Hedging individual mortgage risk

This paper investigates the feasibility of an individual hedging the interest rate risk involved in planning to take out a mortgage at a future point in time. Simulation using market data indicates that a simple futures hedge reduces the variation in mortgage capacity by about one half. Expected mortgage capacity is very close to 100% of the original capacity at a very low cost. Hedging the individual mortgage with a put futures option is less effective in reducing downside risk and has a higher expected cost.     

Hedging labor income risk

We use a detailed panel data set of Swedish households to investigate the relation between their labor income risk and financial investment decisions. In particular, we relate changes in wage volatility to changes in the portfolio holdings for households that switched industries between 1999 and 2002. We find that households do adjust their portfolio holdings when switching jobs, which is consistent with the idea that households hedge their human capital risk in the stock market. The results are statistically and economically significant. A household going from an industry with low wage volatility to one with high volatility ceteris paribus decreases its portfolio share of risky assets by up to 35%, or $15,575.     

Hedging under multiple risk constraints

Motivated by the asset–liability management problems under shortfall risk constraints, we consider in a general discrete-time framework the problem of finding the least expensive portfolio whose shortfalls with respect to a given set of stochastic benchmarks are bounded by a specific shortfall risk measure. We first show how the price of this portfolio may be computed recursively by dynamic programming for different shortfall risk measures, in complete and incomplete markets. We then focus on the specific situation where the shortfall risk constraints are imposed at each period on the next-period shortfalls, and obtain explicit results. Finally, we apply our results to a realistic asset–liability management problem of an energy company, and show how the shortfall risk constraints affect the optimal hedging of liabilities.     

Hedging bonds subject to credit risk

This paper provides a simple and practical approach to hedging bonds that are subject to credit risk. Three new hedge ratios are derived and tested and the roles of basis risk and diversification is investigated. Empirical tests reveal that basis risk is an important factor in hedging corporate bonds. These tests identify a need for new interest rate derivatives where the underlying asset is subject to credit risk.     

The importance of the volatility risk premium for volatility forecasting

In this paper, we study the role of the volatility risk premium for the forecasting performance of implied volatility. We introduce a non-parametric and parsimonious approach to adjust the model-free implied volatility for the volatility risk premium and implement this methodology using more than 20 years of options and futures data on three major energy markets. Using regression models and statistical loss functions, we find compelling evidence to suggest that the risk premium adjusted implied volatility significantly outperforms other models, including its unadjusted counterpart. Our main finding holds for different choices of volatility estimators and competing time-series models, underlying the robustness of our results.     

Historic risk and implied volatility

This study extends the volatility prediction literature with (1) new intraday realized volatility measures and (2) various implied volatility indexes for commodities, currencies, and equities. Predicting volatility is important for academics, investors, and regulators. Applications range from forecasting stock and option returns to constructing early warning systems. Using twenty-three Chicago Board Options Exchange VIX indexes, as opposed to the common S&P 100 and S&P 500 equity indexes, we find a bidirectional lead-lag relationship between implied volatility and realized volatility. The lead-lag relationships are more robust and stronger using suggested intraday volatility measures than using the interday volatility measures that are common in the literature.     

Aggregate volatility risk: International evidence

Using a procedure analogous to that of Ang et al. (2006), this paper documents that aggregate volatility risk does not appear to be priced in European equity markets. Specifically, based on the 2002–2016 period (for which European stock return data is available), the price of aggregate volatility risk is not statistically different from zero. Analysis based on GARCH-class and high-frequency intraday data models support these results. Consequently, contrary to what has been reported in some studies that examine U.S. data, whether aggregate volatility risk is priced in equity markets is an open question.     

Hedging jump risk,expected returns and risk premia in jump-diffusion economies

This article presents a pure exchange economy that extends Rubinstein [Bell J. Econ. Manage. Sci., 1976, 7, 407–425] to show how the jump-diffusion option pricing model of Black and Scholes [J. Political Econ., 1973, 81, 637–654] and Merton [J. Financ. Econ., 1976, 4, 125–144] evolves in gamma jumping economies. From empirical analysis and theoretical study, both the aggregate consumption and the stock price are unknown in determining jumping times. By using the pricing kernel, we determine both the aggregate consumption jump time and the stock price jump time from the equilibrium interest rate and CCAPM (Consumption Capital Asset Pricing Model). Our general jump-diffusion option pricing model gives an explicit formula for how the jump process and the jump times alter the pricing. This innovation with predictable jump times enhances our analysis of the expected stock return in equilibrium and of hedging jump risks for jump-diffusion economies.     

