Akela price bahut noisy hota hai. Agar ek stock 5 din lagataar upar gaya, toh kya yeh strength hai (buy karo!) ya exhaustion (jald hi sell karo)? Traders ko ek bounded, normalized measure of momentum chahiye tha jo:
0 and 100 ke beech rahe (taaki "overbought/oversold" thresholds kisi bhi stock ke liye sense banayein),
Up-moves aur down-moves ka size compare kare, sirf unki direction nahi.
Bilkul yahi J. Welles Wilder ka Relative Strength Index (RSI) karta hai.
Hum chahte hain ek single number [0,100] mein jo bataye: "Recent movement ka kitna fraction upward tha?"
Step 1 — Tug-of-war measure karo. Bulls total upward motion Uˉ contribute karte hain; bears total downward motion Dˉ contribute karte hain. Natural "kaun jeet raha hai" ratio hai:
RS=DˉUˉ.Yeh step kyun? Ek ratio scale-free hota hai — ₹10 stock aur ₹5000 stock dono comparable RS dete hain.
Step 2 — Problem: RS unbounded hai. Agar Dˉ→0 (koi down days nahi), toh RS→∞. Hume [0,∞) ko [0,100] mein squash karna hoga.
Step 3 — Squashing trick. Upward force ka fraction consider karo:
f=Uˉ+DˉUˉ.
Yeh already [0,1] mein hai. 100 se multiply karo percentage paane ke liye. Ab ise RS ke terms mein rewrite karo, upar aur neeche Dˉ se divide karke:
f=Uˉ/Dˉ+1Uˉ/Dˉ=1+RSRS.Yeh step kyun? Hum RS prefer karte hain kyunki yeh intuitive "bull:bear" ratio hai.
Step 4 — Wilder ki algebra. Note karo ki:
100⋅f=100⋅1+RSRS=100⋅1+RS(1+RS)−1=100−1+RS100.
Toh:
RSI=100−1+RS100literally sirf recent movement ka wo percentage hai jo upward tha. Yahi poora raaz hai.
Wilder ka smoothing (kyun 14 har bar reset nahi hota): pehle simple average ke baad, updates use karte hain:
Uˉt=n(n−1)Uˉt−1+Ut,Dˉt=n(n−1)Dˉt−1+Dt.Kyun? Yeh ek exponential-style memory hai taaki RSI smoothly react kare, jump karne ke bajaye jab koi purana bar window se bahar nikle.
Socho pichle 14 dinon mein "buy" team aur "sell" team ke beech ek tug-of-war chal raha hai. RSI bas 0 se 100 tak ka scoreboard hai. Agar buy team ne bahut zyada zor se kheeencha, scoreboard 100 ki taraf jaata hai (woh badi jeet rahe hain — shayad itne thak gaye hain ki aage nahi chal paate). Agar sell team ne dominate kiya, toh 0 ki taraf girata hai. Jab 50 hota hai, toh perfect tie hai. Traders dekhte hain: jab ek team bahut zyada jeet rahi hoti hai (70 ke upar ya 30 ke neeche), toh kabhi kabhi doosri team wapas fight karne waali hoti hai — lekin ek stampede mein, strong team kaafi der tak jeetti reh sakti hai, isliye tum blindly unke against bet nahi karte.