[Quant] Alpha#101

Wilmott Magazine 2016(84) (2016) 72-80 [Paper]
Zura Kakushadze

In this post, we examine Alpha #101 from the paper’s collection of 101 formulaic alphas.

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Formula

\[\frac{\text{close} - \text{open}}{(\text{high} - \text{low}) + 0.01}\]

• close − open : How much did the price rise (or fall) during the day?
• high − low : How much did the price fluctuate during the day?
• + 0.01 : A small constant to prevent division by zero.

In essence, this alpha measures the efficiency of the move relative to volatility.

High alpha value →

• The price rose quietly, with little fluctuation.
• A steady, confident upward move — possibly conviction-driven buying.

Low alpha value →

• High intraday volatility relative to the net move.
• An unstable, noisy price action.

This alpha can serve as a useful signal for short-term trading or momentum screening.

Limitations

• The signal only looks at a single day’s OHLC data.
• It ignores all other information (volume, news, macro, etc.) and should be combined with other indicators.
• In a regime of high market-wide volatility, the interpretation may change significantly.

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Experiment

Setup

Parameter	Value
Universe	Top 30 stocks from the S&P 500
Starting Capital	$1
Period	499 trading days (~2 years)

Applying the signal to 30 stocks over ~500 days produces a total of 15,000 alpha signals.

Procedure

1. Compute the alpha signal for each stock and rank them cross-sectionally.
2. Since close, high, and low prices are only available after market close, the ranking is applied with a one-day lag.
3. Go long the top 50% and short the bottom 50% by rank.
4. Calculate the daily portfolio return across all stocks.
5. Compound the daily returns to get the cumulative PnL.

Results

• The starting point of $1 is the break-even line.
• PnL = Profit and Loss

Key Metrics

• Total Return: 1.69% — Quite low, considering bank deposit rates sit around 2–3% annually.
• Annual Volatility — How much the portfolio value fluctuated over the year.

Why Do We Multiply by √N?

This is a fundamental rule in statistics:

\[\sigma_{N\text{-day}} = \sigma_{1\text{-day}} \times \sqrt{N}\]

Why not just multiply by N?

Daily volatility: 1%

If we simply multiplied:
→ 252-day volatility = 1% × 252 = 252%  (absurd!)

With the square root:
→ 252-day volatility = 1% × √252 = 1% × 15.87 = 15.87%  (realistic)

The underlying principle:

Daily returns are assumed to be independent. Today’s +1% doesn’t dictate tomorrow’s direction — gains and losses can cancel out over time.

Mathematically:

\[\text{Var}_{N} = N \cdot \sigma^2 \quad \Rightarrow \quad \text{Std}_{N} = \sqrt{N} \cdot \sigma\]

Variance scales linearly with $N$; standard deviation scales with $\sqrt{N}$.

Annual Volatility Benchmarks

Asset	Annual Volatility	Note
S&P 500	15–18%	U.S. large-cap 500
NASDAQ	20–25%	Tech-heavy, higher swings
KOSPI	18–22%	Korean equity market
Bitcoin	80–120%	Extreme volatility
U.S. Treasuries	3–5%	Very stable
Our Strategy	7.13%	Remarkably low volatility

Other Metrics

• Sharpe Ratio — Risk-adjusted return:

\[\text{Sharpe} = \frac{\text{Annualized Return}}{\text{Annualized Volatility}}\]

A Sharpe above 1.0 is considered good; above 2.0 is excellent. Our result of 0.119 is very poor.

• Max Drawdown — The largest peak-to-trough decline in portfolio value.
• Win Rate — Percentage of trading days with a positive return.
• Avg Daily Turnover — How much of the portfolio is reshuffled each day.
  • A value of 1.01 means we traded ~101% of the portfolio’s value daily. Higher turnover = higher transaction costs.
• Avg Long / Short Positions — The average number of stocks held long vs. sold short on any given day.

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Disclaimer: This post is purely a study note. All investment decisions should be made based on your own research and judgment.