Chasing Your Tail
Sandeep Patel
Anil Suri
Andrew Weisman
March 28 2007
Presentation to the Q-Group
Structure
1. History of (Risk) World: Part I
2. Advances in Portfolio Construction Analytics
•
Meucci (2006):
Non-Normality, Extreme Co-Movements, Estimation Error,
Drawdown Related Risk Measure, Extension of BlackLitterman to Non-Normal Market Views & Non-Normal
Views.
•
Patel, Suri, Weisman (2007)
Shifting Marginal Distributions to Forward Views,
Resampling Adjustment for Varying Length Histories, &
Adjusting for Liquidity Using Barrier Option Model.
Structure (Con’t)
3. Data Dependence Issues
•
Life is Out of Sample
Post Bubble Drawdowns, Peso Problems, Small Sample
Bias, Inaccurate Data
•
Poor Asset Allocation Advice
4. Normality (You Wish!)
•
Evidence and Observations on Non-Normality
Generally Not Normal, Lack of In-Sample and Out-ofSample Correspondence
Structure (Con’t)
5. Sources of Significant Loss Potential:
•
•
•
Non-Normality of the Asset Menu
Illiquidity
Incentive Structures and Negative Convexity
6. Evidence of “Alpha Migration”
•
•
Econometric Analysis of Cycle Excess Return
Intuition for Alpha Migration
Structure (Con’t)
7. Alpha Migration & Tail Loss Potential
•
•
•
Simple Analytical Framework
Andy’s Laws
Periodic Efficiency & Tail Loss Potential
Preliminary Thoughts:
“Prediction is Very Difficult, Especially About the
Future”
– Niels Bohr
“Everybody’s Got a Plan Till They Get Punched in
the Face”
– Mike Tyson
Zeitgeist
Don't bet the ranch.
Get more bang for your buck.
Maximize output relative to input.
Nothing ventured, nothing gained.
Diversify instead of striving to make a killing.
Don't put all your eggs in one basket; if it drops, you're in trouble.
High volatility is like putting your head in the oven and your feet in the refrigerator.
• Harry Markowitz, Portfolio Selection, 1952
Journal of Finance
• Wins Prize 38 years later: Nobel committee
decides to diversify away idiosyncratic
thought...shares prize with Merton Miller and Bill
Sharpe.
The Universe Consists of:
• Choices
– Risky Assets: Return, Volatility, Correlation
• Beneficent Organizing Principle:
– Diversification
• Promised Land
– Efficient Frontier
The Universe Populated by:
The Borg
– Slavishly Conformist
– Single Information Set
– Rational Utility Maximizing
– Portfolio Constructors
Yada + Yada + Yada =
Capital Asset Pricing Model
• Strong Simplifying Assumptions (Efficiency) Yields
the Capital Asset Pricing Model:
–
–
–
–
–
–
The Market Portfolio sits on the Efficient Frontier
All Investors Should Hold the Same Portfolio
Geared as a Function of Risk Tolerance
Idiosyncratic (Security Specific) Risk is Diversifiable
All About: Reward vs Systematic Risk
Basis for Passive Management
• Mathematics of Portfolio Theory is the Theoretical
Precursor of Value-at-Risk (VaR)
The Tool Kit
•
•
•
•
•
•
•
•
•
•
Alpha
Beta
R-Squared
Correlation
Standard Deviation
Benchmarks
Tracking Error
Efficient Frontier
Scattergrams
Lots of Ratios:
– Sharpe, Treynor, Jensen,Up/Down Capture, Information...
•
•
Value at Risk
Stress Testing
Positional Data
•
•
•
•
Assume it’s available
Assume it’s map-able
Assume you have sufficient infrastructure
Assume you already understand the risk well
enough to design an appropriate set of stresses
• Assume the portfolio will remain constant
• Assume you’re King Leopold II of Belgium
R A M P 0 5 -E F C 1 B 2
p ric e = 7 7 - 2 0
70
85
10 0
p re p a y s
11 5
13 0
The Modern Risk Report
R a t in g (B B /- / B B 0
d e f a u lt s
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
75
90
1 05
1 20
135
14 .34 28
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
9 6 2.00
10 28
4.67
Au g0 5 to O c t13
O c t0 8 to O c t13
0 . 0 0 (0 .0 0 % )
99
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
15 .74 57
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
1 ,0 9 8 . 0 0
11 69
3.69
Au g0 5 to A ug 11
J un 08 to Au g1 1
