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


    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

  • 7/27/2019 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



    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. 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.

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


    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


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


    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),


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


    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