HEDGING INTEREST RATE RISK UNDER TERM STRUCTURE EFFECTS: AN APPLICATION TO FINANCIAL INSTITUTIONS

In this paper we investigate the use of the structured full rank model for hedging the balance sheet of a financial institution. Simulation results suggest that the optimal hedge is insensitive to changes in parameter estimates. In addition, we hedge a portfolio of Treasury bills using both the full information covariance matrix and the structured covariance matrix. We then contrast these results with those obtained from a duration-based model. Empirical results suggest that the structured full rank model is generally more effective in hedging applications than either the full information model or duration-based model.     

Risk minimization in stochastic volatility models: model risk and empirical performance

In this paper the performance of locally risk-minimizing delta hedge strategies for European options in stochastic volatility models is studied from an experimental as well as from an empirical perspective. These hedge strategies are derived for a large class of diffusion-type stochastic volatility models, and they are as easy to implement as usual delta hedges. Our simulation results on model risk show that these risk-minimizing hedges are robust with respect to uncertainty and misconceptions about the underlying data generating process. The empirical study, which includes the US sub-prime crisis period, documents that in equity markets risk-minimizing delta hedges consistently outperform usual delta hedges by approximately halving the standard deviation of the profit-and-loss ratio.     

Currency hedging for single-currency equity portfolios: Does cross-asset risk matter?

Foreign investors who are fully invested in a single-currency domestic equity portfolio are exposed to domestic equity risk, but also to currency risk. The standard approach to hedging the currency risk optimally is to estimate a single optimal hedge ratio, but this approach hedges only exchange rate risk, not cross-asset risk. We provide an alternative approach that estimates two optimal hedge ratios to adjust the currency exposures—one associated with the domestic currency and one associated with the foreign currency—and hedges both exchange rate risk and cross-asset risk. This alternative approach can significantly reduce risk.     

Minimum variance hedging when spot price changes are partially predictable

In many markets, changes in the spot price are partially predictable. We show that when this is the case: (1) although unbiased, traditional regression estimates of the minimum variance hedge ratio are inefficient, (2) estimates of the riskiness of both hedged and unhedged positions are biased upward, and (3) estimates of the percentage risk reduction achievable through hedging are biased downward. For natural gas cross hedges, we find that both the inefficiency and bias are substantial. We further find that incorporating the expected change in the spot price, as measured by the futures-spot price spread at the beginning of the hedge, into the regression results in a substantial increase in efficiency and reduction in the bias.     

Dynamic, nonparametric hedging of European style contingent claims using canonical valuation

The canonical valuation, proposed by Stutzer [1996. Journal of Finance 51, 1633–1652], is a nonparametric option pricing approach for valuing European-style contingent claims. This paper derives risk-neutral dynamic hedge formulae for European call and put options under canonical valuation that obey put–call parity. Further, the paper documents the error-metrics of the canonical hedge ratio and analyzes the effectiveness of discrete dynamic hedging in a stochastic volatility environment. The results suggest that the nonparametric hedge formula generates hedges that are substantially unbiased and is capable of producing hedging outcomes that are superior to those produced by Black and Scholes [1973. Journal of Political Economy 81, 637–654] delta hedging.     

Cross-commodity hedging for illiquid futures: Evidence from China's base metal futures market

This paper evaluates the effectiveness of cross-commodity hedging between China's base metal spot and futures markets, using daily data of metal spot and futures prices in the Shanghai Futures Exchange. The main findings suggest that, compared to unhedged spot portfolios, a naïve hedge increases risk exposure, while static and dynamic hedges can significantly reduce the risk of holding spot assets. Zinc futures and nickel futures outperform other base metal futures in individually hedging lead spot and tin spot respectively, while copper futures constitute a moderately optimal instrument to hedge both lead and tin spot assets.     

Reducing reporting risk: Designating foreign currency forward contracts as cash flow hedges

We present an example that compares the effects on earnings of designating a foreign currency forward contract as either a cash-flow or fair-value hedge of a foreign currency denominated receivable. Entities engaging in exchange transactions not denominated in their functional currency frequently enter into foreign currency forward contracts in order to mitigate their foreign exchange rate risk exposure. The aggregate effect on earnings of the transaction gain or loss on the foreign currency receivable and the gain or loss on the forward contract is known on the date the forward contract is initiated. The effect on each period’s earnings during the term of a forward contract designated as a cash-flow hedge is also known on the date the contract is initiated; whereas the effect on each periods’ earnings from a fair-value hedge cannot be determined until the respective balance sheet dates. Therefore, designating forward contracts as cash-flow hedges may suppress volatility in reported earnings compared to designating forward contracts as fair-value hedges. In addition, the reporting risk (the amount of uncertainty surrounding the pending measure of an item to be reported in the financial statements) is lower when a forward contract is designated as a cash-flow hedge relative to designating it as a fair-value hedge. This suggests foreign currency forward contracts designated as cash-flow hedges are more consistent with the purpose of hedge accounting: to mitigate the effects on earnings of applying different measurement criteria for the hedge and the hedged item.     

