Transcript Document

New Opportunities for Structuring Investment Portfolios
Vineer Bhansali, Ph.D.
Managing Director, Portfolio Manager, PIMCO
Email: [email protected]
For Educational Purposes Only
Not for Broad/Printed Distribution
Quant Congress USA, July 8, 2008
This presentation contains the current opinions of the manager and such opinions are subject to change without notice.
This presentation has been distributed for informational purposes only and should not be considered as investment advice or a
recommendation of any particular security, strategy or investment product. Information contained herein has been obtained from
sources believed to be reliable, but not guaranteed. No part of this presentation may be reproduced in any form, or referred to in
any other publication, without express written permission of Pacific Investment Management Company LLC. ©2008, PIMCO.
0
Last Year’s Quant Congress (July 12, 2007) – Plenary Session/Vineer Bhansali
Using credit derivatives for hedging
The nature of credit risk in the post-default swap era
The need for hedging arises from market segmentation – what is the structure of the market?
Instruments and their valuation – what are the insurance and hedging aspects and how should we value
them? What is the impact of embedded leverage?
Looming uncertainties – settlements, structures, financing frictions, leverage, concentration
Hedge performance measurement
Conclusions: Optimal overlay and hedging vehicles – customization vs. efficiency
For Educational Purposes Only
1
Back in June of 2007 the 7-100 IG tranche economics looked like this
 Tranches are akin to option spreads on indices.
– For instance, a 7-100% tranche on the 7-year Investment-Grade Credit Default Swap Index would cover
losses in excess of 7%.
– The CDX and iTraxx indices allow for customization based on client needs and risk preferences.
Cost Calculation Example: 7-100% Tranche on 10Yr IG8
Expected Loss Table for 10Yr IG8
CDX Index Tranches
Expected Loss
-Running cost (coupon)/year of spread duration = 2 bp
0-3%
95.3%
-Roll-down = 2.67 bp
3-7%
55.6%
7-10%
16.6%
7-100%
2.2%
10-15%
7.8%
15-30%
2.5%
30-100%
1.1%
IG8 10 Y
7.1%
–For 10 year tranche short at 15.63 bp/year
-Total = 4.67 bp
–To short 1 Billion notional, total lifetime cost is about 12 MM
Risk calculation
–The 10 year index spread duration is 7.45, and the tranche
has a delta of 0.53. So each unit of tranche notional provides
approximately 7.45*0.53=3.95% return for 100bp spread
widening.
For Educational Purposes Only
Source: PIMCO
2
Same Tranche - Feb. 2008
 Tranches are akin to option spreads on indices.
– For instance, a 7-100% tranche on the 7-year Investment-Grade Credit Default Swap Index would cover
losses in excess of 7%.
– The CDX and iTraxx indices allow for customization based on client needs and risk preferences.
Cost Calculation Example: 7-100% Tranche on 10Yr IG8
Expected Loss Table for 10Yr IG9
CDX Index Tranches
Expected Loss
-Running cost (coupon)/year of spread duration = 10.1 bp
0-3%
88.3%
-Roll-down = 2.2 bp
3-7%
54.4%
7-10%
36.2%
7-100%
8.0%
10-15%
23.6%
15-30%
12.1%
30-100%
4.8%
IG8 10 Y
12.2%
–For 10 year tranche short at 91 bp/year
-Total = 12.3 bp
–To short 1 Billion notional, total lifetime cost is about 67 MM
Risk calculation
–The 10 year index spread duration is 7.35, and the tranche has
a delta of 0.77. So each unit of tranche notional provides
approximately 7.35*0.77=5.66% return for 100bp spread
widening.
For Educational Purposes Only
Source: PIMCO
3
What’s New this Year?
 Macro Tail Risk
– “Tail Risk Management”, Journal of Portfolio
Management, Summer 2008.