0 . 0 0 (0 .0 0 % )
73
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
16 .59 83
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
1 ,1 7 9 . 0 0
12 55
3.27
Au g0 5 to N o v 11
J un 08 to N ov 1 1
0 . 0 0 (0 .0 0 % )
76
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
16 .99 61
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
1 ,2 1 9 . 0 0
12 96
2.85
A u g 0 5 t o J u l1 7
D e c 0 7 t o J u l1 7
6 9 2 , 7 9 0 . 6 6 (4 . 2 9 % )
1 44
3 5 ,1 0 0 , 8 4 0 . 3 8 (3 . 2 2 % )
3 5 ,1 0 0 , 8 4 0 . 3 8 (3 . 2 2 % )
14 .05 47
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
9 45
10 03
2.53
Au g0 5 to D e c 09
Se p0 7 to J u n0 8
2,52 5,9 01 .99 ( 15 .64 % )
53
2 8 ,5 1 9 , 4 2 3 . 0 5 (2 . 6 2 % )
2 8 ,5 1 9 , 4 2 3 . 0 5 (2 . 6 2 % )
1 4.34 28
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
96 2.00
10 28
4.67
Au g0 5 to O c t13
O c t0 8 t o O c t 1 3
0 . 0 0 (0 .0 0 % )
99
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
1 5.74 53
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
1 ,09 8.00
11 69
3.69
Au g0 5 to A ug 11
J u n 0 8 to A u g 1 1
0 . 0 0 (0 .0 0 % )
73
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
1 6.22 61
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
1 ,14 3.00
12 18
3.54
Au g0 5 to F e b1 3
J u n 0 8 to F e b 1 3
0 . 0 0 (0 .0 0 % )
91
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
1 2.50 54
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
79 6.00
8 47
2.94
Au g0 5 to A ug 10
D ec 07 to J a n0 9
2 , 9 6 0 ,8 9 5 . 8 2 (1 8 . 3 3 % )
61
3 8 , 3 3 0 , 6 8 1 . 5 5 (3 . 5 2 % )
3 8 , 3 3 0 , 6 8 1 . 5 5 (3 . 5 2 % )
9.70 98
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
53 1.00
5 68
2.56
Au g0 5 to A ug 09
Se p0 7 to F e b0 8
4 , 0 0 3 ,3 7 1 . 3 2 (2 4 . 7 9 % )
49
3 1 , 5 9 1 , 2 2 1 . 0 5 (2 . 9 0 % )
3 1 , 5 9 1 , 2 2 1 . 0 5 (2 . 9 0 % )
1 4.3 42 8
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
96 2.0 0
1 02 8
4.6 7
Au g 05 to O c t1 3
O c t0 8 t o O c t 1 3
0 . 0 0 (0 . 0 0 % )
99
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
15 .69 9
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
1 ,09 3.0 0
1 16 5
3.7 2
Au g 05 to A u g1 1
J un 0 8 to Au g 11
0 . 0 0 (0 . 0 0 % )
73
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
1 3.6 68 1
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
90 1.0 0
96 1
3.8 1
Au g 05 to M ar 14
J u n 0 8 t o M a r1 4
1 , 7 5 4 , 1 7 8 . 3 4 (1 0 . 8 6 % )
10 4
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
8.7 90 3
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
44 0.0 0
47 5
3.0 2
Au g 05 to M ar 10
J a n 0 8 t o O c t0 8
4 , 3 9 1 , 8 5 2 . 1 8 (2 7 . 2 0 % )
56
4 1 , 7 7 0 , 6 1 4 .5 1 ( 3 . 8 3 % )
4 1 , 7 7 0 , 6 1 4 .5 1 ( 3 . 8 3 % )
7.1 58 9
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
28 5.0 0
31 3
2.5 2
A u g 0 5 t o A p r0 9
Se p 07 to D ec 0 7
4 , 7 0 6 , 1 9 3 . 4 3 (2 9 . 1 4 % )
45
3 3 , 5 3 9 , 3 4 6 .3 5 ( 3 . 0 8 % )
3 3 , 5 3 9 , 3 4 6 .3 5 ( 3 . 0 8 % )
1 4.3 42 7
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
9 6 2 .0 0
1 02 7
4 .6 7
A u g 0 5 to O c t 1 3
O c t08 to O c t1 3
0 .0 0 ( 0 . 0 0 % )
99
5 6,16 2,1 70 .76 ( 5.1 5% )
5 6,16 2,1 70 .76 ( 5.1 5% )
1 5.3 53 8
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
1 , 0 5 9 .0 0
1 13 0
3 .9 6
A u g 0 5 to J a n 1 2
J u n0 8 to J a n1 2
0 .0 0 ( 0 . 0 0 % )
78
5 6,16 2,1 70 .76 ( 5.1 5% )
5 6,16 2,1 70 .76 ( 5.1 5% )
9.0 30 3
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
4 6 2 .0 0
49 8
3 .5 7
A u g 0 5 to M a r 1 1
J u n0 8 to A pr 09
4 ,4 9 2 , 1 1 7 . 7 6 (2 7 . 8 2 % )
68
5 5,03 8,9 27 .35 ( 5.0 5% )
5 5,03 8,9 27 .35 ( 5.0 5% )
5.0 22 9
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
7 4 .0 0
98
3 .0 1
A u g 0 5 to N o v 0 9
J a n0 8 to A ug 08
5 ,6 9 3 , 5 6 7 . 7 6 (3 5 . 2 6 % )
52
4 4,92 9,7 36 .61 ( 4.1 2% )
4 4,92 9,7 36 .61 ( 4.1 2% )
