The Calendar Ensemble: Building an Event-Driven Alpha Overlay
In the previous article, we established that the Sharpe ratio is the single most important number in portfolio construction. Variance drag scales with the square of volatility, which means a high-Sharpe portfolio can tolerate leverage, survive decumulation, and compound wealth far more efficiently than a low-Sharpe one. We also hinted at something more subtle: strategies with positively skewed return distributions behave differently under leverage than symmetric ones. The skewness term in the geometric growth expansion partially offsets variance drag, pushing the optimal leverage point further out. This article presents a concrete example of such a strategy—one that is transparent, mechanistic, and adds measurable alpha to the core portfolio.
The core of our approach remains the three-asset inverse volatility portfolio: VTI, TLT, and GLD, weighted by inverse trailing volatility, with an 8% volatility target. That portfolio delivered a Sharpe ratio of about 1.0 over the past two decades. What follows is not a replacement for that foundation, but an overlay—a set of calendar-driven trades that exploit well-documented market anomalies around holidays and central bank meetings.
The Pre-Holiday Effect
The pre-holiday effect in equities is one of the oldest documented anomalies in finance. The basic observation is that stock returns in the trading days immediately before major market closures tend to be significantly higher than on ordinary days. The mechanism is straightforward: institutional selling pressure drops before long weekends. Short sellers cover positions rather than carry overnight risk across a closed market. What remains is the natural buy-side flow—pension funds, systematic allocators, retail—pushing prices gently upward in thin liquidity.
To move from anecdote to tradeable signal, we need specifics. For each of the seven major US holidays, the chart below shows the average daily return from D-5 to D+5 for VTI, GLD, and TLT. D0 is the last trading day before the market closure. A colored bar indicates statistical significance at the |t| > 1.5 level; gray bars are noise.
The pattern that emerges is remarkably clean. For equities, the three holidays with the strongest pre-closure drift are Good Friday, Independence Day, and Thanksgiving. The signal concentrates in the D-3 through D0 window—the four trading days leading into the closure. VTI shows consistent positive returns in this range across all three holidays, with t-statistics between 1.4 and 2.3 on individual days. The cumulative return over the four-day window averages about 1% per event.
Gold tells a different story. Around Christmas, New Year, MLK Day, and Presidents Day, it is GLD rather than VTI that shows the reliable drift—and the pattern is shifted. Instead of purely pre-holiday, gold’s strength straddles the closure: the D-1 through D+1 window captures the bulk of the effect. The likely mechanism is different too: year-end rebalancing, central bank purchases, and tax-related repositioning drive gold flows around these winter holidays. The t-statistics for GLD are stronger than for VTI, with Christmas and New Year both exceeding 3.8.
TLT, the bond ETF, shows scattered significance across individual days but no consolidated pattern around any holiday. There is no bond holiday effect worth trading.
The FOMC Drift
The Federal Reserve’s Federal Open Market Committee meets eight times per year on pre-announced dates. Academic research has documented a persistent positive drift in equity prices in the days leading up to and including the announcement—a phenomenon robust enough to account for a meaningful fraction of the equity risk premium over the past two decades.
The data confirms the effect across all three asset classes. VTI shows the strongest announcement-day return at +0.29% (t = 2.94). TLT’s pre-announcement signal is the most statistically robust, with D-1 and D0 both significant and a combined t-statistic of 3.23. Even GLD participates, with a D0 return of +0.18% (t = 1.97)—possibly reflecting uncertainty resolution or flight-to-quality positioning before the announcement. Notably, VTI reverses on D+1 (t = -1.7), which confirms that the trade should close on announcement day rather than holding through.
The FOMC trade is conceptually simple: enter at the close of D-2, exit at the close of D0, and hold equal positions in all three assets. Where the holiday strategy selects specific assets per event, the FOMC drift is a broad risk-on phenomenon that lifts everything.
The Ensemble
Most writing about calendar anomalies treats each effect in isolation—a blog post about the pre-holiday drift, a paper about the FOMC cycle, a backtest of the Santa Claus rally. What is usually missing is a framework for combining them into a single, coherent allocation. That is the point of what we call the calendar ensemble: a collection of event-driven trades that share a common risk budget and a common set of rules for when signals overlap.
The timeline below shows every trade in the calendar ensemble for a full year. Holiday trades are solid bars, FOMC trades are hatched. Each row represents one asset. The visual makes something immediately clear: the two strategies are almost perfectly interleaved. FOMC meetings are typically scheduled away from major holidays, so there is virtually no overlap between holiday and FOMC positions for the same asset. In the rare case where both strategies would want exposure in the same asset on the same day, we do not double the position—we treat it as a single active trade. The calendar event already has the asset in play; adding a second layer would concentrate risk without adding a genuinely independent signal.
