2014 Theses Doctoral

# New Quantitative Approaches to Asset Selection and Portfolio Construction

Since the publication of Markowitz's landmark paper "Portfolio Selection" in 1952, portfolio construction has evolved into a disciplined and personalized process. In this process, security selection and portfolio optimization constitute key steps for making investment decisions across a collection of assets. The use of quantitative algorithms and models in these steps has become a widely-accepted investment practice by modern investors. This dissertation is devoted to exploring and developing those quantitative algorithms and models.

In the first part of the dissertation, we present two efficiency-based approaches to security selection: (i) a quantitative stock selection strategy based on operational efficiency and (ii) a quantitative currency selection strategy based on macroeconomic efficiency. In developing the efficiency-based stock selection strategy, we exploit a potential positive link between firm's operational efficiency and its stock performance. By means of data envelopment analysis (DEA), a non-parametric approach to productive efficiency analysis, we quantify firm's operational efficiency into a single score representing a consolidated measure of financial ratios. The financial ratios integrated into an efficiency score are selected on the basis of their predictive power for the firm's future operating performance using the LASSO (least absolute shrinkage and selection operator)-based variable selection method. The computed efficiency scores are directly used for identifying stocks worthy of investment. The basic idea behind the proposed stock selection strategy is that as efficient firms are presumed to be more profitable than inefficient firms, higher returns are expected from their stocks. This idea is tested in a contextual and empirical setting provided by the U.S. Information Technology (IT) sector. Our empirical findings confirm that there is a strong positive relationship between firm's operational efficiency and its stock performance, and further establish that firm's operational efficiency has significant explanatory power in describing the cross-sectional variations of stock returns. We moreover offer an economic argument that posits operational efficiency as a systematic risk factor and the most likely source of excess returns of investing in efficient firms.

The efficiency-based currency selection strategy is developed in a similar way; i.e. currencies are selected based on a certain efficiency metric. An exchange rate has long been regarded as a reliable barometer of the state of the economy and the measure of international competitiveness of countries. While strong and appreciating currencies correspond to productive and efficient economies, weak and depreciating currencies correspond to slowing down and less efficient economies. This study hence develops a currency selection strategy that utilizes macroeconomic efficiency of countries measured based on a widely-accepted relationship between exchange rates and macroeconomic variables. For quantifying macroeconomic efficiency of countries, we first establish a multilateral framework using effective exchange rates and trade-weighted macroeconomic variables. This framework is used for transforming the three representative bilateral structural exchange rate models: the flexible price monetary model, the sticky price monetary model, and the sticky price asset model, into their multilateral counterparts. We then translate these multilateral models into DEA models, which yield an efficiency score representing an aggregate measure of macroeconomic variables. Consistent with the stock selection strategy, the resulting efficiency scores are used for identifying currencies worthy of investment. We evaluate our currency selection strategy against appropriate market and strategic benchmarks using historical data. Our empirical results confirm that currencies of efficient countries have stronger performance than those of inefficient countries, and further suggest that compared to the exchange rate models based on standard regression analysis, our models based on DEA improve on the predictability of the future performance of currencies.

In the first part of the dissertation, we also develop a data-driven variable selection method for DEA based on the group LASSO. This method extends the LASSO-based variable selection method used for specifying a DEA model for estimating firm's operational efficiency. In our proposed method, we derive a special constrained version of the group LASSO with the loss function suited for variable selection in DEA models and solve it by a new tailored algorithm based on the alternating direction method of multipliers (ADMM). We conduct a thorough evaluation of the proposed method against two widely-used variable selection methods: the efficiency contribution measure (ECM) method and the regression-based (RB) test, in the DEA literature using Monte Carlo simulations. The simulation results show that our method provides more favorable performance compared with its benchmarks.

In the second part of the dissertation, we propose a generalized risk budgeting (GRB) approach to portfolio construction. In a GRB portfolio, assets are grouped into possibly overlapping subsets, and each subset is allocated a risk budget that has been pre-specified by the investor. Minimum variance, risk parity and risk budgeting portfolios are all special instances of a GRB portfolio. The GRB portfolio optimization problem is to find a GRB portfolio with an optimal risk-return profile where risk is measured using any positively homogeneous risk measure. When the subsets form a partition, the assets all have identical returns and we restrict ourselves to long-only portfolios, then the GRB problem can in fact be solved as a convex optimization problem. In general, however, the GRB problem is a constrained non-convex problem, for which we propose two solution approaches. The first approach uses a semidefinite programming (SDP) relaxation to obtain an (upper) bound on the optimal objective function value. In the second approach we develop a numerical algorithm that integrates augmented Lagrangian and Markov chain Monte Carlo (MCMC) methods in order to find a point in the vicinity of a very good local optimum. This point is then supplied to a standard non-linear optimization routine with the goal of finding this local optimum. It should be emphasized that the merit of this second approach is in its generic nature: in particular, it provides a starting-point strategy for any non-linear optimization algorithms.

## Subjects

## Files

- Song_columbia_0054D_12026.pdf application/pdf 1.02 MB Download File

## More About This Work

- Academic Units
- Industrial Engineering and Operations Research
- Thesis Advisors
- Kachani, Soulaymane
- Degree
- Ph.D., Columbia University
- Published Here
- July 7, 2014