 Momentum
– “Cy-Cular Change”, PIMCO Viewpoints, July
2008. www.pimco.com
4
Tail Risk At The Portfolio Level
 Tail risk represents exposure to systematic risk:
– Deleveraging or illiquidity exposure
– Puts pressure on ability to fund levered holdings
– Correlations rise in absolute value, reducing relevance of basis risk
– Risk-Neutral valuation is wrong in this domain
– Tail Risk Hedging cannot be discussed without reference to the whole portfolio
– Factor Approach Captures Systematic Risk
– Principally a handful of factors explain asset movements
For Educational Purposes Only
5
Four Approaches To Tail Risk Hedging
 Move portfolio off the “efficient” frontier, i.e. leave more in “cash”
 Purchase high quality insurance securities
– Short term cash and Treasuries natural asset based hedges for tail risk
– But securities may be overpriced for technical reasons
 Purchase “Option-like” securities
– Out of the money CDX and ITRAXX indices were “given away” due to high demand
 Invest in strategies negatively correlated to tail risk
– ”Trend Following”/Momentum
For Educational Purposes Only
6
Objective Function
There is no unique tail risk hedge for all seasons and all portfolios.
Tail risk instruments are selected in the portfolio such that stress “beta” is lower than
normal beta.
The cost of the insurance, or yield give-up is mathematically equivalent to the certainty
equivalent of the difference between the optimal frontier and the truncated portfolio.
To quantify this, scenario shocks of securities – if expected return under scenarios with
ex-ante probabilities is higher than the market price, the security qualifies as a good
tail-risk security.
For Educational Purposes Only
7
Analogy - Phase Transitions in Water
Solid
Supercritical
Fluid
Compressible
Liquid
Critical Point
Liquid
Triple Point
Gas
Temperature
For Educational Purposes Only
8
Critical Temperature
Pressure
Critical Pressure
Superheated
Vapor
Phase Transitions in Markets
Risk Aversion
Stable
Markets
Critical
Point
Critical Risk Aversion
Unstable
Markets
Decreased
Left Tail Risk
Meta-stable
Markets
Increased
Left Tail Risk
Leverage
For Educational Purposes Only
9
Results in Symmetry Breaking and Momentum
For Educational Purposes Only
10
Consequences
 Momentum re. emerges as an investment factor replacing mean-reversion
 Monetary Policy has little or no effect
 Old benchmarks become irreversibly irrelevant
 Fluctuations happen at all scales simultaneously
 Arbitrage bounds cease to hold
For Educational Purposes Only
11
Credit Markets are suffering from run on liquidity – scale invariance
spread (bp)
IG on the run spread breakdown (LHS)
and average broker CDS (RHS)
from 1/1/08 to 6/9/08
100
90
80
70
60
50
40
30
20
10
0
12/31/07
idiosyncratic
sectorwide
systemic
6/9/2008
ave broker
450
400
350
300
250
200
150
100
50
0
1/30/08
2/29/08
3/30/08
For Educational Purposes Only
Source: PIMCO
12
4/29/08
5/29/08
-20.00
-40.00
-60.00
-80.00
-100.00
Source: J.P.Morgan
For Educational Purposes Only
13
4/13/2008
2/13/2008
12/13/2007
10/13/2007
8/13/2007
6/13/2007
4/13/2007
2/13/2007
12/13/2006
10/13/2006
8/13/2006
6/13/2006
4/13/2006
2/13/2006
12/13/2005
10/13/2005
8/13/2005
6/13/2005
4/13/2005
Negative Basis is persistent and volatile – Breaking of Arbitrage Bounds
60.00
40.00
20.00
0.00
If momentum is a new risk factor then: Sell the Middle Buy the Tails
 Strike effect: People overprice options they can price, but
underprice options they cannot price.
