Correlation matrices are ubiquitous in finance. Some key applications include portfolio construction, risk management, and factor/style analysis. Correlation matrices are usually estimated from historical empirical observations or derived from historically estimated factors. It is widely...

When prices reflect all available information, they oscillate around an equilibrium level. This oscillation is the result of the temporary market impact caused by waves of buyers and sellers. This price behavior can be approximated through an Ornstein-Uhlenbeck (OU) process.Market makers provide...

Machine learning (ML) algorithms utilize the power of computers to solve tasks that are beyond the grasp of classical statistical methods. However, ML is often perceived as a black-box, hindering its adoption. This seminar demonstrates the use of Shapley values to interpret the outputs of ML...

The False Strategy theorem tells us that the optimal outcome of an unknown number of historical simulations is right-unbounded — with enough trials, there is no Sharpe ratio sufficiently enough to reject the hypothesis that a strategy is false. Given the ease with which one can use a computer...

We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs...

For large portfolio managers, a sequence of single-period optimal positions is rarely multi-period optimal. In particular, transaction costs can prevent large portfolio managers from monetizing most of their forecasting power. The solution is to compute the trading trajectory that comes...

High Frequency Trading is pervasive across all electronic financial markets. As algorithms replace an increasing number of tasks previously performed by humans, cascading effects similar to the Flash Crash of May 6th 2010 become more likely. In this study, we bring together a number of different...

We demonstrate a computer program that designs a portfolio consisting of common securities, such as the constituents of the S&P 500 index, that achieves any desired profile via in-sample backtest optimization. Unfortunately, the program also shows that these portfolios typically perform...

We carry out several test cases to illustrate how the Probability of Backtest Overfitting (PBO) performs under different scenarios. We also assess the accuracy of PBO using two alternative approaches (Monte Carlo Methods and Extreme Value Theory).The paper "The Probability of Backtest...

Proofs to the propositions in "Stop-Outs Under Serial Correlation".The paper "Stop-Outs Under Serial Correlation and 'The Triple Penance Rule" to which these Appendices apply is available at the following URL: "http://ssrn.com/abstract=2201302" http://ssrn.com/abstract=2201302