
Value at Risk
22 Day, 95%
MC %
Standalone
Value at Risk
22 Day, 95%
Asset Class
Port.
Weight
Bench.
Weight
Total
100.00
100.00
--
8.78
8.78
6.88
Equity
Fixed Income
73.60
20.69
100.00
--
-26.40
20.69
8.78
0.63
14.05
7.29
5.89
0.23
0.07
0.02
8.76
3.35
Derivatives
[Cash]
5.39
0.32
0.10
0.09
0.08
0.06
-------
5.39
0.32
0.10
0.09
0.08
0.06
-0.62
42.31
2.59
-0.01
6.04
5.38
5.91
0.73
0.00
-0.00
0.00
0.00
-0.00
0.12
0.01
-0.00
0.02
0.03
-0.00
48.48
2.11
-0.01
3.94
4.25
4.32
U.S. Dollar
British Pounds
Euro
Japanese Yen
0.01
-0.00
0.00
0.00
-0.00
6.88
Exchange Traded Options
+
Barone-Adesi & Whaley (JOF Vol42, No.2, June 1987)
1.
2.
3.
Analytical approximation of American option pricing starting with European formula
Many times faster than most other methods
Loses accuracy for long dated options unfortunately (e.g. LEAPS) but acceptable accuracy for
short to mid-maturity options
 “They” used a normal approximation for the implied volatility, but that was written in 1987 before
the 19 Oct 1987 “Black Monday” event inaugurated the volatility “smile”
 Therefore FactSet uses an implied vol that’s fit to “f(strike/price, time to maturity)” from stock’s
option chain, incorporating the observation that implied vols vary as the stock’s price varies from
the option strike (volatility smile effects). This is a very smart methodology
1.
2.
3.
The option pricing first involves solving iteratively for a critical stock price (Eq. 19 in their
paper), below which the option’s call value is given by the Black-Scholes equation and above
which the option’s call value is given by its exercisable proceeds (Price-Strike)
The critical price solution is placed into an analytical expression involving the addition of a early
exercise premium to the Black-Scholes equation (Eq. 20 of their paper)
The next step, given option strike, vols, risk-free rate, time to maturity and stock price from the
MC generating process, is simply to “plug-and-chug” to compute the option’s price
Ramifications for Fixed Income..
+
Due to liquidity issues, seldom have real FI security returns to regress against
factor exposures to compute Betas
+
Hence we used previously calculated “sensitivities” (dur, convex..)
+
Monte-Carlo generated Interest Rate (yield curve) moves, spread and
currency changes
+
Fast Re-Pricing (Taylor Series expansion) schema utilizes these changes to
price “FI” instruments along with time decay
1.
All securities of same currency have same yield curve exposure to the
same set of 17 key rate risk factors (6 Libor & Govt Curves: U.S., Can,
Aus, EUR, Japan, UK)
2.
Different types of instruments have differing spread models, currently
configured for:
 Corporates
 High Yield
 Agency
 U.S. Treasuries
Sovereigns (that we have yield curves for)
U.S. MBS
Treasury Inflation-Protected Securities
Exchange Traded Derivatives
Rotund Posteriors, Hefty Backsides & Pudgy Extremities..
+
Fat-Tails should be considered when skewness &/or kurtosis are prevalent
Rotund Posteriors, Hefty Backsides & Pudgy Extremities..
S FY
UB S I
IN D B
-1
-1
0
1
2
-2
Quant iles of St andard Normal
1
0. 2
-1
1
2
-2
1
2
1
2
-2
-1
0
1
2
Quant iles of St andard Normal
GA M
Ordered R et urns
0. 0
-0. 4
-0. 10
Ordered R et urns
0. 2
0. 4
0. 3
0. 1
0. 0
Ordered R et urns
0
0
P E TM
-0. 2
-1
-1
Quant iles of St andard Normal
0. 2
0. 8
0. 6
0. 4
0. 2
Ordered R et urns
0
Quant iles of St andard Normal
H MN
Quant iles of St andard Normal
2
-0. 2
-2
D Y II
-2
1
0. 1
Ordered R et urns
0. 1
0. 0
Ordered R et urns
-0. 1
0. 1
2
0
LD G
-0. 2
0
-1
Quant iles of St andard Normal
HR
0. 0
Ordered R et urns
-1
Quant iles of St andard Normal
0. 1
0. 2
-2
-0. 2
-2
0. 0
Ordered R et urns
0. 2
2
0. 2
1. 0
0. 5
0. 0
Ordered R et urns
1
R OL
-0. 2
Most stocks are
non-normal, the
evidence is
overwhelming..
0
Quant iles of St andard Normal
RS A S
+
0. 1
-0. 2
-2
0. 0
2
-0. 1
1
-2
-1
0
1
Quant iles of St andard Normal
2
0. 05
0
Quant iles of St andard Normal
0. 0
-1
-0. 2
-0. 4
-2
0. 0
Ordered R et urns
0. 2
0. 0
Ordered R et urns
-0. 2
0. 1
0. 0
Q-Q Plots of 12
randomly selected
small cap stocks
-0. 1
+
Ordered R et urns
0. 4
0. 3
0. 2
0. 3
GB C I
-2
-1
0
1
Quant iles of St andard Normal
2
-2
-1
0
1
Quant iles of St andard Normal
2
VAR techniques are subject to model risk so the parametric
model used for drawing in Monte Carlo influences the value of the VAR calculated..
+
+
Fat-Tails underestimate
95% VAR, but are closer
to it than normal method
+
Normal approximation
leads to overly optimistic
forecasts at 99% VAR
+
95% VAR - 95% VAR Empirical
Normal is acceptable at
95% VAR
Fat-Tails generally result
in conservative and
accurate 99% VAR
YEN/GBP
GBP/USD
S&P 500
DAX 30
CAC 40
NIKKEI 225
DJI
..mean..
Fat-Tails->
Normal
1
-0.017
-0.070
0.039
-0.057
0.113
-0.075
0.115
-0.059
0.124
-0.063
0.073
-0.125
0.208
-0.035
0.094
-0.069
2
-0.135
-0.094
-0.076
-0.057
-0.085
-0.190
-0.072
-0.101
3
-0.108
-0.052
-0.065
-0.056
-0.085
-0.016
-0.055
-0.062
99% VAR - 99% VAR Empirical
YEN/GBP
GBP/USD
S&P 500
DAX 30
CAC 40
NIKKEI 225
DJI
..mean..
Fat-Tails->
Normal
1
-0.451
0.268
-0.248
0.447
-0.162
0.266
-0.258
-0.100
-0.308
0.127
-0.691
1.408
-0.249
0.393
-0.338
0.401
2
0.133
0.426
-0.093
-0.189
-0.049
0.414
0.232
0.125
3
0.515
0.894
0.691
0.182
0.076
2.585
0.550
0.785
Fat-Tailed & Skewed Asset Return Distributions; Frank Fabozzi Series; Wiley Finance 2005, pg 237
VAR techniques are subject to model risk so the parametric model
used for drawing in Monte Carlo influences the value of the VAR calculated..
+
Our own work
suggests that
normal method
under-estimates the
VAR compared to
Fat-Tailed methods,
even at 95%
confidence level
Fat-Tail Value-at-Risk
+ No
“magic bullet” as it doesn’t capture
correlation structural changes which occur in
real “Black Swan” events (not modeling the
volatility of volatility)
Currently @ FactSet
+ Internal discussions on methodology
+ Robustness tests, ease of use, computation time
+ On-going development continuing..