Forecasting gold volatility with geopolitical risk indices

This paper tries to forecast gold volatility with multiple country-specific (GPR) indices and compares the role of combined prediction models and dimension reduction methods regarding the improvement of gold volatility prediction accuracy. For this purpose, GARCH-MIDAS model’s several extensions are used. We find firstly that most country-specific GPR indices have driving effects on gold volatility, and it makes sense to take forecast information from multiple country-specific GPR indices into account when forecasting gold volatility. The out-of-sample empirical results also indicate that the dimension reduction methods yield better predictions compared to the combined prediction models. In addition, dimension reduction technologies have excellent forecasting performance mainly during low gold volatility periods. Finally, our empirical findings are robust after changing the evaluation method, model settings, in-sample length and gold market.     

Asymmetric volatility and risk in equity markets

It appears that volatility in equity markets is asymmetric:returns and conditional volatility are negatively correlated.We provide a unified framework to simultaneously investigateasymmetric volatility at the firm and the market level and toexamine two potential explanations of the asymmetry: leverageeffects and volatility feedback. Our empirical application usesthe market portfolio and portfolios with different leverageconstructed from Nikkei 225 stocks. We reject the pure leveragemodel of Christie (1982) and find support for a volatility feedbackstory. Volatility feedback at the firm level is enhanced bystrong asymmetries in conditional covariances. Conditional betasdo not show significant asymmetries. We document the risk premiumimplications of these findings.     

The world price of jump and volatility risk

We study international integration of markets for jump and volatility risk, using index option data for the main global markets. To explain the cross-section of expected option returns we focus on return-based multi-factor models. For each market separately, we provide evidence that volatility and jump risk are priced risk factors. There is little evidence, however, of global unconditional pricing of these risks. We show that UK and US option markets have become increasingly interrelated, and using conditional pricing models generates some evidence of international pricing. Finally, the benefits of diversifying jump and volatility risk internationally are substantial, but declining.     

Determinants of stock market volatility and risk premia

Summary. We show the dynamics of diverse beliefs is the primary propagation mechanism of volatility in asset markets. Hence, we treat the characteristics of the market beliefs as a primary, primitive, explanation of market volatility. We study an economy with stock and riskless bond markets and formulate a financial equilibrium model with diverse and time varying beliefs. Agents states of belief play a key role in the market, requiring an endogenous expansion of the state space. To forecast prices agents must forecast market states of belief which are beliefs of others hence our equilibrium embodies the Keynes Beauty Contest. A market state of belief is a vector which uniquely identifies the distribution of conditional probabilities of agents. Restricting beliefs to satisfy the rationality principle of Rational Belief (see Kurz, 1994, 1997) our economy replicates well the empirical record of the (i) moments of the price/dividend ratio, risky stock return, riskless interest rate and the equity premium; (ii) Sharpe ratio and the correlation between risky returns and consumption growth; (iii) predictability of stock returns and price/dividend ratio as expressed by: (I) Variance Ratio statistic for long lags, (II) autocorrelation of these variables, and (III) mean reversion of the risky returns and the predictive power of the price/dividend ratio. Also, our model explains the presence of stochastic volatility in asset prices and returns. Two properties of beliefs drive market volatility: (i) rationalizable over confidence implying belief densities with fat tails, and (ii) rationalizable asymmetry in frequencies of bull or bear states.This research was supported by a grant of the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research (SIEPR). We thank Kenneth Judd for constant advice which was crucial at several points in the development of this work. We also thank Kenneth Arrow, Min Fan, Michael Magill, Carsten Nielsen, Manuel Santos, Nicholas Yannelis, Ho-Mou Wu and Woody Brock for comments on earlier drafts. The RBE model developed in this paper and the associated programs used to compute it are available to the public on Mordecai Kurzs web page at http://www.stanford.edu/ mordecai.This revised version was published online in January 2005 with corrections to the Cover date.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

Understanding the price of volatility risk in carry trades

This paper investigates the cross-sectional pricing ability of the short- and long-run components of global foreign exchange (FX) volatility for carry trade returns. We find a negative and statistically significant factor risk price for the long-run component, but no significant pricing effect due to the short-run volatility component. We also document that the dynamics of the long-run component of global FX volatility are related to US macroeconomic fundamentals. Our results are robust to various parametrizations of the volatility models used to obtain the volatility components and they are invariant to alternative asset pricing testing methodologies and sample periods.     