5.5 26 9
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 6 .0 0
15 0
2 .4 7
A u g 0 5 to D e c 0 8
S e p 0 7 to O c t 0 7
5 ,0 9 3 , 0 6 4 . 1 5 (3 1 . 5 4 % )
41
3 4,68 0,1 40 .45 ( 3.1 8% )
3 4,68 0,1 40 .45 ( 3.1 8% )
1 4 .3 4 2 2
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
9 6 2 .0 0
1 02 7
4 .6 7
A u g 0 5 to O c t1 3
O c t 0 8 to O c t1 3
0 .0 0 ( 0 . 0 0 % )
99
6 3 , 1 8 2 ,4 4 2 . 1 1 (5 . 8 0 % )
6 3 , 1 8 2 ,4 4 2 . 1 1 (5 . 8 0 % )
1 4 .9 2 8 3
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
1 , 0 1 8 .0 0
1 08 7
4 .3 2
A u g 0 5 to N o v 1 2
J u n0 8 to N o v 12
0 .0 0 ( 0 . 0 0 % )
88
6 2 , 4 1 2 ,5 2 6 . 1 0 (5 . 7 3 % )
6 2 , 4 1 2 ,5 2 6 . 1 0 (5 . 7 3 % )
7.07 1
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
2 7 2 .0 0
30 2
3.5
A u g 0 5 to S e p 1 0
J u n0 8 to J a n0 9
5 ,2 4 0 , 2 1 5 . 8 3 (3 2 . 4 5 % )
62
5 7 , 4 1 9 ,5 2 4 . 0 1 (5 . 2 7 % )
5 7 , 4 1 9 ,5 2 4 . 0 1 (5 . 2 7 % )
4 .2 9 9 3
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
3 .0 0
26
2 .9 2
A u g 0 5 to J u l0 9
J a n0 8 to J a n0 8
5 ,8 0 8 , 7 3 0 . 2 8 (3 5 . 9 7 % )
48
4 6 , 2 8 1 ,1 3 8 . 8 5 (4 . 2 5 % )
4 6 , 2 8 1 ,1 3 8 . 8 5 (4 . 2 5 % )
4 .7 9 6 1
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
5 4 .0 0
78
2 .4 1
A u g 0 5 to O c t0 8
S e p 0 7 to S e p 0 7
5 ,2 2 6 , 3 4 8 . 3 9 (3 2 . 3 6 % )
39
3 6 , 8 0 3 ,7 7 2 . 5 3 (3 . 3 8 % )
3 6 , 8 0 3 ,7 7 2 . 5 3 (3 . 3 8 % )
R A M P 0 5 -E F C 1 B 2
p ric e = 7 7 - 2 0
70
85
10 0
p re p a y s
11 5
13 0
The Modern Risk Report
R a t in g (B B /- / B B 0
d e f a u lt s
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
Y ie ld
M k t V a lu e
M k t V a lu e w / A c c ru e d
D is c M a rg in
S p re a d
W AL
P a ym e n t W in d o w
P r in c i p a l W i n d o w
P r in c i p a l W r it e d o w n
M a t u rit y # m o s
T o t a l C o l la t L o s s (E n t it le d )
T o t a l C o l la t L o s s (F o re c a s t e d )
75
90
1 05
1 20
135
14 .34 28
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
9 6 2.00
10 28
4.67
Au g0 5 to O c t13
O c t0 8 to O c t13
0 . 0 0 (0 .0 0 % )
99
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
15 .74 57
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
1 ,0 9 8 . 0 0
11 69
3.69
Au g0 5 to A ug 11
J un 08 to Au g1 1
0 . 0 0 (0 .0 0 % )
73
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
16 .59 83
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
1 ,1 7 9 . 0 0
12 55
3.27
Au g0 5 to N o v 11
J un 08 to N ov 1 1
0 . 0 0 (0 .0 0 % )
76
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
3 5 ,1 0 1 , 3 5 6 . 7 3 (3 . 2 2 % )
16 .99 61
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
1 ,2 1 9 . 0 0
12 96
2.85
A u g 0 5 t o J u l1 7
D e c 0 7 t o J u l1 7
6 9 2 , 7 9 0 . 6 6 (4 . 2 9 % )
1 44
3 5 ,1 0 0 , 8 4 0 . 3 8 (3 . 2 2 % )
3 5 ,1 0 0 , 8 4 0 . 3 8 (3 . 2 2 % )
14 .05 47
1 2 , 5 3 5 ,6 6 1 . 2 5
1 2 , 5 3 5 ,6 6 1 . 2 5
9 45
10 03
2.53
Au g0 5 to D e c 09
Se p0 7 to J u n0 8
2,52 5,9 01 .99 ( 15 .64 % )
53
2 8 ,5 1 9 , 4 2 3 . 0 5 (2 . 6 2 % )
2 8 ,5 1 9 , 4 2 3 . 0 5 (2 . 6 2 % )
1 4.34 28
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
96 2.00
10 28
4.67
Au g0 5 to O c t13
O c t0 8 t o O c t 1 3
0 . 0 0 (0 .0 0 % )
99
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
1 5.74 53
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
1 ,09 8.00
11 69
3.69
Au g0 5 to A ug 11
J u n 0 8 to A u g 1 1
0 . 0 0 (0 .0 0 % )
73
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
1 6.22 61
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
1 ,14 3.00
12 18
3.54
Au g0 5 to F e b1 3
J u n 0 8 to F e b 1 3
0 . 0 0 (0 .0 0 % )
91
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
4 2 , 1 2 1 , 6 2 8 . 0 7 (3 . 8 6 % )
1 2.50 54
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
79 6.00
8 47
2.94
Au g0 5 to A ug 10
D ec 07 to J a n0 9
2 , 9 6 0 ,8 9 5 . 8 2 (1 8 . 3 3 % )