 Expiration Effect: Due to particular compensation structures sell
side is seller of long dated puts
 Jump Effect: Markets are discontinuous; models assume
continuity
For Educational Purposes Only
14
Momentum Strategies Outperform in Liquidity Events, and have “good” distributional characteristics
Correlation of Hedge Fund Strategies with VIX
1
10yr ended May 08
Jul 07 - May 08
0.75
Tech bust (Apr-Nov 00)
LTCM (Aug-Nov 98)
0.5
0.25
0
-0.25
-0.5
-0.75
-1
Composite
Hedge Fund
Convertible
Arbitrage
Dedicated
Short Bias
Emerging
Markets
Equity
Market
Neutral
Event Driven
Distressed
For Educational Purposes Only
Source: PIMCO
15
Risk
Arbitrage
Fixed Income Global Macro Long/Short
Arbitrage
Equity
Managed
Futures
MultiStrategy
Whenever VIX>30% most asset classes have negative returns
Monthly Returns (when VIX exceeds 30%)
Date
October-90
October-97
August-98
September-98
September-01
October-01
July-02
August-02
September-02
October-02
January-03
Average
MSCI
Emerging
Markets
-2.0%
-16.5%
-29.3%
6.1%
-15.7%
6.1%
-7.9%
1.4%
-11.0%
6.4%
-0.6%
-5.71%
MSCI EAFE
15.6%
-7.7%
-12.4%
-3.0%
-10.1%
2.6%
-9.9%
-0.2%
-10.7%
5.4%
-4.2%
-3.14%
MSCI World
9.2%
-6.0%
-14.0%
2.0%
-9.1%
2.1%
-8.4%
0.3%
-11.0%
7.4%
-2.9%
-2.77%
Japanese
Yen
S&P 500
-0.7%
-3.4%
-14.6%
6.2%
-8.2%
1.8%
-7.9%
0.5%
-11.0%
8.6%
-2.7%
-2.85%
For Educational Purposes Only
16
-6.0%
0.0%
-3.7%
-2.0%
0.6%
2.4%
0.3%
-1.2%
2.8%
0.6%
0.9%
-0.48%
VIX (%
Change)
3.2%
53.2%
78.5%
-7.5%
28.1%
5.1%
26.1%
1.9%
21.6%
-21.5%
8.9%
17.96%
VIX
30.0
35.1
44.3
41.0
31.9
33.6
32.0
32.6
39.7
31.1
31.2
GSCI
-7.7%
3.2%
-4.6%
12.3%
-10.5%
-3.5%
0.3%
5.8%
5.7%
-4.4%
7.8%
0.39%
10 Yr US
Treasury
-2.0%
-4.5%
-9.4%
-11.2%
-5.0%
-7.8%
-7.0%
-7.1%
-13.2%
8.3%
3.9%
-5.01%
Correlations of Absolute Return Styles shows Trend-Following/Managed Futures is a Lone
Diversifier
Abbreviations:
CA:
DSB:
EM:
EMN:
ED:
FIA:
GM:
LSEH:
Convertible Arbitrage
Dedicated Short Bias
Emerging Markets
Equity Market Neutral
Event Driven
Fixed Income Arbitrage
Global Macro
Long/Short Equity
MF:
Managed Futures
EDMS:
DI:
RA:
MS:
Event Driven Multi-Strategy
Distressed
Risk Arbitrage
Multi-Strategy
Thick line = > 50% correlation
Thin line = 25 – 50% correlation
No line = < 25% correlation
Source: Khandani & Lo, 2007
17
Correlation with other Asset Classes becomes more negative in Crisis Periods
One-Year Correlation of Trend Basic With Other Asset Classes
LIBOR 1M
MSCI US
Lehman US Agg
VIX
One-Year Daily Correlation
0.8
0.6
0.4
0.2
0
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08
-0.2
-0.4
-0.6
1994 bond
and equity
bear markets
1998
Crisis
1999 bond
bear market
Source: PIMCO
18
2000-2002
bear market
in equities
Trend Strategy is
negatively
correlated to other
asset classes when
they perform poorly
5-10% Allocation to Momentum Improves Overall Portfolio Sharpe Ratio
Calendar Year Returns
Optimal Portfolio Sharpe Ratio = 1.2
40/40/20 Sharpe Ratio = 1.0
60/40 Sharpe Ratio = 0.8
35%
30%
25%
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
20%
15%
10%
5%
0%
-5%
Source: PIMCO
Optimal stocks/bonds/Momentum = Sharpe Ratio 1.2
40/40/20 stocks/bonds/Momentum = Sharpe Ratio 1.0
60/40 stocks/bonds = Sharpe Ratio 0.8
For Educational Purposes Only
19
20
07
20
06
20
05
20
04
20
03
20
02
20
01
20
00
19
99
19
98
19
97
19
