hedging efficiency

8/2/2019 Hedging Efficiency

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by - Ankesh Kumar Pandey

Hedging Efficiency


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Introduction

Hedging refers to a method of reducing the risk of losscaused by price fluctuation.

At a macroeconomic level it provides: Commercial Risk Mitigation

Price Discovery Integration of markets

At micro level it provides: Risk Management

Reduction in cost

Competitive Advantage

Primary Hedging instruments: Forwards, Futures,Options and Swaps.

Used individually or in combination to enhance expectedreturns.


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Hedging Risk

The effectiveness of hedging mainly depends on thebasis varying in favour of the hedgers.

Basis at time t1: b1 = S1 - F1

t2 : b2 = S2 - F2For a short hedger price realized for the asset= S2 + F1-F2 =

F1 + b2.

The uncertainty associated with b2 is called as basis risk.

For commodities basis risk is much higher as compared toinvestment assets.

Analysis of this variation in basis supplemented with

computation of profit and losses on hedges for a timeeriod is used to determine the efficienc of hed in .


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Degree of Efficiency of Hedge

E = (Ft Fo)/ (St So C) where (Ft Fo) < (St So C)or

E = 2 - (Ft Fo)/ (St So C) where (Ft Fo) > (St So C)

Where

(Ft Fo): Gains or losses in the futures market and

(St So C): Gains or losses in the spot market.

E < 0, hedging is aggravating

0< E < 100, hedging is under-compensating

E = 100, the hedging is perfect

100 < E < 200, hedging is over-compensating

E>200, hedging is ineffective


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Hedge Ratio and HedgingEfficiency

Two main approaches to hedge effectiveness :

o Risk reduction measure of effectivenessMinimization of risk associated with the cash market for

expected returns considered as the main objective ofhedging.

Applicable to Hedgers.

o

Risk return measure of effectivenessMinimization of risk as well as maximization of returns is

the objective behind hedging.

Applicable to investors.


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Ederington model (1979) In this model hedger is infinitely risk averse.

Minimum variance hedge model

Hedge Ratio =

Hedging Effectiveness =


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Standard Deviation method Reduction in standard deviation of portfolio

returns associated with a hedge.

Advantage of applying regardless of thetechnique employed to obtain the hedge ratio.

Greater the reduction in risk as measured by thestandard deviation of the hedged and unhedgedportfolios, greater is the effectiveness of the

hedge.


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Howard and DAntonios method

(1984, 1987)

It measures Hedging Effectiveness in term of risk andreturn.

Hedging Efficiency =


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Howard and DAntonios

method Flaw: Not necessary for the difference between

returns to be positive.

They proposed a revised measure of effectiveness:

This followed a superior model

Represented as the difference between the sharperatios of hedged and unhedged portfolios.


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Howard and DAntonios

method Advantage: It encapsulated both risk and return in

a single figure.

HBS < 0 : Excess return per unit risk of unhedgedportfolio exceeds that of the hedged portfolio.

HBS = 0 : No difference, but hedger will still beindifferent to hedge because of transaction costsinvolved.

HBS > 0 : Returns per unit of risk of hedged portfoliobeing greater than the unhedged portfolio.


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Lindhals method (1991) Takes into account the aspect of both risk and

return


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Other methods Gjerde (1987) two measures of hedge effectiveness,

including a risk return measure based on linear meanvariance preferences, which incorporates transactioncost and margins.

Cheung, Kwan, and Yip (1990), Lien and Luo (1993),and Lien and Shaffer (1999) minimize the mean-Ginicoefficient.

Eftekhari (1998), Lien and Tse (1998, 2000), andMattos,Garcia, and Nelson (2006) employ objectivesthat include minimization of the generalized

semivariance or higher lower partial moments.


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Chang, J. S. K. and L. Shanker (1987), A Risk-Return Measureof Hedging Effectiveness: A Comment, Journal of Financial andQuantitative Analysis

Empirical proofs of Howard DAntonio method as incorrectand improved it.

The proposed model was also later found to be having aflaw.

The Hedging measure becomes zero as the basis risk

approaches to zero

Ghosh, A. (1993), Hedging with Index Futures: Estimation andForecasting with Error Correction Model, Journal of FuturesMarkets

Study finds that hedge ratios estimated by traditionalmethods are underestimated because of misspecification.

