Time-Dependent Lottery

Definition

Time-dependent lottery starts from the one-month MAX payoff idea but evaluates it relative to the stock's own history rather than only against other stocks. Higher values indicate that the current lottery-like payoff sits unusually high versus the stock's own prior MAX realizations.

The underlying intuition is that investors may judge lottery-like excitement in a relative, time-dependent way. A stock can become especially attractive to lottery-seeking demand when its current spike looks extreme even by its own standards.

Inside the finance research stack, the representative implementation sorts the Russell 1000 cross-section on the time-dependent lottery score and compares the least lottery-like names against the most lottery-like names in a market-neutral spread.

Headline Summary

The first pass on this signal starts with a headline comparison across the sorted signal portfolios and the Russell 1000 benchmark.

Top Quintile contains the lowest-ranked names in the representative sort, while Bottom Quintile contains the highest-ranked names.

The baseline return path shows how the top-ranked bucket, bottom-ranked bucket, and long-short spread evolved through time in the representative Russell 1000 formation.

Start-Date Sensitivity

This section checks whether the signal depends too heavily on when the strategy begins. We restart the same baseline long-short construction every six months and compare how the excess return profile changes across those staggered entry dates.

Each row uses the same monthly market-weighted portfolio construction as the baseline sort, but starts the sample at the stated month and carries it through the final available month. Excess returns are measured relative to the 3-month U.S. Treasury bill rate, proxied by the FRED 'DTB3' series.

Sector Results

Sector results show whether the signal's long-short behavior is broad across the Russell 1000 or concentrated in a smaller set of industries.

The plot shows average monthly excess returns for sector-specific long-short implementations using the same baseline portfolio construction within each sector.

Path-Dependency Distribution

This section tests how sensitive the turnover-constrained implementation is to the path of portfolio formation. We run 1,000 different paths that each try to maximize the signal while allowing 10% turnover at each monthly rebalance.

The realized path starts from the actual T-B portfolio on the first initialization date. The other paths use random initializations on day one, then follow the same monthly turnover budget through time. The plot shows the distribution of average monthly excess returns across those random-start paths, with the realized path marked separately for comparison.