61
3 8 , 3 3 0 , 6 8 1 . 5 5 (3 . 5 2 % )
3 8 , 3 3 0 , 6 8 1 . 5 5 (3 . 5 2 % )
9.70 98
1 2,5 35 ,66 1.25
1 2,5 35 ,66 1.25
53 1.00
5 68
2.56
Au g0 5 to A ug 09
Se p0 7 to F e b0 8
4 , 0 0 3 ,3 7 1 . 3 2 (2 4 . 7 9 % )
49
3 1 , 5 9 1 , 2 2 1 . 0 5 (2 . 9 0 % )
3 1 , 5 9 1 , 2 2 1 . 0 5 (2 . 9 0 % )
1 4.3 42 8
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
96 2.0 0
1 02 8
4.6 7
Au g 05 to O c t1 3
O c t0 8 t o O c t 1 3
0 . 0 0 (0 . 0 0 % )
99
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
15 .69 9
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
1 ,09 3.0 0
1 16 5
3.7 2
Au g 05 to A u g1 1
J un 0 8 to Au g 11
0 . 0 0 (0 . 0 0 % )
73
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
1 3.6 68 1
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
90 1.0 0
96 1
3.8 1
Au g 05 to M ar 14
J u n 0 8 t o M a r1 4
1 , 7 5 4 , 1 7 8 . 3 4 (1 0 . 8 6 % )
10 4
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
4 9 , 1 4 1 , 8 9 9 .4 2 ( 4 . 5 1 % )
8.7 90 3
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
44 0.0 0
47 5
3.0 2
Au g 05 to M ar 10
J a n 0 8 t o O c t0 8
4 , 3 9 1 , 8 5 2 . 1 8 (2 7 . 2 0 % )
56
4 1 , 7 7 0 , 6 1 4 .5 1 ( 3 . 8 3 % )
4 1 , 7 7 0 , 6 1 4 .5 1 ( 3 . 8 3 % )
7.1 58 9
1 2 ,5 3 5 , 6 6 1 . 2 5
1 2 ,5 3 5 , 6 6 1 . 2 5
28 5.0 0
31 3
2.5 2
A u g 0 5 t o A p r0 9
Se p 07 to D ec 0 7
4 , 7 0 6 , 1 9 3 . 4 3 (2 9 . 1 4 % )
45
3 3 , 5 3 9 , 3 4 6 .3 5 ( 3 . 0 8 % )
3 3 , 5 3 9 , 3 4 6 .3 5 ( 3 . 0 8 % )
1 4.3 42 7
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
9 6 2 .0 0
1 02 7
4 .6 7
A u g 0 5 to O c t 1 3
O c t08 to O c t1 3
0 .0 0 ( 0 . 0 0 % )
99
5 6,16 2,1 70 .76 ( 5.1 5% )
5 6,16 2,1 70 .76 ( 5.1 5% )
1 5.3 53 8
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
1 , 0 5 9 .0 0
1 13 0
3 .9 6
A u g 0 5 to J a n 1 2
J u n0 8 to J a n1 2
0 .0 0 ( 0 . 0 0 % )
78
5 6,16 2,1 70 .76 ( 5.1 5% )
5 6,16 2,1 70 .76 ( 5.1 5% )
9.0 30 3
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
4 6 2 .0 0
49 8
3 .5 7
A u g 0 5 to M a r 1 1
J u n0 8 to A pr 09
4 ,4 9 2 , 1 1 7 . 7 6 (2 7 . 8 2 % )
68
5 5,03 8,9 27 .35 ( 5.0 5% )
5 5,03 8,9 27 .35 ( 5.0 5% )
5.0 22 9
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
7 4 .0 0
98
3 .0 1
A u g 0 5 to N o v 0 9
J a n0 8 to A ug 08
5 ,6 9 3 , 5 6 7 . 7 6 (3 5 . 2 6 % )
52
4 4,92 9,7 36 .61 ( 4.1 2% )
4 4,92 9,7 36 .61 ( 4.1 2% )
5.5 26 9
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 6 .0 0
15 0
2 .4 7
A u g 0 5 to D e c 0 8
S e p 0 7 to O c t 0 7
5 ,0 9 3 , 0 6 4 . 1 5 (3 1 . 5 4 % )
41
3 4,68 0,1 40 .45 ( 3.1 8% )
3 4,68 0,1 40 .45 ( 3.1 8% )
1 4 .3 4 2 2
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
9 6 2 .0 0
1 02 7
4 .6 7
A u g 0 5 to O c t1 3
O c t 0 8 to O c t1 3
0 .0 0 ( 0 . 0 0 % )
99
6 3 , 1 8 2 ,4 4 2 . 1 1 (5 . 8 0 % )
6 3 , 1 8 2 ,4 4 2 . 1 1 (5 . 8 0 % )
1 4 .9 2 8 3
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
1 , 0 1 8 .0 0
1 08 7
4 .3 2
A u g 0 5 to N o v 1 2
J u n0 8 to N o v 12
0 .0 0 ( 0 . 0 0 % )
88
6 2 , 4 1 2 ,5 2 6 . 1 0 (5 . 7 3 % )
6 2 , 4 1 2 ,5 2 6 . 1 0 (5 . 7 3 % )
7.07 1
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
2 7 2 .0 0
30 2
3.5
A u g 0 5 to S e p 1 0
J u n0 8 to J a n0 9
5 ,2 4 0 , 2 1 5 . 8 3 (3 2 . 4 5 % )
62
5 7 , 4 1 9 ,5 2 4 . 0 1 (5 . 2 7 % )
5 7 , 4 1 9 ,5 2 4 . 0 1 (5 . 2 7 % )
4 .2 9 9 3
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
3 .0 0
26
2 .9 2
A u g 0 5 to J u l0 9
J a n0 8 to J a n0 8
5 ,8 0 8 , 7 3 0 . 2 8 (3 5 . 9 7 % )
48
4 6 , 2 8 1 ,1 3 8 . 8 5 (4 . 2 5 % )
4 6 , 2 8 1 ,1 3 8 . 8 5 (4 . 2 5 % )
4 .7 9 6 1
1 2 , 5 3 5 , 6 6 1 .2 5
1 2 , 5 3 5 , 6 6 1 .2 5
5 4 .0 0
78
2 .4 1
A u g 0 5 to O c t0 8
S e p 0 7 to S e p 0 7
5 ,2 2 6 , 3 4 8 . 3 9 (3 2 . 3 6 % )
39
3 6 , 8 0 3 ,7 7 2 . 5 3 (3 . 3 8 % )
3 6 , 8 0 3 ,7 7 2 . 5 3 (3 . 3 8 % )
Advances In
Portfolio Construction Analytics
Meucci (2005, 2006)
•
•
•
•
•
Non-Normality
