Effectively Hedging the Interest Rate Risk of Wide Floating Rate Coupon Spreads

Bond issuers frequently immunize/hedge their interest rate exposure by means of interest rate swaps (IRS). The receiving leg matches all bond cash-flows, while the pay leg requires floating rate coupon payments of form LIBOR + a spread. The goal of hedging against interest rate risk is only achieved in full if the present value of this spread is zero. Using market data we show that under a traditional IRS hedging strategy an investor could still experience significant cash flow losses given a 1% shift in the underlying benchmark yield curve. We consider the instantaneous interest-rate risk of a bond portfolio that allows for general changes in interest rates. We make two contributions. The paper analyzes the size of hedging imperfections arising from the widening of the floating rate spread in a traditional swap contract and subsequently proposes two new practical, effective and analytically tractable swap structures; Structure 1: An Improved Parallel Hedge Swap, hedges against parallel shifts of the yield curve and Structure 2: An Improved Non-Parallel Hedge Swap, hedges against any movement of the swap curve. Analytical representations of these swaps are provided such that spreadsheet implementations are easily attainable.Portfolio Immunization; Interest Rate Swaps; Hedging; Floating Rate Spreads; Interest Rate Risk and Yield Curve

An Empirical Review of US Corporate Default Swap Valuation: The Implications of Functional Forms

This paper first develops a reduced form three-factor model for valuing credit default premia that is used to provide implicit prices which are then compared with market prices of credit default swaps to determine if swap rates adequately reflects market risks. This model extends Jarrow (2001) two-factor model by adding three new features to enhance the effectiveness of the model and add to the growing debate on the empirical pricing of credit default swap and the effectiveness of reduce form models. Firstly, the extended model retains Jarrow\u27s mean reverting properties but will be extended to be arbitrage free because of the use of a Cox-Ingersoll-Ross (CIR) process, thus improving the study\u27s ability to estimate the no arbitrage value of the CDS premium. Secondly, a liquidity variable is added to the model to capture the level of liquidity in the market, which conjectively impacts CDS valuation. Thirdly, the model now makes use of an expanded dataset of 53 companies and 15 months of daily data, which should lead to more robust estimators. The paper first develops the Jarrow (2001) two-factor mean reverting model of credit default swap valuation, with a constant recovery rate and a non-linear hazard function. Methodologies were then proposed for extending Jarrow\u27s model to a three-factor model so as to improve the effectiveness of the model in pricing the study\u27s short-term maturities. For the three-factor model the study assumed that CDS prices are a function of the spot rate of interest and CDS market liquidity. The study follows the assumption that default probabilities are implicit in the default swap prices and market and credit risks are correlated across companies and dependent on the state of the macro-economy. The study derived a closed-form expression for CDS prices, and examines its implications for pricing under both the two-product and three-product methodologies. Both models were empirically tested using daily CDS pricing data from December 31, 2002 to July 25th 2003. In both models the parameters of the hazard function were estimated using non-linear regression. Finally, empirical evidence of the model\u27s performance is presented

Stochastic Business Cycle Volatilities, Capital Accumulation and Economic Growth: Lessons from the Global Credit Market Crisis

The recent global economic downturn in a number of economies was preceded by rising credit market risk brought on by a massive financial market failure. This paper develops a small open economy model that analyzes the interaction of business cycle volatilities with capital accumulation and the subsequent impacts on economic growth. We use a stochastic dynamic programming model to test the central hypothesis that rising volatility shocks is an inhibitor to capital accumulation and subsequently economic growth. The model illustrates that traditional capital-based growth models which assume a constant capital stock are not consistent with the business cycle variation in capital accumulation. Furthermore, it appears that an increase in precautionary savings arising from a stochastic shock does not completely translate into productive capital investment need for growth, since risk-averse households will seek out risk-free government or foreign assets. We find this conclusion consistent with the empirical findings of Ramey et al (1995) and Badinger (2009) who both argued that, business cycle volatility is important to the growth discussion because of its robust net negative effect on output growth

Effectively Hedging the Interest Rate Risk of Wide Floating Rate Coupon Spreads

Bond issuers frequently immunize/hedge their interest rate exposure by means of interest rate swaps (IRS). The receiving leg matches all bond cash-flows, while the pay leg requires floating rate coupon payments of form LIBOR + a spread. The goal of hedging against interest rate risk is only achieved in full if the present value of this spread is zero. Using market data we show that under a traditional IRS hedging strategy an investor could still experience significant cash flow losses given a 1% shift in the underlying benchmark yield curve. We consider the instantaneous interest-rate risk of a bond portfolio that allows for general changes in interest rates. We make two contributions. The paper analyzes the size of hedging imperfections arising from the widening of the floating rate spread in a traditional swap contract and subsequently proposes two new practical, effective and analytically tractable swap structures; Structure 1: An Improved Parallel Hedge Swap, hedges against parallel shifts of the yield curve and Structure 2: An Improved Non-Parallel Hedge Swap, hedges against any movement of the swap curve. Analytical representations of these swaps are provided such that spreadsheet implementations are easily attainable

