Nonparametric Sharpe Ratio Function Estimation in Heteroscedastic Regression Models via Convex Optimization

Seung-Jean Kim, Johan Lim, Joong-Ho Won
Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, PMLR 84:1495-1504, 2018.

Abstract

We consider maximum likelihood estimation (MLE) of heteroscedastic regression models based on a new “parametrization” of the likelihood in terms of the Sharpe ratio function, or the ratio of the mean and volatility functions. While with a standard parametrization the MLE problem is not convex and hence hard to solve globally, our parametrization leads to a functional that is jointly convex in the Sharpe ratio and inverse volatility functions. The major difficulty with the resulting infinite-dimensional convex program is the shape constraint on the inverse volatility function. We propose to solve the problem by solving a sequence of finite-dimensional convex programs with increasing dimensions, which can be done globally and efficiently. We demonstrate that, when the goal is to estimate the Sharpe ratio function directly, the finite-sample performance of the proposed estimation method is superior to existing methods that estimate the mean and variance functions separately. When applied to a financial dataset, our method captures a well-known covariate-dependent effect on the Shape ratio.

Cite this Paper

BibTeX
@InProceedings{pmlr-v84-kim18b, title = {Nonparametric Sharpe Ratio Function Estimation in Heteroscedastic Regression Models via Convex Optimization}, author = {Kim, Seung-Jean and Lim, Johan and Won, Joong-Ho}, booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics}, pages = {1495--1504}, year = {2018}, editor = {Storkey, Amos and Perez-Cruz, Fernando}, volume = {84}, series = {Proceedings of Machine Learning Research}, month = {09--11 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v84/kim18b/kim18b.pdf}, url = {https://proceedings.mlr.press/v84/kim18b.html}, abstract = {We consider maximum likelihood estimation (MLE) of heteroscedastic regression models based on a new “parametrization” of the likelihood in terms of the Sharpe ratio function, or the ratio of the mean and volatility functions. While with a standard parametrization the MLE problem is not convex and hence hard to solve globally, our parametrization leads to a functional that is jointly convex in the Sharpe ratio and inverse volatility functions. The major difficulty with the resulting infinite-dimensional convex program is the shape constraint on the inverse volatility function. We propose to solve the problem by solving a sequence of finite-dimensional convex programs with increasing dimensions, which can be done globally and efficiently. We demonstrate that, when the goal is to estimate the Sharpe ratio function directly, the finite-sample performance of the proposed estimation method is superior to existing methods that estimate the mean and variance functions separately. When applied to a financial dataset, our method captures a well-known covariate-dependent effect on the Shape ratio.} }
Endnote
%0 Conference Paper %T Nonparametric Sharpe Ratio Function Estimation in Heteroscedastic Regression Models via Convex Optimization %A Seung-Jean Kim %A Johan Lim %A Joong-Ho Won %B Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2018 %E Amos Storkey %E Fernando Perez-Cruz %F pmlr-v84-kim18b %I PMLR %P 1495--1504 %U https://proceedings.mlr.press/v84/kim18b.html %V 84 %X We consider maximum likelihood estimation (MLE) of heteroscedastic regression models based on a new “parametrization” of the likelihood in terms of the Sharpe ratio function, or the ratio of the mean and volatility functions. While with a standard parametrization the MLE problem is not convex and hence hard to solve globally, our parametrization leads to a functional that is jointly convex in the Sharpe ratio and inverse volatility functions. The major difficulty with the resulting infinite-dimensional convex program is the shape constraint on the inverse volatility function. We propose to solve the problem by solving a sequence of finite-dimensional convex programs with increasing dimensions, which can be done globally and efficiently. We demonstrate that, when the goal is to estimate the Sharpe ratio function directly, the finite-sample performance of the proposed estimation method is superior to existing methods that estimate the mean and variance functions separately. When applied to a financial dataset, our method captures a well-known covariate-dependent effect on the Shape ratio.
APA
Kim, S., Lim, J. & Won, J.. (2018). Nonparametric Sharpe Ratio Function Estimation in Heteroscedastic Regression Models via Convex Optimization. Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 84:1495-1504 Available from https://proceedings.mlr.press/v84/kim18b.html.

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