## N'GOLO KONE PhD. Candidate

### Université de Montréal

## Working Papers

**A Multi-period Portfolio Selection in a Large Financial Market**, (*Job Market Paper)*

This paper addresses a multi-period portfolio selection problem when the number of assets in the financial market is large. Using an exponential utility function, the optimal solution is shown to be a function of the inverse of the covariance matrix of asset returns. Nonetheless, when the number of assets grows, this inverse becomes unreliable, yielding a selected portfolio that is far from the optimal one. We propose two solutions to this problem. First, we penalize the norm of the portfolio weights in the dynamic problem and show that the selected strategy is asymptotically efficient. Second, we penalize the norm of the difference of successive portfolio weights in the dynamic problem to guarantee that the optimal portfolio composition does not fluctuate wildly between periods. This second method helps investors to avoid high trading costs in the financial market by selecting stable strategies over time. Extensive simulations and empirical results confirm that our procedures considerably improve the performance of the dynamic portfolio.

**Test for Trading Costs Effect in a Portfolio Selection Problem with Recursive Utility**, with Marine Carrasco, (*Revision requested by the ** Journal of Financial Econometrics*)

This paper addresses a portfolio selection problem with trading costs on stock market. More precisely, we develop a simple GMM-based test procedure to test the significance of trading costs effect in the economy regardless of the form of the transaction cost. We also propose a two-step procedure to test overidentifying restrictions in our GMM estimation. In an empirical analysis, we apply our test procedures to the class of anomalies used in Novy-Marx and Velikov (2016). We show that transaction costs have a significant effect on investors behavior for most of anomalies. In that case, investors significantly improve the out-of-sample performance by accounting for trading costs.

**Optimal Portfolio Selection using Regularization**, with Marine Carrasco and Nérée Noumon

The mean-variance principle of Markowitz (1952) for portfolio selection gives disappointing results once the mean and variance are replaced by their sample counterparts. The problem is amplified when the number of assets is large and the sample covariance is singular or nearly singular. In this paper, we investigate four regularization techniques to stabilize the inverse of the covariance matrix: the ridge, spectral cut-off, Landweber-Fridman and LARS Lasso. These four methods involve a tuning parameter that needs to be selected. The main contribution is to derive a data-driven method for selecting the tuning parameter in an optimal way, i.e. in order to minimize the expected loss in utility of a mean-variance investor. The cross-validation type criterion takes a similar form for the four regularization methods. The resulting regularized rules are compared to the sample-based mean-variance portfolio and the naive 1/N strategy in terms of in-sample and out-of-sample Sharpe ratio and expected loss in utility. The main finding is that a regularization to covariance matrix drastically improves the performance of mean-variance problem and outperforms the naive portfolio especially in ill-posed cases, as demonstrated through extensive simulations and empirical study.

**Reinsurance demand and Liquidity Creation: A bi-causality analysis,** with Denise Desjardins, Georges Dionne HEC Montréal, (*submitted*)

We analyze the relation between insurers’ liquidity creation and reinsurance demand. Early theoretical contributions on liquidity creation propose that financial institutions enhance economic growth by creating liquidity in the economy. Liquidity creation means, financing relatively illiquid assets with relatively liquid liabilities. However, liquidity creation exposes insurers to financial risks. There is a trade-off between getting higher returns on risky investments and being able to compensate clients at a low cost when unexpected claims happen. Unexpected claims can be protected by reinsurance, which introduces a second trade-off between reinsurance demand and liquidity creation. This trade-off can be more important for insurers that have fewer diversification opportunities. Our main empirical results show positive bi-causal effects between liquidity creation and reinsurance demand for small insurers using GMM and FML methods of estimation. The links between the two activities are not significant for large insurers.

**Regularized Maximum Diversification Investment Strategy**

The maximum diversification portfolio as defined by Choueifaty (2011) depends on the vector of asset volatilities and the inverse of the covariance matrix of assets distribution. In practice, these two quantities need to be replaced by their sample counterparts. This results in estimation error which is amplified by the fact that the sample covariance matrix may be closed to a singular matrix in a large financial market, yielding a selected portfolio far from the optimal one with very poor performance. To address this problem, we investigate three regularization techniques, such as the ridge, the spectral cut-off, and the Landweber-Fridman, to stabilize the inverse of the covariance matrix in the investment process. These regularization schemes involve a tuning parameter that needs to be chosen. So, we propose a data-driven method for selecting the tuning parameter in an optimal way. The resulting regularized rules are compared to several strategies such as the most diversified portfolio, the target portfolio, the global minimum variance portfolio, and the naive 1/N strategy in terms of in-sample and out-of-sample Sharpe ratio.

## Works in Progress

**Return Predictability using Liquidity Variables and Volatility **