Quantitative Finance

The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming is proved in the general setting and a comparison result for possibly discontinuous viscosity solutions of the dynamic programming equation is provided. Detailed numerical experiments illustrate several properties of the optimal investment strategies.

We present explicit formulas - that are also computer code - for 101 real-life quantitative trading alphas. Their average holding period approximately ranges 0.6-6.4 days. The average pair-wise correlation of these alphas is low, 15.9%. The returns are strongly correlated with volatility, but have no significant dependence on turnover, directly confirming an earlier result based on a more indirect empirical analysis. We further find empirically that turnover has poor explanatory power for alpha correlations.

We propose a 4-factor model for overnight returns and give explicit definitions of our 4 factors. Long horizon fundamental factors such as value and growth lack predictive power for overnight (or similar short horizon) returns and are not included. All 4 factors are constructed based on intraday price and volume data and are analogous to size (price), volatility, momentum and liquidity (volume). Historical regressions a la Fama and MacBeth (1973) suggest that our 4 factors have sizable serial t-statistic and appear to be relevant predictors for overnight returns. We check this by using our 4-factor model in an explicit intraday mean-reversion alpha.

In this paper we study a risk-minimizing hedging problem for a semimartingale incomplete financial market where d+1 assets are traded continuously and whose price is expressed in units of the numéraire portfolio. According to the so-called benchmark approach, we investigate the (benchmarked) risk-minimizing strategy in the case where there are restrictions on the available information. More precisely, we characterize the optimal strategy as the integrand appearing in the Galtchouk-Kunita-Watanabe decomposition of the benchmarked claim under partial information and provide its description in terms of the integrands in the classical Galtchouk-Kunita-Watanabe decomposition under full information via dual predictable projections. Finally, we apply the results in the case of a Markovian jump-diffusion driven market model where the assets prices dynamics depend on a stochastic factor which is not observable by investors.

Matrix factorization was used to generate investment recommendations for investors. An iterative conjugate gradient method was used to optimize the regularized squared-error loss function. The number of latent factors, number of iterations, and regularization values were explored. Overfitting can be addressed by either early stopping or regularization parameter tuning. The model achieved the highest average prediction accuracy of 13.3%. With a similar model, the same dataset was used to generate investor recommendations for companies undergoing fundraising, which achieved highest prediction accuracy of 11.1%.

We compare three network portfolio selection methods; hierarchical clustering trees, minimum spanning trees and neighbor-Nets, with random and industry group selection methods on twelve years of data from the 30 Dow Jones Industrial Average stocks from 2001 to 2013 for very small private investor sized portfolios. We find that the three network methods perform on par with randomly selected portfolios.

As the Indian economy grows digitally and becomes more financially inclusive, more and more investors have started to invest in the Indian capital markets. The number of retail and institutional folios with Indian mutual fund schemes have continued to rise for the 74th consecutive month. This study considers 139 mutual fund schemes (98 equity schemes) and aims to ascertain the various metrics and parameters, retail and institutional investors continue to rely on to make investment recommendations. We compare these with the results from a data envelopment analysis model that generates an efficiency frontier based on an optimal risk, cost, and return trade-off. We further put forth an iteration of the DEA model, not only considering risk, cost, and return characteristics but also incorporating metrics such as the information ratio which hold significance for retail and institutional investors. We compare these results with traditional metrics and fund rankings published by established industry rating agencies.

The artificial segmentation of an investment management process into a workflow with silos of offline human operators can restrict silos from collectively and adaptively pursuing a unified optimal investment goal. To meet the investor's objectives, an online algorithm can provide an explicit incremental approach that makes sequential updates as data arrives at the process level. This is in stark contrast to offline (or batch) processes that are focused on making component level decisions prior to process level integration. Here we present and report results for an integrated, and online framework for algorithmic portfolio management. This article provides a workflow that can in-turn be embedded into a process level learning framework. The workflow can be enhanced to refine signal generation and asset-class evolution and definitions. Our results confirm that we can use our framework in conjunction with resampling methods to outperform naive market capitalisation benchmarks while making clear the extent of back-test over-fitting. We consider such an online update framework to be a crucial step towards developing intelligent portfolio selection algorithms that integrate financial theory, investor views, and data analysis with process-level learning.

Utility and risk are two often competing measurements on the investment success. We show that efficient trade-off between these two measurements for investment portfolios happens, in general, on a convex curve in the two dimensional space of utility and risk. This is a rather general pattern. The modern portfolio theory of Markowitz [H. Markowitz, Portfolio Selection, 1959] and its natural generalization, the capital market pricing model, [W. F. Sharpe, Mutual fund performance , 1966] are special cases of our general framework when the risk measure is taken to be the standard deviation and the utility function is the identity mapping. Using our general framework, we also recover the results in [R. T. Rockafellar, S. Uryasev and M. Zabarankin, Master funds in portfolio analysis with general deviation measures, 2006] that extends the capital market pricing model to allow for the use of more general deviation measures. This generalized capital asset pricing model also applies to e.g. when an approximation of the maximum drawdown is considered as a risk measure. Furthermore, the consideration of a general utility function allows to go beyond the "additive" performance measure to a "multiplicative" one of cumulative returns by using the log utility. As a result, the growth optimal portfolio theory [J. Lintner, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, 1965] and the leverage space portfolio theory [R. Vince, The Leverage Space Trading Model, 2009] can also be understood under our general framework. Thus, this general framework allows a unification of several important existing portfolio theories and goes much beyond.

This paper demonstrates how to apply machine learning algorithms to distinguish good stocks from the bad stocks. To this end, we construct 244 technical and fundamental features to characterize each stock, and label stocks according to their ranking with respect to the return-to-volatility ratio. Algorithms ranging from traditional statistical learning methods to recently popular deep learning method, e.g. Logistic Regression (LR), Random Forest (RF), Deep Neural Network (DNN), and the Stacking, are trained to solve the classification task. Genetic Algorithm (GA) is also used to implement feature selection. The effectiveness of the stock selection strategy is validated in Chinese stock market in both statistical and practical aspects, showing that: 1) Stacking outperforms other models reaching an AUC score of 0.972; 2) Genetic Algorithm picks a subset of 114 features and the prediction performances of all models remain almost unchanged after the selection procedure, which suggests some features are indeed redundant; 3) LR and DNN are radical models; RF is risk-neutral model; Stacking is somewhere between DNN and RF. 4) The portfolios constructed by our models outperform market average in back tests.