Pedro Santa-Clara

Idiosyncratic Risk Matters

This paper takes a new look at the tradeoff between risk and return in the stock market. We find a significant positive relation between average stock variance and the return on the market. There is, therefore, a tradeoff between risk and return in the stock market, except that risk is measured as total risk, including idiosyncratic risk, rather than only systematic risk. Further, we find that the variance of the market by itself has no forecasting power for the market return. These relations persist after we control for macroeconomic variables known to forecast the stock market. We show that idiosyncratic risk explains most of the variation of average stock risk through time and it is idiosyncratic risk that drives the forecastability of the stock market. ∗We thank Michael Brandt, Shingo Goto, Monika Piazzesi, Martin Schneider, Avanidhar Subrahmanyam, Walter Torous, Rossen Valkanov, and especially Richard Roll, for their comments and suggestions. We have benefited from the comments of seminar participants at UCLA. †Anderson Graduate School of Management at UCLA, 110 Westwood Plaza, Box 951481, Los Angeles, CA 90095-1481, Phone: (310) 825-8160, E-mail: amit.goyal@anderson.ucla.edu. ‡Anderson Graduate School of Management at UCLA, 110 Westwood Plaza, Box 951481, Los Angeles, CA 90095-1481, Phone: (310) 206-6077, E-mail: pedro.santa-clara@anderson.ucla.edu. Idiosyncratic Risk Matters!

The Presidential Puzzle: Political Cycles and the Stock Market

The excess return in the stock market is higher under Democratic than Republican presidencies: 9 percent for the value-weighted and 16 percent for the equal-weighted portfolio. The difference comes from higher real stock returns and lower real interest rates, is statistically significant, and is robust in subsamples. The difference in returns is not explained by business-cycle variables related to expected returns, and is not concentrated around election dates. There is no difference in the riskiness of the stock market across presidencies that could justify a risk premium. The difference in returns through the political cycle is therefore a puzzle.

Simulated Likelihood Estimation of Diffusions with an Application to Exchange Rate Dynamics in Incomplete Markets

We present an econometric method for estimating the parameters of a diffusion model from discretely sampled data. The estimator is transparent, adaptive, and inherits the asymptotic properties of the generally unattainable maximum likelihood estimator. We use this method to estimate a new continuous-time model of the Joint dynamics of interest rates in two countries and the exchange rate between the two currencies. The model allows financial markets to be incomplete and specifies the degree of incompleteness as a stochastic process. Our empirical results offer several new insights into the dynamics of exchange rates.

The Relative Valuation of Caps and Swaptions: Theory and Empirical Evidence

Although traded as distinct products, caps and swaptions are linked by no-arbitrage relations through the correlation structure of interest rates. Using a string market model framework, we solve for the correlation matrix implied by the swaptions market and examine the relative valuation of caps and swaptions. The results indicate that swaption prices are generated by four factors and that implied correlations are generally lower than historical correlations. We find evidence that long-dated swaptions are priced inconsistently and that there were major distortions in the swaptions market during the hedge-fund crisis of late 1998. We also find that cap prices periodically deviate significantly from the no-arbitrage values implied by the swaptions market.

Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options

We use a novel pricing model to imply time series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex ante risk assessed by investors. Using a simple general equilibrium model, we translate the implied measures of ex ante risk into an ex ante risk premium. The average premium that compensates the investor for the ex ante risks is 70 higher than the premium for realized volatility. The equity premium implied from option prices is shown to significantly predict subsequent stock market returns.

Flexible Multivariate GARCH Modeling With an Application to International Stock Markets

The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk measurement, portfolio selection, and tests of asset pricing models, this is a very important problem in practice. Our model of choice is the Diagonal-Vech version of the Multivariate GARCH(1,1) model. The problem is that the estimation of the general Diagonal-Vech model model is numerically infeasible in dimensions higher than 5. The common approach is to estimate more restrictive models which are tractable but may not conform to the data. Our contribution is to propose an alternative estimation method that is numerically feasible, produces positive semi-definite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator to a number of existing ones.

Flexible Multivariate GARCH Modeling with an Application to International Stock Markets

This paper offers a new approach to estimating time-varying covariance matrices in the framework of the diagonal-vech version of the multivariate GARCH(1,1) model. Our method is numerically feasible for large-scale problems, produces positive semidefinite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator with a number of existing ones.

Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market

A machine for grinding objects, especially helical-or coil-type springs whose opposite ends are to be ground, includes a pair of rotary grinding discs having grinding surfaces spaced in axial direction from each other so as to define a work station. A plate-shaped element having a region mounted for turning movement relative to the work station intermediate the grinding surfaces is formed with a plurality of apertures, each of which is adapted to receive an object which is to be ground by contact with the grinding surfaces. Channels are provided in the plate-shaped element and connect the apertures with a source of fluid for supplying the latter to the apertures.

The dynamics of the forward interest rate curve: A formulation with state variables

An endless track is provided and has a main body made primarily of an elastomeric material and is adapted to be moved in an endless path having a longitudinal axis; and, the main body comprises an inside surface and a ground engaging surface with the ground engaging surface including a main surface and a plurality of ribs arranged in a cellular pattern defined by a plurality of cells with each of the cells having at least one rib thereof arranged at an acute angle with the axis. The ribs are adapted to provide continuous support for the track, resist sliding movement of the track transverse the axis, and confine flowable material, such as snow and mud, on which the track may be supported to minimize sinking thereof during operation of the track.

Beyond the Carry Trade: Optimal Currency Portfolios

We test the relevance of technical and fundamental variables in forming currency portfolios. Carry, momentum and reversal all contribute to portfolio performance, whereas the real exchange rate and the current account do not. The resulting optimal portfolio outperforms the carry trade and other naive benchmarks in an extensive 16 year out-of-sample test. Its returns are not explained by risk and are valuable to diversified investors holding stocks and bonds. Exposure to currencies increases the Sharpe ratio of diversified portfolios by 0.5 on average, while reducing crash risk. We argue that currency returns are an anomaly which is gradually being corrected as hedge fund capital increases. The appendix may be found here: http://ssrn.com/abstract=2771667.