Using Leverage to Offset the Negative Carry of Tail ...in your portfolio Low basis risk No gap risk...

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Using Leverage to Offset the Negative Carry of Tail Protection Across

Different Markets

November 2012

Disclaimer: The methods, tests and results described herein represent exploratory investigations done by Western Asset Management Company and are meant to stimulate discussion. Readers should not rely on these results and

should do their own verifications/investigations before making any decisions.

Robert Gingrich

This presentation is printed on 100% recycled paper

1

Why tail protection?

Some methods for tail protection

Carry and tail protection

Description of the numerical model

Results in different markets and time frames

Overview

2

Tail risk is risk of unusually large investment losses over a short period

Why is tail risk bad? In addition to the fact that losing money is always bad, tail risk can be

particularly harmful for portfolio managers/investors because a tail event tends to lead to

redemptions at the worst time (i.e., forced selling of risk assets right at the time when no one

wants risk assets). Conceptually, money managers are “short a put” on their own portfolio

Tail protection is an attempt to get “long a put” on a portfolio (conceptually)

Puts cost money (and have negative carry), and the balance between the amount of protection

one can get for a certain cost can be very unstable/hard to predict.

In this talk I’ll use a variety of historical simulations to get an estimate of what the

protection/cost tradeoff might be and what methods can improve the tradeoff

Why Tail Protection?

3

Methods to Create Tail Protection

Method Pros Cons

Find a broker and pay them to

insure your portfolio against a

certain level of loss

No “basis risk”

No gap risk

Fees are likely large

Lack of liquidity/depth

Counterparty risk

Buy puts on the main positions

in your portfolio

Low basis risk

No gap risk

Put markets may be illiquid/non-

existent

Hedging individual positions may be

over hedging/expensive

Sell out of or hedge positions

if/when they fall (e.g., CPPI or put

replication)

Low basis risk

Good liquidity if hedging with a

liquid index

Still has the negative carry of a put

You hold the gap risk, i.e., needs fast

execution in a tail event (e.g., Oct

1987)

Buy puts on a liquid index (e.g.,

SPX) that’s well correlated with

the active portfolio

Good liquidity/depth

No gap risk

Some basis risk

Buy alternative/exotic high

convexity/negatively correlated

instruments relying on “when

markets crash correlations go to

one” e.g., currency options,

credit tranches, variance swaps,

VIX options

May find a “diamond in the

rough” i.e., cheap security with

good tail protection properties

Some securities have good

liquidity (e.g., currency options,

TSY futures options)

Low gap risk

Basis risk. Correlations don’t actually

go to one. Every market crash is

different and while the direction of

some markets in a crash may be

predictable, the size of the move can

be hard to predict.

Most exotic options can’t be done in

size

4

S&P options are one of the oldest and most liquid options markets

People have been tracking the implied volatilities for 26 years (VIX/VXO) allowing a longer

historical analysis

One can obtain a volatility surface for maturities out several years and strikes 20% out of the

money going back over a decade

Good liquidity and depth means bid/ask costs are lower and a larger portfolio can be protected

The primary risk of most portfolios is usually well correlated to S&P 500

Why Focus on S&P 500 Index Puts?

5

Define carry as the return one makes if “nothing happens”

Puts (and calls) have negative carry or theta bleed as the time value decays away

Generally, one gets positive carry from strategies that take on risk and negative carry from

strategies the reduce risk like tail protection or buying a put

Claim: any method to cancel the negative carry of tail protection or create “carry neutral” tail

protection necessarily introduces some additional risk to the portfolio (if you know a way to

get positive carry without taking on risk please tell me…)

What Does Tail Protection Cost?

6

Some Methods for “Carry Neutral” Tail Protection

Method Risks Sell calls to fund puts Lose upside in a rally (costly in the long run)

Put skew works against you

Buy receiver swaption (betting that rates go down in a

crash) on a forward rate with significant curve rolldown.

Sensitive to a steepening of the curve

Basis risk

Sell at the money put and buy two out of the money puts for

no cost.

