Futures Applications in Quantitative Portfolio Management

Jay Hymanjhyman@lehman.com

Quantitative Portfolio StrategiesFixed Income Research

March 9, 2006

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Applications of Futures in Portfolio Management

Implement a pure long (or short) view on interest rates

Basis Trading

Management of “excess return” in spread sectors

Index replication

“Portable alpha" strategies

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Extending Portfolio Duration

View: yields to rally => go long durationTypical way to increase portfolio duration may be to extend further out the curve:– Sell 2-year assets– Buy 10-year assetsProblem: This cash-neutral bullish position entails an (usually) unintended flattener The alternative: use leveraged strategies:– Buy bonds on repo to add duration– Go long futures contracts– Can be applied at one point on the curve or across the curve– Low transaction costs allow frequent adjustments

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Basis Trading

In most portfolio applications of futures:– Assume futures behave like a position in the underlying bonds – either a position in

the Cheapest-to-Deliver or using option-adjusted PVBP– Avoid delivery issues by rolling contracts before expiration– Futures-bond basis is just one more small source of portfolio volatility– Can be managed by occasional rebalancing

Basis Trading:– Focus on details of relationships between bonds and futures– Look for bonds that are rich or cheap relative to the contract– Capitalize on expected switches in the Cheapest-to-Deliver– Execute duration-neutral trades, bonds vs. futures contract

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Excess Returns

Corporate bonds and similar assets earn a spread over TreasuriesTotal returns on such assets can be divided into two parts:– Return on Treasuries with similar duration exposures– Excess return over TreasuriesTotal returns of all investment-grade bonds in a currency are highly correlated, and largely driven by the duration of the assetsPerformance in credit portfolios is often measured in terms of excess return

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Excess Returns Enhance Asset Class Comparisons

Total Returns (bp)Excess Returns

(bp)

Treas Corp MBS Corp MBS

Sep-05 -133 -161 -53 -9 -5

Oct-05 -78 -116 -70 -22 -32

Nov-05 48 59 33 7 -13

Dec-05 104 101 98 -15 22

Jan-06 -30 -21 32 24 43

Feb-06 15 45 47 26 42

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Computing Excess Return:Duration Buckets vs. Key Rate Durations

Duration buckets method:The Treasury market is broken down into 6-month duration bucketsThe bond’s duration is mapped onto these bucketsThe bond’s excess return is computed as the difference between its total return and the interpolation of two returns from the appropriate adjacent buckets

Key rate durations method:Hypothetical bonds are constructed at 6 points on the fitted off-the-run Treasury curve. 6 key rate durations are computed for the spread security analyzedA hedge portfolio is formed of the 6 Treasuries and cash to match the spread securities’ key rate durations and market valueThe bond’s excess return is the difference between total returns of the bond and the hedge portfolio

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Hedged Corporates earn Excess Return over Cash

Treasury Corporate FuturesExcess Return

Corporate Hedged

with FuturesCarry at risk-free deposit rate x x xCarry advantage of longer maturity (term premium) x x xCarry advantage of spread x x xRisk of treasury yield change x x xRisk of spread change x x x

Excess return framework creates a separation between two distinct decision processes:– Yield curve allocation (interest rate exposures)– Credit management decisions (sector and issuer exposures)A credit manager buys the bonds he likes, from available supplyYield curve (and currency) exposures can be managed separately using a futures overlay

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Index Replication with Derivatives

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Index Replication: Why Else Do Investors Want to Do It?Index Replication: Why do investors want to do it?

“Fill out” an existing portfolio

Tactical asset allocation

Asset allocation transitions

Management of cash inflows and outflows

“Portable Alpha” strategies

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Example: Replicating Index Returns Using Treasury Futures

Duration Cell Futures Contract

0.0 – 3.0 Two-year Note

3.0 – 5.0 Five-year Note

5.0 – 7.5 Ten-year Note

7.5 + Bond

Duration Cell Futures Contract

0.0 – 3.0 Two-year Note

3.0 – 5.0 Five-year Note

5.0 – 7.5 Ten-year Note

7.5 + Bond

Divide the index by duration into four cellsMatch market value and dollar duration of each cell with cash and one futures contractUse four Treasury futures contracts to match index exposures across the yield curve

Dur.Range

% ofIndex

IndexDur.

$ Dur.Target($mm)

FuturesContr.

Contr.$ Dur.($000s)

Num.Contr.

0–3 20.1 1.93 34 2-yr. 398 853–5 24.4 4.04 93 5-yr. 427 2175–7.5 28.0 6.18 166 10-yr. 607 2737.5+ 27.5 10.23 275 30-yr. 1,142 241

Dur.Range

% ofIndex

IndexDur.

$ Dur.Target($mm)

FuturesContr.

Contr.$ Dur.($000s)

Num.Contr.