Local parametric analysis of derivatives pricing and hedging

A novel methodology for the analysis of derivatives pricing in incomplete markets is tested empirically. The methodology generates hedge ratios and derivatives prices. They are estimated from the correlation structure between the local co-movements of securities prices. First, the hedge ratios from a parsimonious complete-market model are estimated by fitting locally the changes in the derivatives and the underlying securities prices. Second, derivatives prices are obtained from the locally estimated hedge ratios. The methodology, referred to as local parametric estimation, is tested on a dataset of DAX index options and futures transactions from the computerized German Futures Exchange.     

Property and Inflation: The Hedging Characteristics of U.K. Commercial Property, 1967–1994

This paper examines the statistical similarities between U.K. commercial property capital and rental values and the price level. Our aim is to determine whether commercial property is an inflation hedge and, if so, what type of inflation it hedges against. To answer these questions, we use both a multivariate unobserved components model and structural vector autoregressions. We find that commercial property is an inflation hedge but only a weak one. More specifically, we find that property offers some form of partial hedge against changes in the underlying inflation rate but not to either temporary or permanent changes to the price level. We also find that capital values offer a stronger hedge than rental values and that industrial and retail property account for most of this hedging capacity. We find no evidence that property responds differently to high or low inflation but we do find capital and rental values respond more to unexpected inflation than anticipated price changes.     

SINGLE-FACTOR DURATION MODELS: CANADIAN TESTS

Single-factor duration models of bond returns are derived from an underlying stochastic process of the term structure of interest rates. It is shown that beta in these models is a function of the parameters of the stochastic process and of implied measures of duration. Using unsmoothed Canadian monthly prices on default-free government bonds, the single-factor duration model is found to perform well from 1963 to 1986, but the hypothesis of stationarity of the duration-based bond returns model for the period cannot be accepted. Some of the underlying stochastic processes imply stationary models and some of them imply nonstationary bond return models. The models of this paper open the door to a variety of linear bond return models having a strong theoretical support based on a theory of the stochastic motion of the term structure.     

Do commodities make effective hedges for equity investors?

The purpose of this paper is to evaluate whether commodities are effective hedges for equity holders. We employ three different methodologies to calculate time varying hedge ratios. First, we examine time-varying hedge ratios and how much portfolio risk can be reduced relative to a long position in the S&P 500. We calculate hedge ratios from realized variances and covariances; second, we estimate a recursive multivariate GARCH (BEKK) model and calculate the hedge ratios from the estimated covariances; and thirdly, we calculate the hedge ratios by estimating recursive OLS regressions. The results of our paper are very clear. First, commodities are not effective hedges for the S&P 500. Equity market investors and asset managers looking for a way to manage and reduce portfolio risk will be well advised to search for alternative hedges for the S&P 500 than commodities. Second, our results do not support the claim that commodities were a good hedge for the equity market during the financial crisis.     

An ex ante analysis of put-call parity

The authors previously had extended the theoretical put-call parity models developed by Stoll (1969) and Merton (1973) to include a dividend term. Ex post tests of the models were generally consistent with market efficiency, but a sufficient number of hedges had high enough returns to warrant analysis of ex ante results. The purpose of this study was to construct hedges 5 and 15 minutes after they were initially identified as having an ex post return in excess of $20 per hedge. The results indicate that mispriced options adjust and that economic profit is sensitive to the level of transaction costs and unlikely even for member firms.     

A generalized approach to optimal hedging with option contracts

In this paper, we develop a theoretical model in which a firm hedges a spot position using options in the presence of both quantity (production) and basis risks. Our optimal hedge ratio is fairly general, in that the dependence structure is modeled through a copula function representing the quantiles of the hedged position, and hence any quantile risk measure can be employed. We study the sensitivity of the exercise price which minimizes the risk of the hedged portfolio to the relevant parameters, and we find that the subjective risk aversion of the firm does not play any role. The only trade-off is between the effectiveness and cost of the hedging strategy.     

