Using Leverage to Offset the Negative Carry of Tail Protection Across Different Markets

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1 Using Leverage to Offset the Negative Carry of Tail Protection Across Different Markets November 212 Robert Gingrich 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.

2 Overview Why tail protection? Some methods for tail protection Carry and tail protection Description of the numerical model Results in different markets and time frames 1

3 Why Tail Protection? 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 2

4 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/nonexistent 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 3

5 Why Focus on S&P 5 Index Puts? 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 2% 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 5 4

6 What Does Tail Protection Cost? 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 ) 5

7 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 6

8 An Algorithmic Strategy We developed a strategy that has a well defined maximum cost (negative carry) and protection that is persistent over time Uses S&P 5 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 5) 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 11% means that every month 1% of the main portfolio is borrowed at the current risk free rate and reinvested in the main portfolio 7

9 Volatility Surface Use volatility surface data going back to 2 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 5 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 8

strike strike strike strike Volatility Surface 8% 1% Fitted surface 7 Oct 4 VIX=15%.%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 2.%-25.% 25.%-3.% 12% 3 2 1/2 1 tenor 1/4 3.% 25.% 2.% 15.% 1.% 5.%.% 1/12 Fitted Surface 5 Dec 8 VIX=6%.

%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 12% 3 2 1/2 1 tenor 1/4 3.% 25.% 2.% 15.% 1.% 5.%.% 1/12 Actual Surface 5 Dec 8 VIX=6%.%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 2.%-25.% 25.%-3.% 3.%-35.% 35.%-4.% 4.

10 strike strike strike strike Volatility Surface 8% 1% Fitted surface 7 Oct 4 VIX=15%.%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 2.%-25.% 25.%-3.% 12% 3 2 1/2 1 tenor 1/4 3.% 25.% 2.% 15.% 1.% 5.%.% 1/12 Fitted Surface 5 Dec 8 VIX=6%.%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 2.%-25.% 25.%-3.% 3.%-35.% 35.%-4.% 4.%-45.% 45.%-5.% 5.%-55.% 55.%-6.% 8% 1% 12% 3 2 1/2 1 tenor 1/4 7.% 65.% 6.% 55.% 5.% 45.% 4.% 35.% 3.% 25.% 2.% 15.% 1.% 5.%.% 1/12 8% 1% Actual Surface 7 Oct 4 VIX=15%.%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 12% 3 2 1/2 1 tenor 1/4 3.% 25.% 2.% 15.% 1.% 5.%.% 1/12 Actual Surface 5 Dec 8 VIX=6%.%-5.% 5.%-1.% 1.%-15.% 15.%-2.% 2.%-25.% 25.%-3.% 3.%-35.% 35.%-4.% 4.%-45.% 8% 1% 12% tenor 1/2 1/4 75.% 7.% 65.% 6.% 55.% 5.% 45.% 4.% 35.% 3.% 25.% 2.% 15.% 1.% 5.%.% 1/12 9

11 Portfolio Return (%) What Happens if We Buy Short-Dated (1 Month) Options? Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 999.% Put Option Strike 9% Maturity (yr).83 Portfolio Start date 1/31/1986 Leverage factor 1% S&P 5 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) % Value at Risk (monthly) -7.48% -8.41% Average shortfall 5% (monthly) -11.7% -1.95% Max drawdown -51% -54% Increase in Sharpe -.16 Ratio of shortfall 99% Ratio of drawdowns 16% 2 Return with Protection S&P 5 TR Market Return (%) Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 1

12 Portfolio Return (%) Tail Value (% of Main) What Happens if We Buy 1-Year Options but no Monetization/Leverage? Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 999.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 1% No Protection With Protection Excess log return (annual) 5.87% 3.3% Stdev excess log return (annual) 15.93% 12.31% Sharpe Ratio (annualized) % Value at Risk (monthly) -7.48% -4.96% Average shortfall 5% (monthly) -11.7% -8.63% Max drawdown -51% -37% Increase in Sharpe -.1 Ratio of shortfall 78% Ratio of drawdowns 73% 2 Return with Protection S&P 5 TR Market Return (%) Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12

13 Portfolio Return (%) Tail Value (% of Main) Monetize at a Level of 2% of the Main Portfolio Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 1% No Protection With Protection Excess log return (annual) 5.87% 5.44% Stdev excess log return (annual) 15.93% 11.34% Sharpe Ratio (annualized) % Value at rrsk (monthly) -7.48% -4.44% Average shortfall 5% (monthly) -11.7% -6.82% Max drawdown -51% -27% Increase in Sharpe.11 Ratio of shortfall 62% Ratio of drawdowns 54% 2 Return with Protection S&P 5 TR Market Return (%) Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 12