96
19
95
-10%
19
94
Optimal Weights
MSCI
US
0.31
0.34
0.32
0.29
0.28
0.24
0.26
0.30
0.32
0.29
0.41
0.48
0.48
0.31
LBAG
0.64
0.60
0.59
0.61
0.59
0.57
0.57
0.50
0.51
0.58
0.42
0.30
0.32
0.58
Trends
Basic
0.06
0.07
0.08
0.10
0.14
0.19
0.17
0.20
0.17
0.13
0.18
0.22
0.21
0.11
Theory, Practice and Performance of Moving Average Momentum Strategies
20
Are there Anomalies that can be exploited using Priced Based Trading Strategies?
Academic Literature now says Yes
A Study I did in 1993 and 1994, and again in 1999 showed that of all the technical indicators in the “Handbook of
Technical Analysis” Moving Averages were the best performing when combining Risk, Return and Simplicity of Execution.
Subsequently there has been a lot of work on this in the academic literature .
Fung and Hsieh (2001) show that the trend following strategy is like a long position in a lookback
straddle, hence has non-linear factor exposures that cannot be replicated by constant exposures.
Brock, Lakonishok and LeBaron prove that Moving Averages Provide Statistically
Significant Profits (1992)
The Returns earned on “momentum” strategies can be interpreted as compensations earned for bearing risk
during times when inventories are low. “The Fundamentals of Commodity Futures Returns, G. Gorton,
F. Hayashi, G Rouwenhorst, 2008.
For Educational Purposes Only
21
Why do moving average rules work? Some Explanations.
 Behavioral:
– Self-Fullfilling: There are enough people following them that they are self-fulfilling.
– Representativeness Bias: Due to reliance on recent data, speculators are prone to behavioral representative
biases which lead them to buy asset that are rising and sell those that are falling.
 Dynamic Hedging of Options: There is systematic option selling on the tails by hedge funds, and large
moves force them to rebalance and rehedge
 Virtual Replication of Nonlinear Payoffs: There are trend followers (such as Bridgewater) who
replicate the “delta” of a hypothetical option and create momentum (see Fung and Hsieh RFS 2001
paper on trend following replicable using a non-linear option formula equivalent to a lookback straddle).
 Policy Inertia: Policy Makers move in small steps, and the market only slowly builds in the extent of the
policy changes. (see Anthony Morris paper on the Fed’s creation of momentum in Eurodollar contracts)
 Hedging Pressures: There are risk-premia in the market created by the activity of forced hedgers.
Hedge sellers sell at lower than fair price, hedge buyers buy at higher than fair price. Speculators and
trend followers take the other side to reap benefits as adjustment is slow. (See papers by Spurgin and
Scheeneweis).
 Inventory Mismatch/Theory of Storage: Momentum is generated by slow adjustment of inventories to
demand and supply shocks, transferring commercial hedging premium to trend followers.
Whatever the reasons – the performance and persistence of returns of trend followers
warrants closer look, especially in periods of heightened risk.
For Educational Purposes Only
22
The Math of Trend vs. Mean Reverting Strategies (Source: A. Lo)
Momentum coefficient (+ for
momentum, - for mean
reversion) and Scaling Rule
have to be of same sign to
benefit from active
mangement. High Volatility
periods magnify this effect.