Auto-static for the people: risk-minimizing hedges of barrier options

We present and test a method for computing risk-minimizing static hedge strategies. The method is straightforward, yet flexible with respect to the type of contingent claim being hedged, the underlying asset dynamics, and the choice of risk-measure and hedge instruments. Extensive numerical comparisons for barrier options in a model with stochastic volatility and jumps show that the resulting hedges outperform previous suggestions in the literature. We also demonstrate that the risk-minimizing static hedges work in an infinite intensity Levy-driven model, and a number of controlled experiments illustrate that hedge performance is robust to model risk.     

Testing for constant hedge ratios in commodity markets: a multivariate GARCH approach

We develop a new multivariate generalized ARCH (GARCH) parameterization suitable for testing the hypothesis that the optimal futures hedge ratio is constant over time, given that the joint distribution of cash and futures prices is characterized by autoregressive conditional heteroskedasticity (ARCH). The advantage of the new parameterization is that it allows for a flexible form of time-varying volatility, even under the null of a constant hedge ratio. The model is estimated using weekly corn prices. Statistical tests reject the null hypothesis of a constant hedge ratio and also reject the null that time variation in optimal hedge ratios can be explained solely by deterministic seasonality and time to maturity effects.     

Which institutional investor types are the most informed?

We examine the informativeness of quarterly disclosed portfolio holdings across four institutional investor types: hedge funds, mutual funds, pension funds and private banking firms. Overweight positions outperform underweight positions only for hedge funds. By decomposing holdings and stock returns, we find that hedge funds are superior to other institutional investors both at picking industries and stocks and that they are better at forecasting long‐term as well as short‐term returns. Furthermore, our results show that hedge funds, mutual funds and pension funds are able to successfully time the market. The outperformance of hedge funds is not explained by a liquidity premium.     

TESTING HEDGE EFFECTIVENESS FOR FAS 133: THE VOLATILITY REDUCTION MEASURE

Although the authors of this article praise the spirit of the new FASB guidelines for hedge accounting, they find flaws in the recommended tests for determining if a hedge qualifies for such treatment. In some cases, the tests recommended by the FASB pass hedges that clearly should fail, and in others they fail hedges that should be accepted. In place of the recommended testing procedures, the authors propose the use of the volatility reduction measure (VRM)—a measure that is fully compliant with the spirit of the FASB's recommendations, while correcting their major shortfalls.
While the illustrations in this article are from the realm of fixed income, the VRM approach is applicable to any hedge, whether designated as "fair value" or "cash flow." Moreover, by expressing volatility in the units of the widely used "Value at Risk" measure, VRM establishes a natural link between accounting and risk management.     

Tractable hedging with additional hedge instruments

In an uncertain volatility model where only the stock and the money market account are traded, the upper price bound of a European claim is given by the solution of a Black-Scholes-Barenblatt equation. If an additional hedge instrument is available, the price bound can be tightened. This is also true if the set of admissible strategies is restricted to tractable strategies, which are defined as sums of Black-Scholes strategies. We study the structure of both strategies, the general strategies and the tractable strategies, when an additional convex instrument is available. For a call and a bullish vertical spread, we give closed-form solutions for the optimal tractable hedge when the additional instrument is a call option. We show that the position in the additional convex claim as well as the reduction in the price bounds allow to capture the amount of convexity risk a claim is exposed to.     

Arbitrage-free interval and dynamic hedging in an illiquid market

This paper derives two pricing PDEs for a general European option under liquidity risk. We provide two modified hedges: one hedge replicates a short option and the other replicates a long option inclusive of liquidity costs under continuous rebalancing. We identify an arbitrage-free interval by calculating the costs of the two hedges. Unlike in a setting with infinite overall transaction costs, the overall liquidity cost in our model is proved to be finite even under continuous rebalancing. Numerical results on option pricing and the moments of hedge errors of Black–Scholes and our modified hedges are also presented.     

BASIS VOLATILITY: IMPLICATIONS FOR HEDGING

Most hedges placed in futures markets must be lifted before contract expiration, which necessitates incurring “basis risk.” The focus of this paper is on quantifying such risk as a function of the timing of a hedge, its duration, distance from contract expiration, hedge life, and other market-observable variables. The development of basis-risk profiles provides a hedger with estimates of hedging risks that reasonably can be expected before the actual placement of hedges, thus serving as a useful input in the hedging decision.