Marginals Estimated by Kernels
Tail Correlation
t-Copula
Estimation Error
Resampling
Drawdown
Relevant Risk Measures: CVaR
Extension of Black-Litterman to Non-Normal Market
Views & Non-Normal Views
• New Frontier Advisors, FinAnalytica, Axioma and others
Advances In Hedge Fund
Portfolio Construction Analytics
Patel, Suri, Weisman (2007)
• Absence of Priors
• Unequal History
• Illiquidity
• CVaR, CDaR
• Resampling
• Kernels, Copulas
Kullback-Leibler
Masking Technology
Barrier Option Model
Shifting to Forward-Looking Views
• The Expected Excess Return of a Strategy
– Fluctuates as Macro-Economic Environment Changes
– Diminishes as Competition Increases
• Adapt Risk-Neutralized Distribution Techniques Developed for Pricing Options
• Facilitates Blending Alternative Prospective Distributions of Returns and Volatility
Simulated Returns for Managers with
Unequal Track Records
• Panel A: Observed Manager Returns History for 84 months
Simulated Returns for Managers with
Unequal Track Records
• Panel B: Observed Manager Returns History for 24 months
Non-Normality of Hedge Funds
and Sample Size Issues
• Fitted Index Returns:
– Non-Normal & Difficult to Parameterize
• Observed Normality a Poor Guide
– Single Manager Example
– Index Example of Multiple Tests of Normality
– Broad Cross-Section of Individual Funds
The Evidence
Convert Arb
Distressed
Normal(0.022755, 0.032643)
Event Driven Multi Strat
Risk Arb
Logistic(0.029606, 0.018484)
Logistic(0.038308, 0.020054)
14
16
16
12
14
14
12
12
10
10
8
8
6
6
4
4
2
2
0
0
Logistic(0.021537, 0.013287)
20
18
16
10
14
12
8
10
6
8
6
4
-0.0309
5.0%
0.0764
90.0%
Event Driven
5.0%
90.0%
-0.0248
Fixed Income Arb
5.0%
90.0%
-17.5852
14
16
12
20
14
10
12
15
8
10
8
10
6
6
4
5
4
2
2
5.0%
90.0%
-0.0169
>
0.0831
<
5.0%
90.0%
-20.0885
5.0%
44.2317
<
5.0%
-0.0427
90.0%
5.0%
0.0964
0.20
0.15
0.10
0.05
0.00
0
-0.05
Values in Thousandths
-0.10
60.0
29.5
-1.0
-31.5
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
<
-62.0
0
0
80
60
40
20
0
-20
-40
-60
-80
0.10
<
Normal(0.026851, 0.042281)
25
18
Values in Thousandths
>
0.0840
Hedge Fund Index
BetaGeneral(6.6694, 2.4694, -0.087093, 0.054571)
Logistic(0.033078, 0.016981)
0.05
0.00
-0.05
-0.10
-0.15
0
<
>
0.0974
-0.0207
2
-0.20
0.10
0.05
<
0.00
>
-0.05
-0.15
5.0%
0.12
90.0%
0.10
0.08
0.06
0.04
0.02
0.00
5.0%
-0.02
-0.06
<
-0.04
-0.08
0
-0.10
4
2
>
5.0% >
60.6597
The Evidence
Sector
A_D Test Value
Convert Arb
Distressed
Event Driven
Event Driven MS
Fixed Income Arb
Risk Arb
Hedge Fund Index
0.5
1.6
1.9
1.9
1.0
0.7
0.8
Probability Value (p)
0.15 - 0.25
< 0.005
< 0.005
< 0.005
0.005 - 0.01
0.05 - 0.1
0.025 - 0.05
•Difficult to fit to a Distribution
•Risk = Standard Deviation = Big Mistake
•Fitting Distributions to Historical Data
Frequently Underestimates Loss Potential
Alpha?
That’s Funny…
Logistic(0.0127575, 0.0030517)
1.2
0.8
Summary Statistics
0.6
0.4
0.2
30
25
20
15
10
5
0
-5
-10
0.0
-15
Values x 10^2
1.0
Values in Thousandths
<
5.0%
90.0%
3.7720
5.0% >
21.7431
Mean
Mode
Median
St Dev
Skewness
Kurtosis
1.2
1.3
1.3
0.6
-1.1
5.4
…You Didn’t Look
Skewish
ExtValue(-0.044408, 0.15131)
25
20
Summary Statistics
15
Mean
Mode
Median
Std. Dev
Skewness
Kurtosis
10
5
<
5.0%
90.0%
-0.2104
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
0
>
0.4050
0.2
1.3
1.3
6.5
-7.2
55.5
January 1991 – June 1998
p-values of Tests of Normality
Strategies
Normality Tests: p-value with Non-Normal Distributions
1
2
3
4
5
6
7
8
Cramer
Anderson- Pearson( Shapiro- Shapiro- Jarque- Kolmogoro
Lilliefors
von
Darling Chi-square)
Wilk
Francia Bera v-Smirnov
Mises
1
HFRI Emerging Markets
0.33
0.04
0.28
0.19
0.83
0.91
0.50
-
2
HFRI Equity Hedge
0.34
0.03
0.24
0.03
0.11
0.35
0.03
-
3
HFRI Macro
0.08
0.03
0.17
0.04
0.57
0.75
0.50
-
4
HFRI Distressed Securities
0.01
0.05
0.03
0.46
0.04
0.22
0.01
-
5
HFRI Merger Arbitrage
0.00
0.16
0.00
0.32
0.02
0.21
0.04
-
6
HFRI Event-Driven