This yearly ensemble—seven holidays and eight FOMC meetings—is the first layer of a broader event-driven architecture. Calendar events that occur on a monthly or weekly cycle, such as turn-of-month flows or intraweek patterns, belong in separate sleeves with their own risk budgets and overlap logic. The principle remains the same: discrete, predictable events with structural mechanisms, aggregated into an ensemble rather than traded as isolated curiosities.
Two Windows, Four Parameters
A legitimate concern with any calendar strategy is overfitting. If you test enough combinations of holidays, assets, and windows, something will look significant by chance. The design of this strategy addresses that concern directly through consolidation.
The entire holiday strategy has exactly four free parameters: entry and exit day for VTI, entry and exit day for GLD. These four values are applied uniformly—every VTI holiday uses the same D-4 to D0 window, every GLD holiday uses the same D-2 to D+1 window. There is no per-holiday optimization. The asset assignment is not fitted either; it follows from the barplot analysis above, where VTI and GLD show clearly differentiated patterns. The holiday selection is simply all major US market closures. With 146 trades over 21 years and four parameters, the observation-to-parameter ratio is 36:1—well above the 10:1 threshold that econometric practice considers safe.
But parameter counting alone is not sufficient. A strategy can have few parameters and still be fragile if the chosen values sit on a sharp peak in performance space. To test this, we perturb each parameter by ±1 day and evaluate all 81 resulting combinations.
Every one of the 81 combinations produces a positive mean return. Every one exceeds t = 2.0. The Sharpe ratio ranges from 0.24 to 0.50; our chosen parameters score 0.44, ranking 18th out of 81. This is not a razor-thin optimum that collapses when you shift a day—it is a broad plateau where the strategy works regardless of the precise window boundaries.
The final robustness test is a permutation analysis. We keep the exact same window parameters but replace the holiday dates with random calendar dates, maintaining the same number of events per year. We repeat this 5,000 times and compare the resulting Sharpe distribution against the observed value.
The result is unambiguous. The observed mean trade return of 1.08% lies entirely outside the permutation distribution (mean 0.16% ± 0.17%). The p-value is below 0.0001 for both mean return and Sharpe ratio. The specific calendar dates carry genuine edge that random dates with identical trade structure cannot replicate.
Event-Based Equity
When evaluating calendar strategies, the natural unit of analysis is the individual trade, not the daily return. Most days the strategy is flat—no position, no return. Measuring it on a daily grid dilutes the signal into a sea of zeros, inflating kurtosis to 91 and making the distribution unrecognizable. On the event grid—one observation per closed trade—the true character of the strategy becomes visible.
The combined strategy delivers an annualized Sharpe ratio of 1.40 with a skewness of +3.39. This is exactly the kind of return distribution we want as a portfolio overlay: high Sharpe for capital-efficient growth, positive skew for favorable behavior under leverage. The maximum event-based drawdown of 2.3% reflects the inherently bounded risk of short-duration trades—you can only lose what the asset moves over three or four days.
Adding It to the Core
The calendar strategy on its own generates about 3% annually. The question is what happens when we layer it on top of the inverse volatility portfolio. The overlay adds holiday positions at 30% of portfolio value and FOMC positions at 10% per asset, on top of whatever the core strategy already holds. On trading days where the holiday and core positions overlap—which they will, since VTI and GLD are in both—the total exposure temporarily increases.
The CAGR rises from 8.1% to 11.3%—an increase of 3.3 percentage points—while volatility only increases by 0.7 percentage points. The Sharpe ratio jumps from 1.01 to 1.28. And the maximum drawdown barely moves: -19.5% for the baseline versus -19.7% for the fully overlaid portfolio. The FOMC component actually reduces the drawdown relative to holidays-only, because its three-asset diversification partially hedges the concentrated VTI and GLD positions of the holiday trades.
The reason the overlay is so capital-efficient is time diversification. The calendar strategy is invested roughly 9% of trading days. The remaining 91% of the time, the portfolio returns are identical to the baseline. The few days of additional exposure occur on dates with demonstrated positive drift, so they contribute disproportionately to returns relative to the risk they add.
Transparent Alpha
Nothing in this approach requires predicting market direction. Calendar anomalies are among the most studied phenomena in empirical finance. The pre-holiday effect in equities has been documented for over four decades; the FOMC drift for over two. Both are driven by identifiable structural mechanisms—liquidity withdrawal before market closures, uncertainty resolution around monetary policy announcements—rather than fleeting sentiment patterns.
The strategy described here trades seven holidays and eight FOMC meetings per year, using two consolidated time windows with four free parameters. Every neighboring window combination is profitable. A permutation test confirms that the edge resides in the specific calendar dates, not in the parameterization. Layered on top of the core three-asset portfolio, it adds over three percentage points of annual return with negligible additional risk.
This is what we mean by going beyond passive: not stock picking, not macro forecasting, but the systematic harvesting of structural market effects that have persisted for decades and show no sign of being arbitraged away. The calendar overlay is one module in a broader architecture. It will not be the last.
Good stuff
Very good article… Thanks for that