Designing Financial Features: The Math Behind RSI, MACD, and Rolling Statistics

First metric: Daily Return

Not a difficult one. It returns the percentage change between today's and yesterday's stock prices.

Why? Seeing day-to-day changes can be useful and later used in the gold layer for analysis.

The math is:

(today - yesterday) / yesterday

Example:

• —day 1: 150.0 → NaN
• —day 2: 152.3 → (152.3 - 150.0) / 150.0 = +0.0153 (+1.53%)
• —day 3: 149.8 → (149.8 - 152.3) / 152.3 = -0.0164 (-1.64%)

Simple, right? In code, we use pandas:

close.pct_change()

Second metric:Moving Averages (MA7, MA21, MA50)

Moving average shows the average price over the last X days.

Why? Individually, they show the direction of the stock, not very powerful alone, but when analyzed together they can provide strong signals. Golden cross and death cross are the most relevant examples.

The math is:

MA(X) = (day_t + day_(t-1) + ... + day_(t-X+1)) / X

As we can see, for example, MA7 will only return a valid result after the 7th day.

df["ma_7"] = close.rolling(7).mean()

Third metric: RSI (Relative Strength Index)

Probably the most complex in this list, so let's go step by step.

RSI returns a number between 0 and 100:

• —70+ → overbought
• —30- → oversold

Why? It helps analyze market momentum. Sometimes stocks are not priced only by their real value, hype, news, or unexpected events can influence behavior.

Let's dive into the math:

• —Period = 14 (default market value)
• —Delta = difference between current day and previous day
• —Gain = delta if positive, otherwise 0
• —Loss = absolute delta if negative, otherwise 0

Then:

• —Average Gain = exponential moving average (EWM) of gains
• —Average Loss = exponential moving average (EWM) of losses
• —RS = avg_gain / avg_loss

If α is close to 1  →  fast decay (focus on recent data)
If α is close to 0  →  slow decay (longer memory)

α = 1 / (1 + com) = 1 / 14

RSI = 100 - (100 / (1 + RS))

def _rsi(close: pd.Series, period: int = 14) -> pd.Series:
    delta = close.diff()
    gain = delta.clip(lower=0)
    loss = -delta.clip(upper=0)
    avg_gain = gain.ewm(com=period - 1, min_periods=period).mean()
    avg_loss = loss.ewm(com=period - 1, min_periods=period).mean()
    rs = avg_gain / avg_loss.replace(0, float("nan"))  # Avoid division by zero
    return 100 - (100 / (1 + rs))

Fourth indicator: MACD (Moving Average Convergence Divergence)

MACD shows the momentum of the stock using EMA (Exponential Moving Average) to weight recent values more heavily.

Unlike a simple moving average where all days have equal weight, EMA applies exponential decay:

EMA(t) = Price(t) × α + EMA(t-1) × (1 - α)

Where alpha is defined as:

α = 2 / (span + 1)

span = 12  →  α ≈ 0.154  (more reactive, short-term)
span = 26  →  α ≈ 0.074  (smoother, long-term)

So EMA12 reacts faster to price changes, while EMA26 captures the longer trend.

MACD = EMA12 - EMA26

The MACD Signal line is an EMA of the MACD itself (span=9), used to identify buy/sell triggers.

The MACD Histogram is the difference between MACD and Signal:

MACD Histogram = MACD - Signal

Fifth metric: Volatility (21-day)

Simple but useful, evaluates the standard deviation of daily returns over the last 21 days. Higher volatility means bigger price oscillations in the period. We use it to set risk/reward accuracy.

Code (MACD + Volatility)

ema12 = close.ewm(span=12, adjust=False).mean()
ema26 = close.ewm(span=26, adjust=False).mean()
df["macd"] = ema12 - ema26
df["macd_signal"] = df["macd"].ewm(span=9, adjust=False).mean()
df["macd_hist"] = df["macd"] - df["macd_signal"]
df["volatility_21"] = df["daily_return"].rolling(21).std()

With that, we complete our silver layer.

Conclusion

We can create from raw data some really interesting and useful indicators to aggregate information and extract real value from it. Data without purpose is useless, we need to learn how to extract meaning from it. And that's the point of this article: not the math, not the code, but that we can get real-world insights from data. That's what makes this work worthwhile.