0.50
0.05
0.46
0.74
0.72
0.79
0.14
-
7
HFRI Convertible Arbitrage
0.04
0.22
0.00
0.11
0.00
0.09
0.01
-
8
HFRI Equity Market Neutral
0.50
0.29
0.25
0.15
0.51
0.81
0.23
-
9
HFRI Fixed Income Arbitrage
0.05
0.26
0.05
0.20
0.12
0.36
0.05
-
10
HFRI Fund Weighted Composite
0.06
0.06
0.03
0.21
0.14
0.41
0.50
-
January 1991 – December 2006
p-values of Tests of Normality
Strategies
Normality Tests: p-value with Non-Normal Distributions
1
2
3
4
5
6
7
8
Cramer
Anderson- Pearson( Shapiro- Shapiro- Jarque- Kolmogoro
Lilliefors
von
Darling Chi-square) Wilk
Francia Bera v-Smirnov
Mises
1
HFRI Emerging Markets
0.50
0.00
0.58
0.24
0.64
0.96
0.49
-
2
HFRI Equity Hedge
0.50
0.00
0.23
0.41
0.08
0.32
0.02
-
3
HFRI Macro
0.02
0.00
0.00
0.01
0.02
0.22
0.05
-
4
HFRI Distressed Securities
0.02
0.00
0.01
0.04
0.01
0.12
0.00
-
5
HFRI Merger Arbitrage
0.03
0.02
0.03
0.22
0.05
0.26
0.02
-
6
HFRI Event-Driven
0.12
0.00
0.06
0.08
0.04
0.24
0.01
-
7
HFRI Convertible Arbitrage
0.04
0.03
0.00
0.05
0.01
0.19
0.04
-
8
HFRI Equity Market Neutral
0.24
0.04
0.12
0.43
0.29
0.73
0.14
-
9
HFRI Fixed Income Arbitrage
0.00
0.06
-
0.00
-
0.03
0.00
-
10
HFRI Fund Weighted Composite
0.29
0.00
0.23
0.04
0.77
0.63
0.50
-
Normality Tests
120%
% with Non-Normal Distribution
100%
80%
60%
Lilliefors
40%
Cr amer von Mise s
Ande rson-Darli ng
Pear so n( Ch i-squar e)
Shap iro-W ilk
Shap iro-Fran ci a
20%
Ja rque -Bera
Kolmog orov-Sm irnov
0%
10
20
30
40
50
60
70
80
90
100
110
120
130
Data Pts required to be in population
140
150
160
170
180
190
Sources of Tail Loss Potential
• Non-normality of Underlying Asset Returns
• Illiquidity: More Than Meets the
Econometricians Eye
• Incentive Structures in Shorting Options
• Regulatory Risk – Split-Strike, PIPEs,
Random Shorting, Death Spiral Converts
Extreme Events in Commodity Price Changes
Smooth Idea
RNAVt = Reported NAV at time t
TNAVt = True (or liquidation value) NAV at time t
RNAV0 = TNAV0
δ = Proportional Valuation Lag, where 0 ≤ δ ≤ 1
Δ t = RNAVt − TNAVt = Over-valuation at time t.
L = Barrier value for Δ t
(Where Δ t ≥ L a payout occurs.)
Smoothing Algorithm:
RNAVt = RNAVt −1 + δ (TNAVt − RNAVt −1 )
Building the Model
• Utilize Basic Option Modeling Assumptions:
– Geometric Brownian Motion.
– Risk Neutral Valuation.
– Option Value Equal to Discounted Payoff.
• Model as a Barrier Option:
– Barrier Exceeded When Reported Portfolio Value Greater Than
True (Liquidation) Value by More Than a Specified Percent.
– Barrier Payout Equals =
(Percentage Overstatement + Potential Liquidation Penalty)
– Option Price Equal Discounted Value of Payout.
– Express Option Cost on an Annualized-Percent-of-Portfolio basis.
Smoothing of Illiquid Portfolios:
Viewed as a Barrier Option
Reported NAV Vs Actual NAV
mean = .15, sigma = .30, lag valuation = .15
0.4
3,000
0.3
2,500
L20
0
1,500
-0.1
1,000
-0.2
Diff
Market
Manager
-0.3
500
Period
59
57
55
53
51
49
47
45
43
41
39
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
-0.4
1
Percent Difference
2,000
0.1
Value of $1,000 Invested
0.2
Δt
C
TNAV Volatility
L (Threshold) = 5.0%
6%
8%
10%
12%
0.1
13%
17%
20%
22%
0.2
5%
11%
15%
18%
δ ( Smoothing parameter)
0.3
1%
5%
10%
13%
0.4
0%
1%
3%
7%
0.5
0%
0%
0%
2%
Note: C (Penality parameter is fixed at 20%)
14%
23%
21%
17%
11%
4%
16%
25%
22%
19%
14%
8%
18%
26%
23%
21%
17%
11%
TNAV Volatility
6%
8%
10%
12%
0.1
9%
14%
18%
21%
0.2
1%
5%
9%
14%
0.3
δ ( Smoothing parameter)
0%
1%
3%
6%
0.4
0%
0%
0%
1%
0.5
0%
0%
0%
0%
Note: C (Penality parameter is fixed at 20%)
L (Threshold) = 7.5%
14%
23%
17%
10%
3%
0%
16%
25%
20%
13%
6%
1%
18%
26%
22%
16%
8%
2%
TNAV Volatility
6%
8%
10%
12%
0.1
5%
11%
15%
19%
0.2
0%
1%
5%
8%
δ ( Smoothing parameter)
0.3
0%
0%
0%
1%
0.4
0%
0%
0%
0%
0.5
0%
0%
0%
0%
Note: C (Penality parameter is fixed at 20%)
L (Threshold) = 10.0%%
14%
21%
12%
4%
0%
0%
16%
24%
16%
7%
1%
0%
18%
26%
19%
10%
2%
0%
The Experiment
Simulate “Alpha-Transfer”