Additional bid/ask costs

Moderately down market

Put skew works against you

Lever up the main portfolio (increasing its positive carry) Basis risk

Flat market still has negative carry

7

We developed a strategy that has a well defined maximum cost (negative carry) and protection

that is persistent over time

Uses S&P 500 puts bought with a monthly percentage contribution from a “main” portfolio (e.g.,

US equities, HY bonds, world equities, EM equities, commodities)

Choose a maturity (e.g., 3M, 1Y) and a strike (% of current S&P 500) and roll the entire option

portfolio to the new maturity/strike each month

Monetization: if the value of the option portfolio exceeds a given percentage of the main

portfolio, the excess options will be sold and used to purchase more of the main portfolio

Leverage: a leverage value of 110% means that every month 10% of the main portfolio is

borrowed at the current risk free rate and reinvested in the main portfolio

An Algorithmic Strategy

8

Use volatility surface data going back to 2000 to capture a variety of bull and bear markets and

because there was liquidity during that time

Do a quadratic regression of each point on the surface against VIX

Use VIX/VXO (which goes back to 1986) to extrapolate the surface to earlier times

I emphasize historical simulation because the relationship between S&P 500 and its volatility

surface is complicated/has memory, i.e., I haven’t seem a model of the relationship between

the two that seems reliable over time

Volatility Surface

9

Volatility Surface

80%

100%

120%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1/121/4 1/2

1 2

3

stri

ke

tenor

Actual Surface 07 Oct 04 VIX=15%

0.00%-5.00% 5.00%-10.00%10.00%-15.00% 15.00%-20.00%

80%

100%

120%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1/121/4 1/2

1 2

3

stri

ke

tenor

Fitted surface 07 Oct 04 VIX=15%

0.00%-5.00% 5.00%-10.00% 10.00%-15.00%15.00%-20.00% 20.00%-25.00% 25.00%-30.00%

80%

100%

120%

0.00%5.00%10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%50.00%55.00%60.00%65.00%70.00%

1/121/4 1/2

1 2

3

stri

ke

tenor

Fitted Surface 05 Dec 08 VIX=60%0.00%-5.00% 5.00%-10.00% 10.00%-15.00%15.00%-20.00% 20.00%-25.00% 25.00%-30.00%30.00%-35.00% 35.00%-40.00% 40.00%-45.00%45.00%-50.00% 50.00%-55.00% 55.00%-60.00%

80%

100%

120%

0.00%5.00%10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%50.00%55.00%60.00%65.00%70.00%75.00%

1/121/4 1/2

1 2

3

stri

ke

tenor

Actual Surface 05 Dec 08 VIX=60%0.00%-5.00% 5.00%-10.00% 10.00%-15.00%

15.00%-20.00% 20.00%-25.00% 25.00%-30.00%

30.00%-35.00% 35.00%-40.00% 40.00%-45.00%

10

What Happens if We Buy Short-Dated (1 Month) Options?

Tail Fund

Cost bps/yr 250

Upfrtont cost 250

Max % portfolio 999.0%

Put Option

Strike 90%

Maturity (yr) 0.083

Portfolio

Start date 1/31/1986

Leverage factor 100%

S&P 500 TR No Protection With Protection

Excess log return (annual) 5.87% 3.27%

Stdev excess log return (annual) 15.93% 15.57%

Sharpe Ratio (annualized) 0.37 0.21

5% Value at Risk (monthly) -7.48% -8.41%

Average shortfall 5% (monthly) -11.07% -10.95%

Max drawdown -51% -54%

Increase in Sharpe -0.16

Ratio of shortfall 99%

Ratio of drawdowns 106%

-25

-20

-15

-10

-5

0

5

10

15

20

-25 -20 -15 -10 -5 0 5 10 15 20

Por

tfolio

Ret

urn

(%)

Market Return (%)

Return with Protection S&P 500 TR

Source: Western Asset, Bloomberg, Credit Suisse. As of 30 Sep 12

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-25

-20

-15

-10

-5

0

5

10

15

20

-30 -20 -10 0 10 20

Por

tfolio

Ret

urn

(%)

Market Return (%)



0

20

40

60

80

100

120

1982 1987 1993 1998 2004 2009 2014

Tai

l Val

ue (%

of M

ain)


What Happens if We Buy 1-Year Options but no Monetization/Leverage?

No Protection With Protection










Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio



12

-25

-20

-15

-10

-5

0

5

10

15

20

-30 -20 -10 0 10 20

Por

tfolio

Ret

urn

(%)

Market Return (%)



Monetize at a Level of 20% of the Main Portfolio

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio







5% Value at rRsk (monthly) -7.48% -4.44%



Increase in Sharpe 0.11



0

5

10

15

20

25

1982 1987 1993 1998 2004 2009 2014

Tai

l Val

ue (%

of M

ain)


13

Expected Return is Still Lower

0

20

40

60

80

100

120

140

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)

S&P 500 TR value Portfolio with Protection Cash Value


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0

20

40

60

80

100

120

140

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)



With Moderate Leverage

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio













15

What about Estimated Bid/Ask Spread?

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio



VIX Bid/Ask

15% 0.30%

60% 0.70%

Without Bid/Ask











With Bid/Ask











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0

20

40

60

80

100

120

140

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)



Can Leverage make up for Bid/Ask Spread?