0–3 20.1 1.93 34 2-yr. 398 853–5 24.4 4.04 93 5-yr. 427 2175–7.5 28.0 6.18 166 10-yr. 607 2737.5+ 27.5 10.23 275 30-yr. 1,142 241

Example: Replicating Corporate Index Return Using Treasury Futures

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Replicating Bond indices with derivative instruments

Treasury Futures

Interest-rate Swaps

TBAs (for MBS)

CDX + I. rate swaps (for Credit)

Select combinations of replicating instrumentsMatch index exposures to replicating instrument exposures (requires high quality analytics)…e.g. using key-rate durationsChoose rebalancing frequency

For details, see “Replicating the Lehman Brothers Aggregate Bond Index with Liquid Instruments”, Lehman Brothers 2004

Instruments

Replication Technique

Pros ConsLiquidity, Cost Margin, tracking error, less

maturity choicesWide maturity choice, Collateral, ISDAsGood for non-Treas. Very good tracking, Requires monthly rollsLow admin. costRaises carry return Collateral, ISDAs, notVery liquid perfect match for index

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– CDX improved simulated returns (through exposure to tightening credit spreads) and had the largest impact on reducing overall replication risk.

– Replacing replicating instruments for the UST and MBS with the indices themselves further reduced tracking error.

CDX was first issued in October 2003, and therefore we supplemented the CDX data by valuing portfolios of CDS instruments constructed from the issuers that composed the CDX basket as of October 2003, for the period from August 2002 to September 2003. We would caution that a look-forward bias is introduced by doing this. CDX-IG by construction comprises investment-grade-only issuers. In constructing a basket in October 2003 valued back to July 2002, we are certain to avoid some issuers that were downgraded over the period that may have been included in a basket actually constructed in 2002.

Replication Results for U.S. Aggregate IndexAugust 2002 – December 2005

Replication MethodologyMean

Outperformance (bp/m)

Empirical Realized

Tracking Error Volatility (bp/m)

Risk Model Tracking Error

Volatility Forecast (bp/m)

Treasury Futures (3.3) 18.8 20.0

Swaps (6.9) 16.1 18.0

Futures + Swaps (5.8) 15.9 14.7

Futures + Swaps + TBA (5.0) 15.2 12.8Futures + Swaps + TBA + CDX 0.9 8.8 8.4

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Replication Results for Global Aggregate Index August 2002 – December 2005

Replication strategy Tracking Error Mean Outperformance(b.p. per month) (b.p. per month)

Global Aggregate UnhedgedBond Futures 14.9 (4.7)Swaps 9.0 (4.8)

Swaps 8.7 (4.2)

Swaps + Futures 8.9 (4.4)Swaps + Futures + CDX/iTRAXX 6.3 (0.9)Swaps + Futures + CDX/iTRAXX + TBAs 6.6 (0.4)

Global Aggregate HedgedBond Futures 13.6 (4.9)

Swaps + Futures 8.6 (3.8)Swaps + Futures + CDX/iTRAXX 6.0 (0.3)Swaps + Futures + CDX/iTRAXX + TBAs 5.9 0.2

In prior periods, replication strategies have delivered out-performance…historic returns are not good predictors of future returns. However, prior tracking errors have also been somewhat higher. Expected tracking errors would be 2-4bp higher than stated.

In prior periods, replication strategies have delivered out-performance…historic returns are not good predictors of future returns. However, prior tracking errors have also been somewhat higher. Expected tracking errors would be 2-4bp higher than stated.

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RBISM Basket DescriptionWhat are RBI Baskets?

Replicating Bond Indices (RBI) baskets are portfolios of derivative instruments designed to track relevant Lehman indices. RBI Baskets have been developed using over a decade worth of research by Lehman’s Quantitative Portfolio Strategies group.

The basket is reconstituted each month, using a mechanistic algorithm, to match, as closely as possible, the term structure and spread exposures of the relevant Lehman index. The goal is to reduce the tracking error to the broader index to as small as possible.

RBI baskets can be created on any Lehman Index or custom index. The broader the Lehman Index desired to be replicated, the lower the likely tracking error.

RBI is a service mark of Lehman Brothers, patent pending

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Comparison between RBI baskets and full index swaps

Comparison

Full Aggregate Index Swaps RBI Baskets

No tracking error but low liquidity– Traded as a match book– $25-50 million for less than 1 yr maturities– Traded on month endsFull index swaps are difficult to unwind

Ability to trade any dayAbility to trade any sizeAbility to trade for any maturity Ability to customize by using different RBI basketsAbility to create derivative products (options, etc.) on RBI basketsInvestor takes tracking error risk

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An Introduction to Portable Alpha

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◆ Alpha is defined as the premium an investment/portfolio will earn in excess of that return due to its market exposure.

