Module 5 — Strategy Design

Moving Averages and Smoothing

Trend, reversion, and the diagnostic discipline that separates real edge from a curve fit.

Module lessons

Moving Averages and SmoothingMomentum vs Mean ReversionWhy Most Backtests Lie

Learning objectives

  • ▸Compute SMA, EMA, and weighted MAs.
  • ▸Understand lag tradeoffs.
  • ▸Implement a basic MA-crossover signal.

FORMULA

Simple vs exponential

SMA_n(t) = (1/n) · Σ_{k=0..n-1} P_{t-k}
EMA: S_t = α·P_t + (1-α)·S_{t-1},   α = 2 / (n+1)
EMA reacts faster than SMA of equivalent length.

TEXT

Lag is the curse of every smoother

A 50-day SMA tells you what was true ~25 days ago, not today. You can never eliminate the lag of a causal smoother — you can only trade off lag against noise. This is also why simple MA crossovers underperform in choppy markets: they generate whipsaws.

CODE

MA crossover signal

fast = prices.rolling(20).mean()
slow = prices.rolling(50).mean()

# +1 long, -1 short, 0 flat
signal = np.sign(fast - slow).fillna(0)
# shift by 1 to avoid look-ahead
position = signal.shift(1)
strategy_ret = position * prices.pct_change()
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