Hedging house price risk with futures contracts after the bubble burst

This paper extends the existing literature on managing house price risk. While previous work finds that a hedger would have reduced a large amount of variance in housing returns in Las Vegas, Nevada using Chicago Mercantile Exchange (CME) futures contracts, we show that neither static nor dynamic strategies would have maintained an effective hedge during the significant decline in housing prices. The inability to hedge house price risk using CME futures contracts ultimately calls into question the long-term viability of housing futures.     

Stochastic volatility and time-varying country risk in emerging markets

This study suggests an alternative method to estimate time-varying country risk. We first apply a new multivariate stochastic volatility (SV) model to a set of emerging stock markets. To estimate the SV model, we use a Bayesian Markov chain Monte Carlo simulation procedure. By applying the deviance information criterion, we show that the new model performs well relative to alternative multivariate SV models. We then compute the conditional betas for the different markets and compare the results with an often-used procedure based on multivariate GARCH models. We show that the new multivariate SV model more accurately captures the time-varying nature of country risk. The conditional betas show signs of large variations, indicating the importance of taking time-varying country risk into consideration when managing emerging market portfolios.     

The effects of Federal funds rate surprises on S&P 500 volatility and volatility risk premium

In this paper, we examine the effects of expected and surprise components in Federal funds target rate changes on realized and implied volatility. We find that surprise changes in the target rate significantly increase volatility. Consistent with the efficient market hypothesis, our analysis suggests that the expected component of a target rate change as well as the target rate change itself, do not significantly affect volatility. We also show that larger than expected decreases in the Federal funds target rate tend to lower the volatility risk premium.     

Rothschild-Stiglitz's definition of increasing risk and the relationship between volatility and risk premium

This paper analyzes the relationship between volatility and risk premium under the capital asset pricing model and Rothschild and Stiglitz's [Rothschild, M. and J.E. Stiglitz. (1970) Increasing risk I: a definition. Journal of Economic Theory, 2, 225-243.] definition of increasing risk. Especially examined are the conditions of the widely used assumption of constant correlation, which results in a linear relationship. Though both the above model and definition are widely known and accepted, their compatibility has remained unclear in the literature. According to this paper, they are in harmony with the linear relationship, if the correlation between a stock and the market portfolio is less than 0.7. Otherwise a conflict may arise.     

Hedging inflation risk in a developing economy: The case of Brazil

Inflation shocks are one of the pitfalls of developing economies and are usually difficult to hedge. This paper examines the optimal strategic asset allocation for a Brazilian investor seeking to hedge inflation risk at different horizons, ranging from one to 30 years. Using a vector-autoregressive specification to model inter-temporal dependency across variables, we measure the inflation hedging properties of domestic and foreign investments and carry out a portfolio optimisation. Our results show that foreign currencies complement traditional assets very efficiently when hedging a portfolio against inflation: around 70% of the portfolio should be dedicated to domestic assets (equities, inflation-linked (IL) bonds and nominal bonds), whereas 30% should be invested in foreign currencies, especially the US dollar and the euro.     

Robust estimation of historical volatility and correlations in risk management

Financial time series have two features which, in many cases, prevent the use of conventional estimators of volatilities and correlations: leptokurtotic distributions and contamination of data with outliers. Other techniques are required to achieve stable and accurate results. In this paper, we review robust estimators for volatilities and correlations and identify those best suited for use in risk management. The selection criteria were that the estimator should be stable to both fractionally small departures for all data points (fat tails), and to fractionally large departures for a small number of data points (outliers). Since risk management typically deals with thousands of time series at once, another major requirement was the independence of the approach of any manual correction or data pre-processing. We recommend using volatility t-estimators, for which we derived the estimation error formula for the case when the exact shape of the data distribution is unknown. A convenient robust estimator for correlations is Kendall's tau, whose drawback is that it does not guarantee the positivity of the correlation matrix. We chose to use geometric optimization that overcomes this problem by finding the closest correlation matrix to a given matrix in terms of the Hadamard norm. We propose the weights for the norm and demonstrate the efficiency of the algorithm on large-scale problems.