Asset Pricing

Man versus Machine Learning in Market Timing Portfolios (in progress)

By reconciling ex post and ex ante market timing behaviour of a portfolio manager, relative to a benchmark, we derive a market timing matrix operator (MTMO) that classifies and ranks market timing portfolios in large dimensional asset returns. This behaviour driven result is in contrast to data mining classifiers in machine learning. In fact, our MTMO is useful as a pretest estimator in penalized regression and machine learning classification schemes because it admits statistical tests. We applied the MTMO to 13,720 daily returns for the 52 stock price anomalies portfolios from Haddad,Kozak & Santosh (2020) (HKS) to capture cross-sectional variation in expected returns, and 332 intraday overnight stock returns from Pelger (2020). We find that the annualized cumulative returns for timers versus non timers over the sample period are 787.7% vs. 49.4% for anomalies; and 11.6% vs. 1.8% for intraday overnight returns. Fama-French size and value portfolios are included among significant market timers for anomalies, and we show how a transformed MTMO matrix (G) doubles the active returns from Fama-French 5-factors (Z-matrix).

Factor Pricing and Market Timing with benchmark perturbation (in progress)

Assuming that stock returns are predictable, and that there are tradeable factors that help explain equity risk premia, what is the limiting distribution of the empirical alpha process generated by a portfolio manager (PM) in that milieu, and how can we test whether the PM has market timing ability? We answer those questions with a new econometric test and market timing classifier for PMs' factor pricing and market timing ability, based on identifying restrictions on the core of active returns strategies, for an active portfolio and a benchmark. The test is based on a novel application of Tracy-Widom law to an endogenous covariance shrinkage estimator (call a G-matrix) decomposed into parts due to active portfolio timing, and benchmark perturbation. The shrinkage parameter is based on the spectrum of a transformed benchmark perturbation. We applied the test to 13,720 daily returns for the 52 stock price anomalies portfolios in Haddad, Kozak & Santosh (RFS, 2020) (HKS) to capture cross-sectional variation in expected returns, and 332 intraday overnight stock returns from Pelger (2020). The test separates statistically significant market timing portfolios from non timers. And the annualized cumulative returns for anomalies timers is 787.7% vs. 49.4% for non-timers; and 11.6% vs. 1.8% for intraday overnight returns. Fama-French size and value portfolios are included among significant market timers for HKS data, and we show how the G-matrix doubles the active returns from Fama-French 5-factors (Z-matrix). The likelihood ratio function for G versus Z matrices has an empirical Bayes feature that allows for a simple computation of the shrinkage constant between hedge factors covariance and benchmark covariance matrices compared to extant optimization approaches. The shrinkage matrix is useful as a pretest estimator in LASSO and machine learning classification schemes.

Market Instability, Investor Sentiment, and The Probability Weighting Functions Implied by Index Option Prices

How do financial markets switch from states of optimism to pessimism and vice versa? How does a seemingly stable financial market become unstable and crash? The answers lie in a natural experiment with risk based sources of probability weighting functions (pwfs), i.e., source functions, implied by S\&P 500 index option prices. Source functions reflect a ranking of assets and the weight investors place on each rank. We derive a novel behavioural process (hereinafter BELLE), from noise in decision making in the presence of risk, which describes switching behavior and (in)stability of the risk based source functions over time. The BELLE process characterizes critical tipping points for investor sentiment, probabilistic risk attitudes about tail events, and early warning signals of market instability and crash. Those critical values predict (1) state transitions in sentiment, (2) the degree of investors' optimism and pessimism in the market, and (3) mania, panic and crash for the market's irrational exuberance or high uncertainty about asset quality. The model is robust to different sources of risk. SLIDES

Asset Pricing With Myopic Loss Aversion To Credit Default (in progress)

Information flows in bond markets follow a Cauchy bridge process. We prove that positive jumps in the bridge process mimic a proxy for myopic loss aversion to credit default. Joint work with Sure Mataramvura.

4. Smart Beta and Alpha Representation Theorem

Arbitrage with Betas Of Hope and Fear (in progress)

We introduce a confidence representation theorem that splits the CBOE VIX with Gallup Daily Economic Confidence Index (GDECI) into distinct confidence sets of hope and fear, and then use the beta for each confidence set to identify arbitrage opportunities between the portfolios constructed in each of the two sets. Data show that daily returns on the Wilshire 5000 is enclosed in a convex [concave] envelope for VIX in over [under] confident regimes. Thereby upholding convex risk-return tradeoffs, and inducing a pseudo put-call parity decomposition of returns. Moreover, we find that returns on VIX are uncorrelated with the Fama-French hedge factors. This paves the way for constructing risk parity portfolios and augmenting the Fama-French model with a hedge factor tail risk strategy that is long variance futures and short spot variance when there is market fear, and short variance futures and long spot variance when confidence is high.