Three essays in financial econometrics

Yen, Yu-Min (2012) Three essays in financial econometrics. PhD thesis, London School of Economics and Political Science.

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Abstract

Sparse Weighted Norm Minimum Variance Portfolio. In this paper, I propose a weighted L1 and squared L2 norm penalty in portfolio optimization to improve the portfolio performance as the number of available assets N goes large. I show that under certain conditions, the realized risk of the portfolio obtained from this strategy will asymptotically be less than that of some benchmark portfolios with high probability. An intuitive interpretation for why including a fewer number of assets may be beneficial in the high dimensional situation is built on a constraint between sparsity of the optimal weight vector and the realized risk. The theoretical results also imply that the penalty parameters for the weighted norm penalty can be specified as a function of N and sample size n. An efficient coordinate-wise descent type algorithm is then introduced to solve the penalized weighted norm portfolio optimization problem. I find performances of the weighted norm strategy dominate other benchmarks for the case of Fama-French 100 size and book to market ratio portfolios, but are mixed for the case of individual stocks. Several novel alternative penalties are also proposed, and their performances are shown to be comparable to the weighted norm strategy. Bond Variance Risk Premia (Joint work with Philippe Mueller and Andrea Vedolin). Using data from 1983 to 2010, we propose a new fear measure for Treasury markets, akin to the VIX for equities, labeled TIV. We show that TIV explains one third of the time variation in funding liquidity and that the spread between the VIX and TIV captures flight to quality. We then construct Treasury bond variance risk premia as the difference between the implied variance and an expected variance estimate using autoregressive models. Bond variance risk premia display pronounced spikes during crisis periods. We show that variance risk premia encompass a broad spectrum of macroeconomic uncertainty. Uncertainty about the nominal and the real side of the economy increase variance risk premia but uncertainty about monetary policy has a strongly negative effect. We document that bond variance risk premia predict excess returns on Treasuries, stocks, corporate bonds and mortgage-backed securities, both in-sample and out-of-sample. Furthermore, this predictability is not subsumed by other standard predictors. Testing Jumps via False Discovery Rate Control. Many recently developed nonparametric jump tests can be viewed as multiple hypothesis testing problems. For such multiple hypothesis tests, it is well known that controlling type I error often unavoidably makes a large proportion of erroneous rejections, and such situation becomes even worse when the jump occurrence is a rare event. To obtain more reliable results, we aim to control the false discovery rate (FDR), an efficient compound error measure for erroneous rejections in multiple testing problems. We perform the test via a nonparametric statistic proposed by Barndorff-Nielsen and Shephard (2006), and control the FDR with a procedure proposed by Benjamini and Hochberg (1995). We provide asymptotical results for the FDR control. From simulations, we examine relevant theoretical results and demonstrate the advantages of controlling FDR. The hybrid approach is then applied to empirical analysis on two benchmark stock indices with high frequency data.

Item Type:	Thesis (PhD)
Additional Information:	© 2012 Yu-Min Yen
Library of Congress subject classification:	H Social Sciences > HB Economic Theory H Social Sciences > HG Finance
Sets:	Departments > Finance
URI:	http://etheses.lse.ac.uk/id/eprint/445

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