All seminars are held in 1011 Evans Hall at UC Berkeley, unless otherwise notified.
ABSTRACT: We study the competition of two strategic agents for liquidity in the benchmark portfolio tracking setup of Bank, Soner, Voss (2017), both facing common aggregated temporary and permanent price impact à la Almgren and Chriss (2001). The resulting stochastic linear quadratic differential game with terminal state constraints allows for an explicitly available open-loop Nash equilibrium in feedback form. Our results reveal how the equilibrium strategies of the two players take into account the other agent's trading targets: either in an exploitative intent or by providing liquidity to the competitor, depending on the ratio between temporary and permanent price impact. As a consequence, different behavioral patterns can emerge as optimal in equilibrium. These insights complement existing studies in the literature on predatory trading models examined in the context of optimal portfolio liquidation problems.
Preprint available on arXiv: arXiv:1911.05122.
ABSTRACT: In Gatheral et al. 2014, it has been shown that volatility exhibits a fractional behavior with a Hurst exponent $H < 0.5$, changing the typical perception of volatility. In their study, Gatheral and his co-authors used the realized volatility. In this analysis we explore the finding using two other estimators of spot volatility. The first set of estimators is known as range-based volatility estimators, and are calculated based on the open, close, high and low prices. We find that the log-volatility based on these estimators behaves like a fractional Brownian motion with $H$ lower than $0.1$. We also find that rough fractional stochastic volatility model (RFSV) is a relevant volatility model. Moreover, the prediction power of this model outperforms that of the AR, HAR and GARCH models in most cases. We revisit again this finding by studying implied volatility-based approximations of the spot volatility. Using at-the-money options on the S\&P500 index with short maturity, we are able to confirm that volatility is rough. The Hurst parameter found here, of order $0.3$, is slightly larger than that usually obtained from historical data. This is easily explained from a smoothing effect due to the remaining time to maturity of the considered options.
One paper can be found in the following link:
ABSTRACT: We propose an approximation of kernel ridge regression (KRR) based on random features and a multi-layer structure. KRR is popular in statistics and machine learning for nonparametric regressions over reproducing kernel Hilbert spaces. We study the minimum number of random features and the size of layers can be chosen for preserving minimax optimality of the approximate KRR estimate. We show that the multi-layer kernel machines only require O(n^1.5 log(n)) time and O(n log(n)) memory, which is significantly better compared to O(n^3) time and O(n^2) memory in computing KRR. For various classes of random features, we prove that the multilayer structure is more effective in reducing the computational complexity than the single-layer while keeping statistical minimax optimality. The analysis is supported by simulations and real data examples.
ABSTRACT: "I never blame myself when I’m not hitting. I just blame the bat and if it keeps up, I change bats. After all, if I know it isn’t my fault that I’m not hitting, how can I get mad at myself?" - Yogi Berra
We have all perceived streaks of hits and misses when watching sports. Often people will blame a magical streakiness that leads players to be "hot" or "cold." Are we to believe in this streakiness or should we believe Yogi Berra that there is no one to blame for strings of hits and misses, especially not the fault of the player themselves? In this talk, I will present a nonparametric approach to analyzing the existence of the hot hand in baseball as well as numerous other inference questions in baseball. I will discuss the advantages of a nonparametric approach over other parametric approaches. Our (joint work with Lisa Goldberg) analysis of player plate appearances in the 2018 Major League Baseball season provides no evidence of a batter hot hand.
ABSTRACT: Medium-horizon portfolio volatility predictions are of significant value to long-term investors, such as Defined Benefit pension plans, insurance companies, sovereign wealth funds, endowments, and individual owners of Defined Contribution pension plans. In this paper, we propose a simple, accurate, and efficient nonparametric method predict the conditional variance of log return (CVLR) at an arbitrary horizon. At a relatively short horizon, we introduce a regression framework for the stochastic volatility model. Beyond the short horizon, we study the properties of the dispersion function, which is defined as the ratio of the CVLR function and its converged stationary value, in the weak interaction case (e.g. for portfolios of large stocks). We provide tight upper and lower bounds of the CVLR function at longer horizons based on the results from the regression and analytical properties of the dispersion function. Empirical results suggest that our method is very promising. Finally, we provide a mean-field single-factor framework, validated by varied empirical evidence, for the optimization of portfolios defined by weights on multiple country indices.
ABSTRACT: In 1952, Harry Markowitz transformed finance by framing the portfolio construction problem as a tradeoff between the mean and the variance of return. This application of quadratic optimization is at the basis of breakthroughs such as the Capital Asset Pricing Model (CAPM) and Arbitrage Pricing Theory (APT). The classical Markowitz problem may be solved in closed form. However, when the portfolio weights face inequality constraints, one has to resort to a numerical optimization routine. This occurs for constrains as simple and as useful in practice as the long only constraint. We show that it is still possible to obtain closed form solution to this and related constrained problems when we assume a factor model. This approach provides significant gains in either accuracy or computational efficiency. Through our closed-form formulae we are also able to study the structure of the composition and the sensitivity of constrained Markowitz portfolios in terms of various macroeconomic variables. We illustrate our results will several case studies.