Standard Deviation — Market ka Thermometer

Imagine karo ki do stocks hain. Stock A ke monthly returns hain: 2, 3, 2, 4, 3, 2, 3 percent. Average roughly 2.7 percent. Stock B ke returns hain: minus 5, 10, minus 3, 15, minus 8, 12, 2 percent. Average bhi roughly 3.3 percent.

Dono ka average return almost same hai. Lekin B bahut zyada unpredictable hai. Kabhi bada plus, kabhi bada minus. Standard deviation is unpredictability ko measure karta hai. A ka standard deviation low hoga, B ka bahut high.

Investors generally same return ke liye lower standard deviation prefer karte hain. Iska reason simple hai: high volatility ka matlab hai ki kisi bhi given month ya quarter mein aapka portfolio bahut neeche bhi ja sakta hai, chahe long term average return achha ho.

Agar stock returns normally distributed hain, toh ek powerful rule apply hota hai. Approximately 68 percent returns mean ke ek standard deviation ke andar aate hain. 95 percent returns mean ke do standard deviations ke andar aate hain. 99.7 percent returns teen standard deviations ke andar aate hain.

Example: NIFTY ka historical annual standard deviation roughly 20 percent hai aur average return roughly 12 percent. Iska matlab roughly 68 percent years mein NIFTY ka return minus 8 se 32 percent ke beech hoga. Aur 95 percent years mein minus 28 se 52 percent ke beech.

Yahan problem aati hai. Real markets mein extreme events, yani jo 3 standard deviation se bahar hote hain, theoretically normal distribution mein almost impossible hote hain. Lekin actual mein yeh events bahut zyada frequently occur karte hain. 2008 financial crisis, COVID crash, 2020 March mein kya hua, yeh sab theoretically bahut rare the lekin hue.

Historical volatility past returns se calculate hoti hai. Yeh backward looking hai. India VIX aur options pricing mein jo volatility use hoti hai woh implied volatility hai, jo forward looking hai. Yeh market ka estimate hai ki aage kitna movement aayega.

Jab IV (Implied Volatility) historical volatility se bahut zyada ho toh options relatively expensive hote hain. Sellers ke liye favorable time. Jab IV historically low ho toh options relatively cheap hote hain, buyers ke liye better value.

Standard deviation annualize karne ke liye daily standard deviation ko square root of 252 se multiply karte hain. 252 approximately trading days per year hote hain India mein.