# alternative models for hedging yield curve risk an empirical comparison

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7/27/2019 Alternative Models for Hedging Yield Curve Risk an Empirical Comparison

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Swiss Finance InstituteResearch Paper Series N10 31Alternative Models For HedgingYield Curve Risk: An EmpiricalComparisonNicolaCARCANOUniversit della Svizzera Italiana and Bank VontobelHakim DALL'OUniversit della Svizzera Italiana and Swiss Finance Institute

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Established at the initiative of the Swiss Bankers' Association, the Swiss

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This paper can be downloaded without charge from the Swiss Finance

Institute Research Paper Series hosted on the Social Science Research

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http://ssrn.com/abstract=1635291

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ALTERNATIVE MODELS FOR HEDGING YIELD CURVE RISK: AN EMPIRICALCOMPARISON 1

Nicola Carcano

urich.Universit della Svizzera Italiana, Lugano and Bank Vontobel, Z

icola.carcano@sunrise.chn . Via Sole 14, CH 6977 Ruvigliana.

Hakim DallO

Universit della Svizzera Italiana, Lugano and Swiss Finance Institute.

hakim.dallo@usi.ch. Telephone:

Via Buffi 13, CH 6900 Lugano.

0041 058 666 4497 Fax: 0041 058 666 4734

ABSTRACTWe develop alternative models for hedging yield curve risk and test them by

hedging US Treasury bond portfolios through note/bond futures. We show that

traditional implementations of models based on principal component analysis,

duration vectors and key rate duration lead to high exposure to model errors and to

sizable transaction costs, thus lowering the hedging quality. Also, this quality varies

from one test case to the other, so that a clear ranking of the models is not possible.

We show that accounting for the variance of modeling errors substantially reduces

both hedging errors and transaction costs for all considered models. Also, this

allows to clearly rank these models: erroradjusted principal component analysis

ystematically and significantly outperforms alternative models.s

eywords: Yield curve risk, interest rate risk, immunization, hedging.K

EL codes: G11; E43J

1 We are grateful to Robert R. Bliss for having allowed us to use his yield curve estimates and to Ray Jireh

and Daniel Grombacher from the CME for having provided us with the relevant data underlying the bondfuture contracts. All errors or omissions should only be charged to the authors.

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mailto:nicola.carcano@sunrise.chmailto:nicola.carcano@sunrise.chmailto:nicola.carcano@sunrise.ch7/27/2019 Alternative Models for Hedging Yield Curve Risk an Empirical Comparison

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1. IntroductionWe define yield curve risk as the risk that the value of a financial asset might change

due to shifts in one or more points of the relevant yield curve. As such, it represents

one of the most widely spread financial risks impacting a very diversified range of

entities: not only financial institutions, like banks (both central and private),

insurance companies, portfolio managers, and hedge funds, but also pension funds,

real estate as well as many other industrial companies. Generalizing, we may say

that each institution having to match future streams of assets and liabilities is

exposed up to a certain extent to yield curve risk.

The simplest way to cope with yield curve risk is to match positive with

negative cashflows as much as possible. This approach of cash-flowmatchingis not

only theoretically straightforward, but also very effective in minimizing yield curve

risk. Unfortunately, the dates and the amounts of future cashflows are often subject

to constraints in practice, so that implementing an accurate cashflow matching

might not be possible.

When cashflow matching is not possible, socalled immunization techniques

are employed to manage yield curve risks. These techniques have the goal of making

the sensitivity of assets and liabilities to yield curve changes as much as possible

similar to each other. The key idea behind these techniques is that if assets and

liabilities react in a similar way to a change in the yield curve, the overall balance

sheet will not be largely affected by this change.

Originally, academicians and practitioners focused on the concept ofduration

firstly introduced by Macaulay (1938) for implementing immunization

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techniques. Duration represents the first derivative of the priceyield relationship of

a bond and was shown to lead to adequate immunization for parallel yield curve

shifts1. Accordingly, we can claim that the first models relying on duration were

targeting generic interest rate risk and not really yield curve risk, since the different

points of the yield curve were not allowed to move independently from each other.

The first step to move from generic interest rate risk to yield curve risk was

made with the introduction of the concept of convexity (see, for example, Klotz

(1985)). Convexity is related to the second derivative of the priceyield relationship

of a bond. However, the impact of interest rate changes taking place over a few days

or weeks is normally wellapproximated by duration. Accordingly, the importance of

convexity is commonly not related to its added value in the description of the price

yield relationship. As highlighted by Bierwag et al. (1987) and recently confirmed by

Hodges and Parekh (2006), this importance is due to the fact that immunization

strategies relying on duration and convexitymatching are consistent with plausible

twofac otor processes describing n nparallel yield curve shifts.

Later research took the argument supporting duration and convexity

matching even further: socalled M-square and M-vectormodels were introduced by

Fong and Fabozzi (1985), Chambers et al. (1988), and Nawalka and Chambers

(1997). Similarly as for convexity, most of these models relied on the observation

that furtherorder approximations of the priceyield relationship lead to

immunization strategies which are consistent with multifactor processes accurately

describing actual yield curve shifts. We will identify this class of models as duration

vector (DV) models. An accurate review of them is given in Nawalka and et. (2003),

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who also introduce a generalization of the DV approach identified as generalized

duratio vn ector(GDV).

A parallel development of immunization models relied on a statistical

description of the factors underlying yield curve shifts. This description was based

on a technique known as principal component analysis (PCA). PCA identifies

orthogonal factors explaining the largest possible proportion of the variance of

interest rate changes. Litterman and Scheinkman (1988) showed that a PCA relying

on 3 components allows to capture the three most important characteristics

displayed by yield curve shapes: level, slope, and curvature. Accordingly,

immunization models matching the sensitivity of assets and liabilities to these three

components should lead to highquality hedging.

A third class of widely used immunization models relies on the concept ofkey

rate duration (KRD) introduced by Ho (1992). These models explain yield curve

shifts based on a certain number of points along the curve the key rates and on

linear approximations based on time to maturity for the remaining rates.

Yield curve hedging techniques used in practice very often rely on one of the

three abovementioned classes of models. However, we are not aware of a conclusive

evidence on the relative performance of these three approaches2. Moreover, several

studies performing empirical tests of these hedging models reported puzzling

results. Particularly, models capable to better capture the dynamics of the yield

curve were not always shown to lead to bet