in a Two Trader/Two Style World:
•
Trader Vic
– Long Lower Probability
Bets:
• Less Frequent Wins
• Larger Periodic Payouts
• Smaller Periodic
Losses
• Long Options
•
Trader Joe
– Long Higher Probability
Bets:
• More Frequent Wins
• Smaller Periodic
Payouts
• Larger Periodic Losses
• Short Options
Case 1
•
•
•
•
•
Joe sells Out of the Money Options to Vic
Struck 2 Std Dev Out of the Money
Options Valued at Black-Scholes + 10%
Underlying Process: GBM
Options Purchased at Start of a Month and
Expire at the End of Every Month
• Joe Takes in 35 BP’s of Premium
• Vic Spends 35 BP’s of Capital on Premium
• Risk Free Rate: 5%
Case 1: Joe takes Alpha from Vic
α
Premium
Option
Vic (Long Option)
Joe (Short Option)
Alpha Transferred to Short Option
Short Monthly Return Histogram:
Distribution for + Alpha SO/N17
•Short Profile:
•High Mean: 5.67%
1.800
Mean=5.670704E-02
1.600
•Higher Mode: 9.63%
1.400
1.200
1.000
•Truncated Profit: 9.63%
0.800
0.600
0.400
0.200
0.000
-0.8
-0.575
-0.35
-0.125
5%
0.1
90%
-.1483
•Average Net Present Value of
Incentive Fees Over Ten Year Period:
166.90
.0963
Long Monthly Return Histogram:
•Long Profile:
Distribution for +Alpha LO/N35
1.400
•Low Mean: 4.59%
Mean=4.589801E-02
1.200
1.000
•Lower Mode: 0.80%
0.800
•Truncated Loss
0.600
0.400
0.200
0.000
0
0.35
90%
.008
0.7
1.05
5%
.2377
1.4
•Average Net Present Value of
Incentive Fees Over Ten Year Period:
97.52
Case 2
•
•
•
•
•
Joe sells Out of the Money Options to Vic
Struck 2 Std Dev Out of the Money
Options Valued at Black-Scholes
Underlying Process: GBM
Options Purchased at Start of Month and Expire
at the End of Every Month
• Joe Takes in 35 BP’s of Premium
• Vic Spends 35 BP’s of Capital on Premium
• Risk Free Rate: 5%
Case 2: No Alpha Exchange
α
Premium
Option
Vic (Long Option)
Joe (Short Option)
No Alpha Transfer
Short Monthly Return Histogram:
•Short Profile:
•High Mode: 9.63%
Distribution for 0 Alpha SO/N17
1.600
Mean=5.227088E-02
1.400
•Mediocre Mean: 5.23%
1.200
1.000
•Truncated Profit
0.800
0.600
0.400
0.200
0.000
-1
-0.7
-0.4
-0.1
5%
90%
-.1744
0.2
5%
•Average Net Present Value of
Incentive Fees Over Ten Year
Period: 156.10
.0963
•Long Profile:
Long Monthly Return Histogram:
Distribution for 0 Alpha LO/N35
•Lower Mode: 0.80%
0.900
0.800
Mean=0.0504102
•Truncated Loss
0.700
0.600
0.500
•Average Net Present Value of
Incentive Fees Over Ten Year
Period: 126.93
0.400
0.300
0.200
0.100
0.000
•Mediocre Mean: 5.04%
0
0.625
90%
.008 .2646
1.25
1.875
5%
2.5
Case 3
•
•
•
•
•
Joe sells Out of the Money Options to Vic
Struck 2 Std Dev Out of the Money
Options Valued at Black-Scholes -10%
Underlying Process: GBM
Options Purchased at Start of Month and Expire
at the End of Every Month
• Joe Takes in 35 BP’s of Premium
• Vic Spends 35 BP’s of Capital on Premium
• Risk Free Rate: 5%
Case 3: Vic takes Alpha from Joe
α
Premium
Option
Vic (Long Option)
Joe (Short Option)
Alpha Transferred to Long Option
Short Monthly Return Histogram:
Distribution for - Alpha SO/N17
1.600
Mean=4.690464E-02
1.400
•Short Profile:
•High Mode: 9.63%
•Low Mean: 4.69%
1.200
1.000
0.800
•Truncated Max
0.600
0.400
0.200
0.000
-1
-0.7
-0.4
-0.1
5%
90%
-.2075
0.2
5%
.0963
•Average Net Present Value of
Incentive Fees Over Ten Year
Period: 146.44
Long Monthly Return Histogram:
•Long Profile:
Distribution for - Alpha LO/N35
1.000
0.900 Mean=5.527177E-02
0.800
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
0
0.625
90%
.0135 .2644
•Low Mode: 1.35%
•High Mean: 5.53%
•Truncated Loss
1.25
5%
1.875
2.5
•Average Net Present Value of
Incentive Fees Over Ten Year
Period: 143.98
Performance Comparison
Short
Option
Long
Option
- Alpha
+ Alpha
0 Alpha
Short to Long
Alpha Transfer
Mean: 4.7%
Mode: 9.6%
Mean: 5.7%
Mode: 9.6%
Mean: 5.2%
Mode: 9.6%
Mean: 4.7%
Mode: 9.6%
Fee: 146.4
Fee: 166.9
Fee: 156.1
Fee: 146.4
Mean: 4.6%
Mean: 5.5%
Mean: 5.0%
Mean: 5.5%
Mode: 0.8%