14 USD (millions) Expected Return is Still Lower 14 S&P 5 TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 13

15 USD (millions) With Moderate Leverage 14 Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 11% No Protection With Protection Excess log return (annual) 5.87% 6.% Stdev excess log return (annual) 15.93% 12.73% Sharpe Ratio (annualized) % Value at Risk (monthly) -7.48% -5.12% Average shortfall 5% (monthly) -11.7% -7.76% Max drawdown -51% -31% Increase in Sharpe.1 Ratio of shortfall 7% Ratio of drawdowns 61% S&P 5 TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12

16 What about Estimated Bid/Ask Spread? Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 11% VIX Bid/Ask 15%.3% 6%.7% Without Bid/Ask No Protection With Protection Excess log return (annual) 5.87% 6.% Stdev excess log return (annual) 15.93% 12.73% Sharpe Ratio (annualized) % Value at Risk (monthly) -7.48% -5.12% Average shortfall 5% (monthly) -11.7% -7.76% Max drawdown -51% -31% Increase in Sharpe.1 Ratio of shortfall 7% Ratio of drawdowns 61% With Bid/Ask No Protection With Protection Excess log return (annual) 5.87% 5.16% Stdev excess log return (annual) 15.93% 13.28% Sharpe Ratio (annualized) % Value at Risk (monthly) -7.48% -5.27% Average shortfall 5% (monthly) -11.7% -8.17% Max drawdown -51% -39% Increase in Sharpe.2 Ratio of shortfall 74% Ratio of drawdowns 76% 15

17 USD (millions) Can Leverage make up for Bid/Ask Spread? Increasing leverage to 125% Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 125% VIX Bid/Ask 15%.3% 6%.7% No Protection With Protection Excess log return (annual) 5.87% 5.95% Stdev excess log return (annual) 15.93% 15.49% Sharpe Ratio (annualized) % Value at Risk (monthly) -7.48% -6.9% Average shortfall 5% (monthly) -11.7% -9.63% Max drawdown -51% -44% Increase in Sharpe.2 Ratio of shortfall 87% Ratio of drawdowns 86% 14 S&P 5 TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 Yes, but only barely

18 USD (millions) What about a Different Time Frame? Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/2 Leverage factor 1% VIX Bid/Ask 15%.3% 6%.7% No Protection With Protection Excess log return (annual).12%.38% Stdev excess log return (annual) 16.31% 1.5% Sharpe Ratio (annualized).1.4 5% Value at Risk (monthly) -8.37% -4.5% Average shortfall 5% (monthly) -1.76% -5.64% Max drawdown -51% -34% Increase in Sharpe.3 Ratio of shortfall 52% Ratio of drawdowns 67% S&P 5 TR value Portfolio with Protection Cash Value Improved returns without leverage Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12

19 Portfolio Return (%) High-Yield US Corporate (Correlation to S&P 5 is 58%) Tail Fund Cost bp/yr 125 Upfrtont cost 125 Max % portfolio 1.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 1% 15 VIX bid_ask 15%.3% 6%.7% Return with Protection No Protection With Protection Excess log return (annual) 4.94% 4.1% Stdev excess log return (annual) 9.5% 7.44% Sharpe Ratio (annualized) % value at Risk (monthly) -3.33% -3.11% Average shortfall 5% (monthly) -6.36% -4.92% Max drawdown -33% -24% Increase in Sharpe -.1 Ratio of shortfall 77% Ratio of drawdowns 72% Barclays US High-Yield TR Market Return (%) Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 18

20 USD (millions) High-Yield US Corporate (Correlation to S&P 5 is 58%) 12 Barclays US HY TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 19

21 Portfolio Return (%) World Equities (Correlation to S&P 5 is 69%) Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 1% 2 Return with Protection VIX Bid/Ask 15%.3% 6%.7% No Protection With Protection Excess log return (annual) 3.84% 2.64% Stdev excess log return (annual) 18.41% 15.22% Sharpe Ratio (annualized) % Value at Risk (monthly) -9.46% -7.22% Average shortfall 5% (monthly) % -9.17% Max drawdown -56% -43% Increase in Sharpe -.4 Ratio of shortfall 73% Ratio of drawdowns 76% EAFE (World Equity) TR Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 Market Return (%)