◆ Beta is defined as the return an investment will earn due to general exposure to the market or an index.

What is Portable Alpha?

A Portable Alpha Strategy is a product that marries the alpha from one strategy with the beta from a different strategy.

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What is Alpha?

Formally, Alpha is defined as the “Abnormal rate of return…in excess of what would be predicted by an equilibrium model like CAPM…” Bodie, Kane & Marcus, e.g.

Many investors think of alpha as the rate of return (on a portfolio) in excess of benchmark, i.e.

MP RR += 1α =PR Return on portfolio

Return on Market portfolio

εβα +∑+= MIP RR .2

=MR

=IβEffect on Asset I of the

return on the market

If some of Alpha is a return due to market exposure (e.g. overweight credit), its use in a portable alpha strategy may raise overall market exposure above 100%.

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Example: a fixed income manager wishes to transport their Alpha generated from bonds into an equity return

What is Portable Alpha? An example

Return on Alpha portfolio

Investor

Long S&P 500Index

Return on undesired Beta exposure

Return on desired Beta portfolio

Long Fixed Income Portfolio

Short Fixed Income Exposure

Return = S&P 500 return + Alpha

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Example: an Israeli fixed income manager wishes to market a global fixed income product, driven by Alpha generated from within the Israeli domestic bond market

Example: Shekel alpha on a global bond portfolio

Return on Alpha portfolio

Investor

Long (Replication of) Global Aggregate Index

Return on undesired Beta exposure

Return on desired Beta portfolio

Long Israeli Bond Portfolio

Short ShacharBond Futures

Return = Lehman Global Agg return + Shachar Bond Alpha

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What is the benefit of Portable Alpha, and why the recent interest?

◆ Portable alpha strategies can be used to achieve a variety of objectives:

◆ Separate Alpha from Beta

◆ Diversify Alpha sources

◆ Increase return potential for overall portfolio at time of low market returns

◆ Reasons for recent increase in portable alpha demand:

◆ Low returns to beta exposure

◆ Difficulty in finding alpha from “traditional” sources

◆ Need for more alpha in response to changing pension fund behavior

◆ Caveats

◆ How sustainable is alpha?

◆ Is alpha just unobservable beta?

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An example of the benefits of portable alpha:Increased portfolio efficiency

Allocations between stocks and bonds with and without portable alpha

Assumptions

Equ. F.I.

Return 8% 5%

Risk 15% 4%

Alpha 1.0% 0.5%

T.E. 2.0% 1.0%

Correlations

Alphas: 0.00Betas: 0.25

4.0%

4.5%

5.0%

5.5%

6.0%

6.5%

7.0%

7.5%

8.0%

8.5%

0.0% 5.0% 10.0% 15.0% 20.0%Risk

Ret

urn

Portable Equity Alpha Alpha allocation = Beta allocation

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Inverting the investment allocation process

◆ Traditional Model:

1. Asset allocation

2. Manager selection

◆ But, if alpha is so scarce maybe the process should be inverted:

1. Manager selection

2. Asset allocation

◆ Portable alpha allows the selection of alpha sources to be separated from beta

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Transforming the investment management process:Opportunities and threats

◆ Portable alpha allows a scalable process to be built

◆ Investment policy is designed to generate absolute return “alpha” portfolio

◆ Alpha portfolio can be combined with any replicable beta

◆ Manager can easily offer a large spectrum of fixed income services

◆ Portable alpha allows fixed income managers to broaden their product offerings:

◆ Transport alpha to create new fixed income product offerings

◆ Transport alpha to create new asset class offerings

◆ But, portable alpha can also allow other alpha generators to create fixed income offerings to compete with traditional offerings:

◆ Equity managers can offer higher alphas

◆ Hedge funds/Fund-of-Funds can offer very high alphas (maybe)

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Summary

Futures allow the decoupling of portfolio risks in many waysUsing futures overlays, each aspect of a global bond portfolio can be managed separately from the others:– Currency exposures– Yield curve exposures in multiple currencies, maturities– Spread over Treasury curveExample: overweight in US corporates, the EUR yield curve, and a

portfolio of emerging market currencies

Portable alpha strategies use futures to translate expertise in one market onto products benchmarked against another

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I, Jay Hyman, hereby certify (1) that the views expressed in this research report accurately reflect my personal views about any or all of the subject securities or issuers referred to in this report and (2) no part of my compensation was, is or will be directly or indirectly related to the specific recommendations or views expressed in this report.

Any reports referenced herein published after 14 April 2003 have been certified in accordance with Regulation AC. To obtain copies of these reports and their certifications, please contact Larry Pindyck (lpindyck@lehman.com; 212-526-6268) or Valerie Monchi (vmonchi@lehman.com; 44-(0)207-011-8035).

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