Credit Risk Dynamics in Response to Changes in the Federal Funds Target: The Implication for Firm Short-Term Debt

The recent credit crisis has raised a number of interesting questions regarding the role of the Federal Reserve Bank and the effectiveness of its expected and unexpected interventions in financial markets, especiallyduring the crisis, given its mandate. This paper reviews and evaluates the impact of expected and unexpected changes in the federal funds rate target on credit risk premia. The paper\u27s main innovation is the use of an ACH-VAR (autoregressive conditional hazard VAR) model to generate the Fed\u27s expected and unexpected monetary policy shocks which are then used to determine the effects of a Federal Reserve policy change on counterparty credit risk and more importantly short-term firm debt financing. The findings answer a longstanding question sought by researchers on the effect of policy makers\u27 announcements on firm debt financing. The results clearly show that the Federal Reserve influences short-term debt financing through the credit channel for both expansionary and contractionary monetary policies. In particular, we find that the growth in counterparty risk appears less responsive to anticipated responses in the Fed funds rate that fail to materialize than to an unanticipated increase in the federal funds rate. Finally, we also document that the results appear to validate the Feds interventions in financial markets to stem counterparty risk and to make liquidity more readily available to firms

Forecasting And Stress-Testing The Risk-Based Capital Requirements For Revolving Retail Exposures

This paper presents a tractable and empirically sound technique for generating stressed probabilities of default (PDs) which are then used to derive loss rates for the provisioning of a bank’s risk-based capital. This work is in response to the recent regulatory findings attributed to the Supervisory Capital Assessment Program (SCAP) stress tests of 2009 which revealed weaknesses in the existing regulatory and economic capital approaches. The SCAP projected losses of approximately $82.4 Billion in banks’ credit card portfolios for 2010, highlighting the need for better forecasting and stress testing of revolving retail exposures. This study proposes a timely model that will improve the ability of banks to determine the capital adequacy of revolving retail exposures. Using options theory we discuss why an obligor may default and produce estimates of expected losses from our stressed PDs so as to determine loss provisions. This method relies on the simulation of PD distributions via changes in selected macroeconomic variables and the card holder’s debt to income ratio (DTIR). The methodology offers the flexibility of being tractable and scalable to data in the issuer’s credit card portfolio by geography and credit quality of the obligor

Solving the Non-Linear Dynamic Asset Allocation Problem: Effects of Arbitrary Stochastic Processes and Unsystematic Risk on the Super Efficient Portfolio Space

In this paper we propose a methodology that we believe improves the effectiveness of several common assumptions underlying Modern Portfolio Theory's dynamic optimization framework. The paper derives a general outline of a stochastic nonlinear-quadratic control for analyzing and solving a non-linear mean-variance optimization problem. The study first develops and then investigates the role of unsystematic (credit) risk in this continuous time stochastic asset allocation model where the wealth generating process has a non-negative constraint. The paper finds that given unsystematic risk, wealth constraints and higher order moments the market price of risk is non-constant and the investor's optimal terminal return may be lower than previously indicated by a number of classical models. This result provides a convenient solution to practitioners seeking to evaluate competing investment strategies.Dynamic Optimization; Credit Risk; Mean-Variance Analysis; Linear Quadratic Control; Credit Default Swaps; Capital Market Line; Gram-Charlier expansion; unsystematic risks

The Impact of the FOMC\u27s Monetary Policy Actions on the growth of Credit Risk: the Monetary Policy - Liquidity Paradox

Credit risk is influenced by interest rates and market liquidity. This paper examines the direct and indirect impacts of unexpected monetary policy shifts on the growth of corporate credit risk, with the aim of quantifying the size and direction of the response. The results surprisingly indicate that monetary policy and liquidity impulses move counter to each other in their effects on credit risk ( The monetary policy-liquidity paradox ). The analysis indicates that while contractionary monetary policy creates tight money which subsequently leads to a slowing in the growth of credit risk and a reduction of liquidity in credit markets, reduced liquidity indirectly affects credit risk by accelerating its growth. The net effect of these transitory opposing forces generates the final impact on credit risk. An unexpected policy shifts is captured via a combination of the forward Fed fund rate curve and the Fed\u27s FOMC policy announcements. Following the approach of Bernanke and Kuttner (2005), Hausman and Wongswan (2006) who examined asset prices under FOMC announcements, the study found that the estimated credit risk responses to FOMC announcements vary across credit qualities. Hence the analyses indicates that a typical unanticipated 25 basis point cut in the target fed funds rate generally resulted in an acceleration in the growth of credit risk by 0.50 percent for AAA rated corporate grade debt, and by 3.5 percent for BB rated corporate debt. Moreover, the study found a direct effect of the FOMC\u27s policy instrument on market liquidity which had a significant effect on the growth in credit risk. The results indicate that a 1 percentage point increase in liquidity for AAA and CCC rated bonds resulted in a 0.7% and 52.45% decrease in the rate of growth in credit risk respectively