23
It is critical to identify trending vs. Mean-Reverting Markets
24
Testing for Momentum Commodities - Fit to Time Series Models to extract
persistence and momentum states.
Dependent Variable: W_1_COMDTY
Method: Least Squares
Date: 03/06/08 Time: 16:56
Sample (adjusted): 4/06/1990 1/31/2008
Included observations: 4650 after adjustments
Convergence achieved after 3 iterations
W_1_COMDTY=C(1)+C(2)*(W_1_COMDTY(-1)-C(1))
Positive autocorrelation says
this (wheat) is a momentum
commodity.
Variable
C(1)
C(2)
Coefficient Std. Error t-Statistic Prob.
4.25E-06 0.000133 0.032015
0.045517 0.014654 3.106115
R-squared 0.002071
Adjusted R-squared
0.001857
S.E. of regression
0.008641
Sum squared0.347047
resid
Log likelihood15496.22
Durbin-Watson
1.996628
stat
0.9745
0.0019
Mean dependent var 4.18E-06
S.D. dependent var 0.008649
Akaike info criterion -6.664179
Schwarz criterion
-6.661407
Hannan-Quinn criter.-6.663204
Negative-autocorrelation but not
significant for SPX.
Dependent Variable: SP1_CMDTY
Method: Least Squares
Date: 03/06/08 Time: 16:56
Sample (adjusted): 4/06/1990 1/31/2008
Included observations: 4650 after adjustments
Convergence achieved after 3 iterations
SP1_CMDTY=C(1)+C(2)*(SP1_CMDTY(-1)-C(1))
Variable
Coefficient Std. Error t-Statistic Prob.
C(1)
C(2)
0.000118 0.000116 1.011954
-0.026129 0.014673 -1.780722
R-squared 0.000682
Adjusted R-squared
0.000467
S.E. of regression
0.008136
Sum squared0.307654
resid
Log likelihood15776.35
Durbin-Watson
2.000064
stat
For Educational Purposes Only
25
0.3116
0.075
Mean dependent var 0.000118
S.D. dependent var 0.008138
Akaike info criterion -6.784666
Schwarz criterion
-6.781894
Hannan-Quinn criter. -6.78369
Basics of a Moving Average/Momentum System
 Decide on entry and exit rules, i.e. which set of averages to use and what the crossover rules are
 Decide on how to scale positions initially
– E.g. 2% of dollar capital per position for large risks or 10bp for small risks
 Decide on pyramiding or scaling up rule
– Rules decide how to add to winners and cut losers
– Usually based on dollar volatility where volatility is measured using actual data or implied option
volatilities
– The tradeoff is between large gains and risk of ruin
 Other choices to be made
– Is the system always “in” the market?
– Is there a max position size?
– Are there stops at portfolio level and individual security level?
– How to minimize transactions costs?