VIX Bid/Ask

15% 0.30%

60% 0.70%

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio



Increasing leverage to 125%











Yes, but only barely…

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0

2

4

6

8

10

12

14

16

1995 1998 2001 2004 2006 2009 2012 2014

US

D (m

illio

ns)



What about a Different Time Frame?

VIX Bid/Ask

15% 0.30%

60% 0.70%

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio













Improved returns

without leverage

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-20

-15

-10

-5

0

5

10

15

-20 -15 -10 -5 0 5 10 15

Por

tfolio

Ret

urn

(%)

Market Return (%)

Return with Protection Barclays US High-Yield TR


High-Yield US Corporate (Correlation to S&P 500 is 58%)

VIX bid_ask

15% 0.30%

60% 0.70%

Tail Fund

Cost bp/yr 125

Upfrtont cost 125


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio







5% value at Risk (monthly) -3.33% -3.11%






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High-Yield US Corporate (Correlation to S&P 500 is 58%)

0

20

40

60

80

100

120

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)

Barclays US HY TR value Portfolio with Protection Cash Value


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World Equities (Correlation to S&P 500 is 69%)

VIX Bid/Ask

15% 0.30%

60% 0.70%

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio













-25

-20

-15

-10

-5

0

5

10

15

20

-25 -20 -15 -10 -5 0 5 10 15 20

Por

tfolio

Ret

urn

(%)

Market Return (%)

Return with Protection EAFE (World Equity) TR


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World Equities (Correlation to S&P 500 is 69%)

0

20

40

60

80

100

120

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)

EAFE (World Equity) TR value Portfolio with Protection Cash Value


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EM Equities (Correlation to S&P 500 is 67%)

VIX Bid/Ask

15% 0.30%

60% 0.70%

Tail Fund

Cost bps/yr 300

Upfrtont cost 300


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio










Increase in sharpe 0.00



-40

-30

-20

-10

0

10

20

30

-40 -30 -20 -10 0 10 20 30

Por

tfolio

Ret

urn

(%)

Market Return (%)

Return with Protection MSCI Emerging Market TR


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EM Equities (Correlation to S&P 500 is 67%)

0

50

100

150

200

250

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)

MSCI Emerging Market TR value Portfolio with Protection Cash Value


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Commodities (Correlation to S&P 500 is 16%)

VIX Bid/Ask

15% 0.30%

60% 0.70%

Tail Fund

Cost bps/yr 250

Upfrtont cost 250


Put Option

Strike 90%

Maturity (yr) 1.000

Portfolio













-40

-30

-20

-10

0

10

20

30

-40 -30 -20 -10 0 10 20 30

Por

tfolio

Ret

urn

(%)

Market Return (%)

Return with Protection GSCI (Commodity) TR


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Commodities (Correlation to S&P 500 is 16%)

0

20

40

60

80

100

120

140

160

1982 1987 1993 1998 2004 2009 2014

US

D (m

illio

ns)

GSCI (Commodity) TR value Portfolio with Protection Cash Value


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Starting the Simulation in 2000

Barcap US HY TR No Protection With Protection










EAFE (world equity) TR No Protection With Protection





Average Shortfall 5% (monthly) -13.17% -8.02%





MSCI Emerging Market TR No Protection With Protection










GSCI (Commodity) TR No Protection With Protection










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Appendix

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Biographies

Note: Western Asset experience reflects current position title and hire date.

ROBERT GINGRICH11 Years Experience

– Western Asset Management Company – Risk Modeler/ Manager, 2010-

– Pacific Investment Management Company – Financial Engineer, 2004-2010

– Jet Propulsion Laboratory – National Research Council Research Associate, 2001-2003

– California Institute of Technology, M.S., Ph.D. Theoretical Physics

– University of California, Santa Cruz, B.S., B.A.

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Risk Disclosure

For RFPs and

Presentations – US

© Western Asset Management Company 2012. This publication is the property of Western Asset Management Company and is intended for the sole use of

its clients, consultants, and other intended recipients. It should not be forwarded to any other person. Contents herein should be treated as confidential and

proprietary information. This material may not be reproduced or used in any form or medium without express written permission.

Past results are not indicative of future investment results. This publication is for informational purposes only and reflects the current opinions of Western

Asset Management. Information contained herein is believed to be accurate, but cannot be guaranteed. Opinions represented are not intended as an offer or

solicitation with respect to the purchase or sale of any security and are subject to change without notice. Statements in this material should not be considered

investment advice. Employees and/or clients of Western Asset Management may have a position in the securities mentioned. This publication has been

prepared without taking into account your objectives, financial situation or needs. Before acting on this information, you should consider its appropriateness

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Using Leverage to Offset the Negative Carry of Tail ...in your portfolio Low basis risk No gap risk...

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