3.1.10
Intuition The 80/20 core ideaEk linear scale equal dollar moves ko equal distance maanta hai. Ek log scale equal percentage moves ko equal distance maanta hai. Kyunki investors paisa compound karte hain aur percent returns mein sochte hain (10% gain same lagta hai chahe stock 10 k ah oy a log scale kisi bhi cheez ke liye honest scale hai jo exponentially grow karti hai — aur yahi exactly woh tarika hai jaise stock prices aur indices long run mein behave karte hain.
Definition Vertical axis scalingEk price scale yeh decide karta hai ki price chart ka y-axis prices ko screen height par kaise map karta hai.
Linear (arithmetic) scale : axis par distance absolute (dollar) change ke proportional hoti hai. Toh 10 → 20 100 → 110 Logarithmic (log/ratio) scale : axis par distance percentage (ratio) change ke proportional hoti hai. Toh 10 → 20 100 → 200
Maano price P y
Linear rule. Hum choose karte hain y y = k P P 1 P 2 Δ y = k ( P 2 − P 1 ) . equal \ moves → equal distance . Ek 10 k am o v e ha r j a g ah s am e d ik h t ahai . ∗ Y e h l o n g c ha r t s k e l i y e b u r ak y u nhai ? ∗ K y u nk i 20 p a r ba d ibaa t hai ( + 50% ) l e k in
Log rule. Ab choose karo y y = k ln P . Δ y = k ( ln P 2 − ln P 1 ) = k ln P 1 P 2 .
Exponential growth ka consequence. Maano ek stock rate r P ( t ) = P 0 e r t . y = k ln P ( t ) = k ln ( P 0 e r t ) = k ln P 0 + k r t .
Intuition Log chart kyun growth ko "straight" karta haiEquation y = ( k ln P 0 ) + ( k r ) t straight line hai t jiska slope k r constant % growth rate log chart par ek straight line ban jaati hai , aur slope seedha tumhe growth rate batata hai. Steepening line = accelerating returns; bending-down line = slowing returns.
Worked example Example 2 — Equal % moves = parallel channelsEk stock 100 100 , 110 , 121 , 133.1 , …
Linear bars: 10 , 11 , 12.1 , 13.31 growing bars, toh linear chart par tops se kheenchi trendline upar ki taraf curve karti hai.
Log distances: ln 1.1 = 0.0953 identical bars, toh log chart par yahi run bilkul straight line ki tarah plot hoti hai.
Yeh step kyun? Trendlines tabhi geometric sense deti hain jab equal moves = equal distance. Compounding asset ke liye yeh log chart hota hai, toh support/resistance lines wahan zyada reliable hoti hain.
Common mistake "Line steeper ho gayi, toh stock faster grow kar raha hai." (log chart par)
Kyun sahi lagta hai: linear chart par, steeper hota hi hai faster. Catch: log chart par ek straight line already constant % growth matlab hai; extra steepening matlab % rate badh raha hai. Fix: Log charts par slope = growth rate padho, curvature nahi. Ek straight rising line steady compounding hai, stalling nahi.
Common mistake "Log aur linear short-term / small ranges ke liye same hain."Kyun sahi lagta hai: chhote range par yeh do almost identical dikhte hain. Kyun true-ish: small x ln ( 1 + x ) ≈ x Fix: divergence price range ke saath badhta hai. Intraday scalping ke liye difference negligible hai; multi-year investing ke liye yeh decisive hai.
Common mistake "Log scale crash ko hide karta hai — bada drop chhota lagta hai, toh yeh misleading hai."Kyun sahi lagta hai: ek −50% aur ek −50% same size lagte hain chahe ek 5000 points ka ho. Fix: yeh ek feature hai, bug nahi — log scale tumhe bata raha hai ki return impact identical hai . Tumhara portfolio dono ways mein half ho jaata hai.
log Fix: Data abhi bhi real prices hain; sirf gridlines ki spacing badlti hai (gridlines 10, 100, 1000 par equally spaced hain). Prices tumhare P&L mein kabhi actually logs nahi liye jaate.
Recall Feynman: ek 12-year-old ko explain karoEk ladder imagine karo. Ek normal (linear) ladder par, har rung 1 foot apart hai — yeh measure karne ke liye acha hai ki tum kitne feet chade. Lekin paisa feet se nahi badhta, yeh multiply karke badhta hai. Toh hum ek magic (log) ladder banate hain jahan har rung ka matlab hai "do guna paisa" instead of "ek dollar aur." Is magic ladder par 1 se bada step hai jitna 1000 se paisa double kiya . Isliye adults bahut saalon wale charts ke liye magic ladder use karte hain: yeh dikhata hai tum kitne amir hue percent mein, sirf dollars mein nahi.
"LINE = dollars, LOG = ratio." Aur: "Log par, straight line = steady percent." (Straight → Steady.)
#flashcards/stock-market
Linear price scale par equal distance kya represent karta hai?Equal absolute (dollar/point) change .
Log price scale par equal distance kya represent karta hai?Equal percentage (ratio) change .
Log scale par ek move ki screen distance kaunse expression ke barabar hoti hai? k ln ( P 2 / P 1 ) ratio par depend karta hai.
Constant % growth log chart par straight line kyun dikhti hai? Kyunki y = k ln ( P 0 e r t ) = k ln P 0 + k r t t k r
Log chart par ek straight trend line ka slope kya batata hai? Growth rate r k
20 → 40 200 → 240 20 → 40 ln 2 = 0.693 200 → 240 ln 1.2 = 0.182
Log aur linear tiny ranges par similar kyun lagte hain? Kyunki ln ( 1 + x ) ≈ x x
Decades-long index history ke liye kaunsa scale use karein aur kyun? Log , taaki early aur recent eras percent moves ki tarah comparably visible hon instead of large recent numbers se dwarf hone ke.
Log chart par gridlines 10, 100, 1000 kaise spaced hain? Equally — har step ×10 hai.
Kya log chart actual price data ko change karta hai? Nahi — sirf axis spacing badlti hai; plotted prices real prices hain.
Charts, Trends & Dow Theory Support and Resistance — trendlines sahi scale par zyada reliable hoti hainDow Theory — long horizons par trends log scale par best padhi jaati hainCompound Annual Growth Rate (CAGR) — P = P 0 e r t Percentage vs Absolute Returns Reading Long-Term Index Charts
Price scale maps price to screen height
Investors think in returns
Exponential growth P = P0 e^rt