For Educational Purposes Only
26
Base Case (No Costs or Slippage) of a Simple and Stupid System (S-Cubed)
1000
Trends Basic Returns, 2/1992-5/2008
Return (bp)
Std Dev (bp)
Sharpe Ratio
800
400
3 yr
466
1272
0.37
Average Monthly Gain (%)
5 yr
51
1242
0.04
10 yr
541
1292
0.42
Since 1992
1000
1261
0.79
T-Stat
3.39
-2.26
55%
Average Monthly Loss (%)
Hit Ratio (monthly)
200
0
Max Drawdown (since 1991)
Calmar Ratio (3Yr)
-200
-400
-19.9%
0.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08
700
0%
Monthly Return Distribution
-5%
600
-10%
-15%
Drawdown
500
-20%
400
-25%
-30%
300
-35%
Growth of 100
-40%
200
-45%
For Educational Purposes Only
1/27/2008
1/27/2007
1/27/2006
1/27/2005
1/27/2004
1/27/2003
1/27/2002
1/27/2001
1/27/2000
1/27/1999
1/27/1998
1/27/1997
1/27/1996
1/27/1995
1/27/1994
-50%
1/27/1993
100
1/27/1992
bps
600
1 yr
1527
1513
1.01
Input target Return for 15
years scaled to
compare strategies
Realized Distribution
Normal Distribution
14%
12%
10%
8%
6%
4%
2%
0%
Mean: 84 bp
Std Dev: 368 bp
Skew: 0.61
-8 -6 -4 -2 0 2 4 6 8 10 12 14
%
27
Source: PIMCO
3.0
Pyramiding and Profit Stops With No Costs or Slippage: S Cubed + Scaling + Stops
• Go long/short based on momentum signals
• Pyramid up
• Upside volatility stop
3500
Trends Basic Returns, 2/1992-5/2008
Return (bp)
Std Dev (bp)
Sharpe Ratio
bps
3000
2500
1 yr
1729
1320
1.31
3 yr
1002
1141
0.88
5 yr
297
1095
0.27
10 yr
585
1094
0.53
Since 1992
1000
1072
0.93
2000
Average Monthly Gain (%)
1500
Average Monthly Loss (%)
Hit Ratio (monthly)
1000
T-Stat
2.84
-1.79
57%
3.6
500
Max Drawdown (since 1991)
Calmar Ratio (3Yr)
0
-500
-1000
600
Monthly Return Distribution
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 0%
550
-5%
500
-10%
450
-15%
Drawdown
400
-20%
350
-25%
300
-30%
Growth of 100
250
-35%
For Educational Purposes Only
1/27/2008
1/27/2007
1/27/2006
1/27/2005
1/27/2004
1/27/2003
1/27/2002
1/27/2001
1/27/2000
1/27/1999
1/27/1998
1/27/1997
1/27/1996
-50%
1/27/1995
100
1/27/1994
-45%
1/27/1993
-40%
150
1/27/1992
200
-16.5%
0.8
Realized Distribution
Normal Distribution
14%
12%
10%
8%
6%
4%
2%
0%
Mean: 84 bp
Std Dev: 309 bp
Skew: 0.74
-6 -4 -2 0 2 4 6 8 10 12 14
%
28
Source: PIMCO
Pyramiding and Profit Stops With 3 Basis Point Cost/Slippage: S Cubed + Scaling + Slippage + Stops
• Go long/short
• Pyramid Up
• Upside volatility stop
• Add Slippage
Trends Basic Returns, 2/1992-5/2008
4000
Return (bp)
Std Dev (bp)
Sharpe Ratio
3500
bps
3000
2500
2000
1 yr
1997
1641
1.22
3 yr
989
1417
0.70
Average Monthly Gain (%)
1500
500
10 yr
489
1359
0.36
Since 1992
1000
1332
0.75
T-Stat
3.56
-2.27
54%
Average Monthly Loss (%)
Hit Ratio (monthly)
1000
5 yr
130
1360
0.10
0
Max Drawdown (since 1991)
Calmar Ratio (3Yr)
-500
-1000
-1500
600
Monthly Return Distribution
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 0%
550
-5%
500
-10%
450
-23.3%
0.5
Realized Distribution
Normal Distribution
15%
-15%
Drawdown
400
-20%
350
-25%
300
-30%
250
-40%
Std Dev: 387 bp
5%
Skew: 0.77
0%
-8 -6 -4 -2 0 2 4 6 8 10121416
1/27/2008
1/27/2007
1/27/2006
1/27/2005
1/27/2004
1/27/2003