Mode: 1.4%
Mode: 0.8%
Mode: 1.4%
Fee: 97.5
Fee: 144.0
Fee: 127.0
Fee: 144.0
Option Alpha Trivia
• Short Optionality Results in a Significant
Increase in Per Unit Cost of Alpha
• Short Option Strategies Have Modal Rates
of Return That are Largely Insensitive to
Alpha
• Feasible Cases in Which Negative Alpha
Strategies are Preferable to a Manager
Alpha Migration
• Markets are Periodically Efficient
• Develop a Factor Model to Explain Hedge
Fund Index Return
– Fung and Hsieh (2001, 2002), Agarwal and
Naik (2000,2004), Jaeger and Wagner (2005)
• Dynamic Behavior of alpha
• 24-month Rolling Regressions
• Plot Rolling 12-month alpha
Rolling 24 Month Alphas: Feb 96 –Jun 06
Factor Model Results
January 1994 – June 2006
Alpha
Lag1
Converts
Distressed
Emerging
Markets
Fixed
Income
Managed
Futures
Global
Macro
Long/Short
Equity
Market
Neutral
0.22
0.0
0.20
0.0
0.37
0.0
0.63
0.0
0.64
0.78
0.63
0.0
0.47
0.6
0.0
0.0
Fama French Momentum Factor
0.0
0.7
0.0
ML Global Emg. Mkts. Sovreign Plus Bond Index
0.0
0.0
0.0
ML USD Emerging Mkts Sovreign Plus Bond Index
MSCI Emerging Markets Index
0.1
Russell 1000 Value - Russell 1000 Growth
Russell 2000 - Russell 1000
1.4
0.7
0.7
US Dollar Index
0.0
0.0
2.3
0.4
0.1
0.0
0.8
0.0
Fung Hsieh PTFS - Bonds
Fung Hsieh PTFS - FX
2.4
Fung Hsieh PTFS - Stocks
0.0
0.2
0.6
S&P 500 Deep-out-of-the-money Calls
0.0
0.0
0.1
S&P 500 Out-of-the-money Calls
0.0
R square
3
3
63%
0.1
0.0
0.0
0.7
Swiss Partners Group Futures Index
Number of Factors: with optionality
0.3
0.9
0.7
ML Option Volatility Estimate Index
Number of Factors: long only
0.1
0.1
WTI Crude Oil
S&P 500 Out-of-the-money Puts
0.0
0.1
US Trade Weighted Dollar Index
S&P 500 Deep-out-of-the-money Puts
0.0
0.0
Russell 2000 Value - Russell 2000 Growth
CBOE BuyWrite Monthly Index
0.0
2.6
0.0
1.1
0.0
0.0
4.1
0.0
Russell 1000
US High Yield Master Index
0.87
0.0
2.9
0.0
ML Global Bond Index ex-US
US 30 Day Treasury Bills
0.21
0.4
Total
Index
0.6
Dow Jones AIG Commodity Index
ML All Convertibles, Ex Mandatory, Inv. Grade
Risk Arb
2
3
70%
4
1
79%
1
4
43%
0.0
0.1
3
3
44%
3
2
33%
0.8
7
1
85%
2
1
31%
5
2
51%
5
2
63%
A Manager as a Discrete Process
Binomial Model
E[α i ] = f (φi , ς i ) Excess Return in Period i
φi =
ςi =
Inefficiency Set
Specific Skill Set
Pwi =
Probability of Winning in period i
Pli =
Probability of Losing in period i
Wi =
Win in Period i
Li =
Loss in Period i
E [α i ] = Wi Pwi − Li Pl i
Discrete Binomial Model
Expected Loss Potential
Wi = W
Constant Absolute Rate of Return Target
Pwi = Pw
Constant Ex Ante Probability of Win
Pli = Pl
Constant Ex Ante Probability of Loss
WPw − E [α i ]
Li =
Pl
Expected Loss Potential in Period i
Periodically Efficient Markets Hypothesis
φ = The Inefficiency Set Periodically Declines Towards Zero
ς = The Proprietary Skill Set Becomes Increasingly Diffuse
E[α ] = f (φ , ς )
0
WPw
Lv =
Pl
Tail Loss Potential
Law 1: Losses are Proportional to Wins
Law 2: Losses are Inversely Proportional to
their Probability of Occurrence
The Evidence
Binomial Loss Estimation
Conv Arb Evt Drvn
Dist
Risk Arb
L/S
Equity
HF INDX
P(w)
0.8
0.8
0.8
0.8
0.7
0.7
W
0.0
0.0
0.1
0.0
0.1
0.0
Est L
-13.5%
-21.3%
-24.8%
-16.5%
-14.1%
-11.9%
Obs L
-9.3%
-16.3%
-15.7%
-9.5%
-9.5%
-12.2%
95% Bound
-7.7%
-12.0%
-14.0%
-7.5%
-7.5%
-6.6%
5% Bound
-27.8%
-48.2%
-56.0%
-30.3%
-30.3%
-23.2%
1.5
1.3
1.6
1.4
1.4
1.0
Ratio
•Binomial Loss Estimates Produce Appropriate Scale Results
•Estimated Loss Estimates Well Outside Distributional Expectations
•Outliers to be Expected
•Not ‘Perfect Storm’ Effects…But Perfectly Normal Effects
•Risk is Better Understood as the Result of a Process
MSCI EM/World TR Index (Non-Rolling, Obs = 5,000)
2001-2006 Indices
(Non-Rolling, Obs = 5,000)
Conclusion
• Advances in Portfolio Construction
Analytics Handle Many Known Issues
• Peso Problems Remain a Challenge
• A Simple Betting Process Model Provides
Promising Results