Learn moving-average crossover systems — Hinglish notes

4.6.8 · Stock-Market › Trading Strategies

WHAT is a moving average?

WHY average at all? Price $P_{t}$ = trend + noise. $n$ points ka average lene se zero-mean noise cancel ho jaata hai (law of large numbers ki wajah se noise term $1/ n$ ki tarah shrink karta hai) jabki slow trend roughly intact rehta hai. Bada $n$ ⇒ smoother lekin laggier.

Deriving the EMA from scratch

Humein ek smoother chahiye jo (a) SMA se faster react kare aur (b) kabhi bhi saari purani prices store na kare. Socho: kya ho agar aaj ki smoothed value, aaj ki price aur kal ki smoothed value ka blend ho?

$EMA_{t} = α P_{t} + (1 - α) EMA_{t - 1}, 0 < α < 1$

Why this step? Yeh ek recursive ek-line update hai — sasta aur self-correcting. Ise ek baar unroll karo: $EMA_{t} = α P_{t} + α (1 - α) P_{t - 1} + α (1 - α)^{2} P_{t - 2} + \dots$

Toh weights geometrically decay karte hain — recent prices dominate karti hain. Ek $n$ -period SMA ke "center of mass" se match karne ke liye hum choose karte hain: $α = \frac{2}{n + 1}$

Why $\frac{2}{n + 1}$ ? EMA ka weighted mean lag $\frac{1 - α}{α}$ periods hai. Ise SMA ke average lag $\frac{n - 1}{2}$ ke barabar set karke solve karo: $\frac{1 - α}{α} = \frac{n - 1}{2} \Rightarrow \frac{2}{α} - 2 = n - 1 \Rightarrow α = \frac{2}{n + 1} .$

WHAT is a crossover?

WHY the spread trick? Do wiggly lines ko dekhne ki jagah, ek number $S$ dekho. Crossover simply " $S$ zero hit karta hai" hai, jo code aur backtest karna bahut aasaan hai.

Figure — Learn moving-average crossover systems

HOW to run the system (step-by-step)

Do windows chuno: fast $n_{f}$ aur slow $n_{s}$ jahan $n_{f} < n_{s}$ (classic: daily ke liye 50/200; intraday ke liye 9/21).
Har bar dono MAs compute karo.
$S (t)$ compute karo aur sign flip check karo.
Golden Cross par long jao; Death Cross par exit karo / short jao.
Backtest karo, phir risk rules add karo (stop-loss, position size).

Common mistakes

Recall Feynman: explain to a 12-year-old

Socho tum ek ulte-seedhe hiking trail par fog mein chal rahe ho. Har pathar ko dekhne ki jagah, tum pichle 10 steps (fast lens) aur pichle 200 steps (slow lens) ki average direction dekhte ho. Jab teri short-term direction apni long-term direction se upar jaati hai, pahad shayad chadh raha hai — climbing shuru karo (buy). Jab neeche jaaye, waapas jao (sell). Lenses future nahi dekh sakte; woh sirf fog saaf karte hain taaki tum turn thoda late par lekin clearly notice kar sako.

Active recall

Window n ka Simple Moving Average kya hota hai?

Pichle n closing prices ka arithmetic mean,

\frac{1}{n} \sum_{i = 0}^{n - 1} P_{t - i}

Averaging noise ko kyun reduce karta hai?

Zero-mean noise window ke across cancel ho jaata hai (~

1/ n

shrink karta hai) jabki slow trend survive karta hai.

Golden Cross vs Death Cross?

Golden = fast MA slow ke UPAR cross karta hai (buy); Death = fast slow ke NEECHE cross karta hai (sell).

Spread S(t) define karo.

S (t) = MA_{f a s t} (t) - MA_{s l o w} (t)

; crossover S ka sign change hota hai.

EMA recursion formula?

EMA_{t} = α P_{t} + (1 - α) EMA_{t - 1}

EMA ka alpha = 2/(n+1) kyun hota hai?

Yeh EMA ke average lag

(1 - α) / α

ko SMA ke lag

(n - 1) /2

se match karta hai.

EMA compute karo agar alpha=0.2, prev EMA=50, price=55.

0.2 (55) + 0.8 (50) = 51

MAs leading hote hain ya lagging?

Lagging — sirf past prices se bane hote hain; yeh confirm karte hain, predict nahi.

Crossover systems ka main failure mode kya hai?

Sideways/range-bound markets mein whipsaws (bahut saare false signals, commission bleed).

Window n choose karne mein core trade-off kya hai?

Lag vs noise: bada n = smoother lekin slower; chhota n = faster lekin noisier.

Connections

Simple vs Exponential Moving Averages
Trend-Following vs Mean-Reversion Strategies
Whipsaw and Transaction Costs
Backtesting a Trading Strategy
Support and Resistance
Signal Lag and Filtering