Tests for presence or absence of co-integrating

relationship between spot and future prices and estimatesappropriate model to determine optimal hedge ratio.


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Horsnell, Brindle and Greaves (1995), The hedging efficiencyof crude oil markets.

Hedging performance in crude oil market isdependent on time structure of prices.

Variance reduction measures of hedging efficiencytend to over estimate efficiency as they overlook basisrisk inherent in time series.

Pennings and Meulenberg (1997), The hedging performance innew agricultural futures markets: A note.

Frequently used effectiveness measures do not takeinto consideration liquidity risk involved in trading.

Proposes new measure: an extension of Ederingtonsmethod.


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T.J.Brailsford, K.Corrigan and R.A.Heaney (2000),A comparison measure of hedging effectiveness: A casestudy using Australian index futures contract.

Key Findings:

Assessment of hedge effectiveness alters dependingon the measure/method employed.

Each measure falls within the Markowitz meanvariance framework.

Howard DAntonio (1987) and Lindahl (1991) sufferfrom flaws on empirical application.

Need for development of new measure ofeffectiveness that overcomes problems with existingmeasures.


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Yang and Awokuse (2003), Asset storability andhedging effectiveness in commodity futures market.

Key Findings:

Describes hedging to be effective only if mean futurereturns are zero.

R-squared value of OLS regression not always areliable indicator of hedging effectiveness.

Hedging effectiveness most appropriate if evaluatedon out of sample data.

GARCH framework works well for storablecommodities and not for non storable commodities.


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Alexander and Barbosa (2006), Effectiveness ofminimum variance hedging.

Key Findings:

Minimum variance hedging provides an out of samplehedging performance that is superior to nave futures

hedge. In commodity markets econometric models may

produce more efficient mean variance hedge ratios.Yet these models do not account for margins andtransaction costs.

Extends Ederingtons methodology by computing aconditional effectiveness measure that allows one toevaluate the dynamic characteristics of hedging.

More advanced the model greater is the variability in

hedge ratio and more frequently the portfolio has tobe rebalanced.


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Moon, Yu, Hong and Chen (2010), Risk managementof commodities and hedging strategies.

Key Findings:

Essential factor in hedging is the determination ofoptimal hedge ratio.

Studies econometric models and determines the onewhich offers maximum risk reduction on spot prices.

Spot and future prices contain time varyingdistribution and conditional co variance because ofwhich classical linear regression cannot be used.

Spot and future prices also exhibit long term co-integration hence an error correction model isappropriate.

GARCH model determines dynamic hedge ratios.


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Ederingtons method and

Advanced Hedge Models

Ru = ln (St+1/ St), considering continuouscompounding

Rh

= ln (St+1

/ St) h * ln (F

t+1/ F

t)

Variance of unhedged position = (s)2

Variance of Hedged position = (s)2 + h2(F)

2

2hsf

Hedging Effectiveness

E = 1 (Variance (Hedged)/ Variance(Unhedged))


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Econometric Methods forHedging Efficiency

Ordinary Least Squares (OLS): In this method changes in spotprice is regressed with changes in future price and the minimumvariance hedge ratio is the slope of the equation. The R-square valueof the model represents the hedging effectiveness.

RSt= + RFt + t

Vector Autoregressive models (VAR): It is preferred over OLSbecause it eliminates the problem of serial correlation among theresiduals and treats future prices as endogenous variable.

Hedge Ratio = h =


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Vector Error Correction Model (VECM): If the two series maybe co-integrated then error correction model is more appropriatewhich accounts for long run equilibrium between spot and futureprices.


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Econometric Methods forHedging Efficiency Multivariate GARCH model: Generalized Autoregressive

Conditional Hetroscedasticity model is applied to account forARCH effect in the residuals of error correction model. It isapplied for the calculation of dynamic hedge ratios which varyover time based on conditional variance and co-variance of spot

and future prices.

Time varying Hedge Ratio = h =


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OLS, VAR and VECM methods result in constant hedgeratio and are based on the assumptions that the spot andfuture price distributions are time in variant and noconditional covariance exist between them. GARCHmethod results in time varying hedge ratio and alsoconsiders covariance between spot and future prices.

Best model is the one which fulfils following assumptions: No auto-correlation between residuals. Residuals are normally distributed. There is no ARCH effect in residuals.

The model should also consider following conditions: Co-integration between spot and future prices. Conditional variance and co-variance of spot and future prices.

hedging efficiency

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