1/27/2002
1/27/2001
1/27/2000
1/27/1999
1/27/1998
1/27/1997
1/27/1996
1/27/1995
-50%
1/27/1994
100
1/27/1993
-45%
1/27/1992
150
For Educational Purposes Only
Mean: 84 bp
-35%
Growth of 100
200
10%
%
29
Source: PIMCO
2.8
Strategy Is Long Gamma (Realized Volatility)
Portfolio Risk is Broadly Balanced but puts
higher allocation to trending contracts
• Trend-following provides cheaper
gamma exposure than through
options (Kulp, Djupsjöbacka,
Estlander, 2005)
Average Allocated Capital (VaR)
9.0%
Natural Gas
Cocoa
8.0%
Hogs
Avg Return vs Avg Position Size
Live Cattle
7.0%
Wheat
Soybean
6.0%
3.0%
Heating Oil
Crude Oil
Silver
Gold
Copper
Dollar--Yen
Dollar-Euro
2.0%
Dollar-Canadian
Dollar-Pound
1.0%
Eurodollar
5Y Tsy
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
0.0%
10Y Tsy
Annual Return
4.0%
% of Portfolio
5.0%
Corn
25%
20%
15%
10%
5%
0%
R2 = 0.36
-5%
-10%
-15%
0.0%
0.2%
30Y Tsy
0.4%
0.6%
0.8%
Average Capital (% of Portfolio)
S&P 500
For Educational Purposes Only
30
Source: PIMCO
1.0%
Comparison with Trend-Following Benchmark (MLM or Mount Lucas Management Index)
Mt. Lucas (MLM) Index vs. Trends Basic (Non-Pyramiding)
Jan 1991 - May 2008
160
150
140
130
120
110
Trends Basic (non-pyramiding version)
MLM Index (ex interest)
100
F
eb
-9
A 2
ug
-9
2
F
eb
-9
A 3
ug
-9
3
F
eb
-9
A 4
ug
-9
4
F
eb
-9
A 5
ug
-9
5
F
eb
-9
A 6
ug
-9
6
F
eb
-9
A 7
ug
-9
7
F
eb
-9
A 8
ug
-9
8
F
eb
-9
A 9
ug
-9
9
F
eb
-0
A 0
ug
-0
0
F
eb
-0
A 1
ug
-0
1
F
eb
-0
A 2
ug
-0
2
F
eb
-0
A 3
ug
-0
3
F
eb
-0
A 4
ug
-0
4
F
eb
-0
A 5
ug
-0
5
F
eb
-0
A 6
ug
-0
6
F
eb
-0
A 7
ug
-0
7
F
eb
-0
8
90
Since inc. rtn
Std dev
Skew
Kurtosis
Max drawdown
Sharpe ratio
For Educational Purposes Only
Mt. Lucas
Trends Basic
Index
Non-pyramiding
2.4%
1.8%
5.6%
3.5%
(0.17)
0.55
2.64
0.29
-11.3%
-8.6%
0.44
0.52
31
Source: PIMCO
Optimizing Properly Makes System Robust to Volatility
Basic Sharpe Ratio, 1/1992-3/2008
Moving Average Length (days)
… risk-averse
investor can capture
high returns of 200400 day moving
averages while
using stops to
reduce volatility
Optimal parameter
values are {moving
average length,
stop threshold,
pyramid ceiling} =
{320, 4.5, 8}
Gradual change in
performance with
change in
parameter values
indicates robust
system with edge,
i.e. earning risk
premium
Upside Stop Threshold (times volatility)
For Educational Purposes Only
32
Source: PIMCO
Optimizing Properly Makes System Robust to Drawdowns
Minimum Calmar Ratio of Three Contiguous 5-Year Periods, 4/1993-3/2008
Moving Average Length (days)
Optimal
parameter values
are {MA length,
stop threshold,
pyramid ceiling}
= {320, 4.5, 8}
Upside Stop Threshold (times volatility)
For Educational Purposes Only
33
Source: PIMCO
Conclusion
 Local models calibrated to a mean-reverting world might still
work, BUT ignoring the emergence of momentum and fat-tails is
extremely dangerous in the new environment, especially given
the low cost of insuring against such outcomes.
 This does not require fancy quant modeling, only requires paying
attention to leverage, market structure, and deep risk-premium
markets.
34