22 USD (millions) World Equities (Correlation to S&P 5 is 69%) 12 EAFE (World Equity) TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 21

23 Portfolio Return (%) EM Equities (Correlation to S&P 5 is 67%) Tail Fund Cost bps/yr 3 Upfrtont cost 3 Max % portfolio 24.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 12/31/1987 Leverage factor 1% 3 VIX Bid/Ask 15%.3% 6%.7% Return with Protection No Protection With Protection Excess log return (annual) 8.25% 6.79% Stdev excess log return (annual) 24.59% 2.51% Sharpe Ratio (annualized) % Value at Risk (monthly) % -9.59% Average shortfall 5% (monthly) -17.6% % Max drawdown -62% -57% Increase in sharpe. Ratio of shortfall 79% Ratio of drawdowns 92% MSCI Emerging Market TR Market Return (%) Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12

24 USD (millions) EM Equities (Correlation to S&P 5 is 67%) 25 MSCI Emerging Market TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 23

25 Portfolio Return (%) Commodities (Correlation to S&P 5 is 16%) Tail Fund Cost bps/yr 25 Upfrtont cost 25 Max % portfolio 2.% Put Option Strike 9% Maturity (yr) 1. Portfolio Start date 1/31/1986 Leverage factor 1% 3 Return with Protection VIX Bid/Ask 15%.3% 6%.7% No Protection With Protection Excess log return (annual) 3.4% 1.77% Stdev excess log return (annual) 2.72% 19.71% Sharpe Ratio (annualized) % Value at Risk (monthly) -9.88% -1.42% Average shortfall 5% (monthly) -14.5% % Max drawdown -68% -57% Increase in Sharpe -.7 Ratio of shortfall 91% Ratio of drawdowns 84% GSCI (Commodity) TR Market Return (%) Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12

26 USD (millions) Commodities (Correlation to S&P 5 is 16%) 16 GSCI (Commodity) TR value Portfolio with Protection Cash Value Source: Western Asset, Bloomberg, Credit Suisse. As of 3 Sep 12 25

27 Starting the Simulation in 2 Barcap US HY TR No Protection With Protection Excess log return (annual) 5.55% 5.2% Stdev excess log return (annual) 1.96% 8.51% Sharpe Ratio (annualized) % Value at Risk (monthly) -3.83% -3.15% Average shortfall 5% (monthly) -7.83% -5.54% Max drawdown -33% -24% Increase in Sharpe.8 Ratio of shortfall 71% Ratio of drawdowns 72% EAFE (world equity) TR No Protection With Protection Excess log return (annual).18%.59% Stdev excess log return (annual) 18.67% 12.94% Sharpe Ratio (annualized).1.5 5% Value at Risk (monthly) -1.34% -5.49% Average Shortfall 5% (monthly) % -8.2% Max drawdown -56% -42% Increase in Sharpe.4 Ratio of shortfall 61% Ratio of drawdowns 74% MSCI Emerging Market TR No Protection With Protection Excess log return (annual) 6.5% 6.3% Stdev excess log return (annual) 24.91% 18.2% Sharpe Ratio (annualized) % Value at Risk (monthly) -1.76% -8.17% Average shortfall 5% (monthly) % -1.1% Max drawdown -62% -41% Increase in Sharpe.11 Ratio of shortfall 61% Ratio of drawdowns 66% GSCI (Commodity) TR No Protection With Protection Excess log return (annual) 2.19% 1.63% Stdev excess log return (annual) 24.91% 23.1% Sharpe Ratio (annualized).9.7 5% Value at Risk (monthly) -13.1% -12.% Average shortfall 5% (monthly) % % Max drawdown -68% -57% Increase in Sharpe -.2 Ratio of shortfall 86% Ratio of drawdowns 84% 26

28 Appendix 27

29 Biographies ROBERT GINGRICH 11 Years Experience Western Asset Management Company Risk Modeler/ Manager, 21- Pacific Investment Management Company Financial Engineer, Jet Propulsion Laboratory National Research Council Research Associate, California Institute of Technology, M.S., Ph.D. Theoretical Physics University of California, Santa Cruz, B.S., B.A. Note: Western Asset experience reflects current position title and hire date. 28

30 Risk Disclosure Western Asset Management Company 212. 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 having regard to your objectives, financial situation or needs. It is your responsibility to be aware of and observe the applicable laws and regulations of your country of residence. 29

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