Learn about the yield curve and its shapes — Hinglish notes

2.1.7 · Stock-Market › Equity & Fixed Income

Yield curve KYA hai?

Credit quality constant kyun rakhte hain? Kyunki ek bond ki yield reflect karti hai dono — borrower kitna risky hai aur aap kitne time ke liye lend kar rahe ho. "Price of time" study karne ke liye, hume "price of default risk" hatani padti hai. Government bonds ko (almost) risk-free treat kiya jaata hai, toh jo bachta hai woh pure time hai.

Curve par ek single point kaise banta hai? (Yield derive karna)

Ek bond fixed cash flows ka promise karta hai. Uski aaj ki price un cash flows ki present value hoti hai. Yield to maturity ( $y$ ) woh single discount rate hai jo present value ko market price ke equal banata hai.

Ek zero-coupon bond ke liye jo face value $F$ pay karta hai $n$ saalon mein price $P$ par:

$P = \frac{F}{( 1 + y ) ^{n}}$

Yeh form kyun? Agar $1 aaj$ n $s aa l o nm e in$ (1+y)^n $banj aa t ahai, t o h$ n $s aa l o nm e inmi l n e w a l a$ F $aaj s i r f$ F/(1+y)^n$ worth hai. Hum invert karte hain woh rate find karne ke liye jo market charge kar rahi hai:

$y = (\frac{F}{P})^{1/ n} - 1$

Yeh step kyun? Hum $F$ ko $P$ se divide karte hain total growth factor paane ke liye, $n$ -th root lete hain per-year growth factor paane ke liye, phir 1 subtract karte hain factor ko rate mein convert karne ke liye.

Teen shapes

Figure — Learn about the yield curve and its shapes

"Normal" upward-sloping kyun hota hai?

Do forces long yields ko upar push karti hain:

Term (liquidity) premium: 30 saalon ke liye paisa lock karna riskier hai (inflation surprises, opportunity cost), toh investors extra reward maangte hain. KYU: apna cash easily wapas nahi le sakte, toh tum inconvenience ke liye charge karte ho.
Growth/inflation expectations: ek healthy economy expect karti hai ki future rates badhenge, toh long bonds ko compete karne ke liye zyada offer karna padta hai.

Inversion recession signal kyun karta hai?

Inverted curve ka matlab hai ki market expect karti hai ki central bank future mein short-term rates cut karega — aur cut karne ki wajah sirf ek hoti hai — slowing economy. Investors, recession se darte hue, aaj ke long rates lock karne ki koshish karte hain, long-bond prices upar bid karte hain aur long yields short yields se neeche aa jaate hain.

Worked examples

Common mistakes

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho tum apne dost ko paisa udhaar de rahe ho. Agar woh kal wapas kare, toh tum ek chota sa shukriya chahte ho. Agar woh 10 saal tak rakhta hai, toh tum bada shukriya chahte ho kyunki tum zyada wait kiya aur kuch bhi ho sakta tha. Yield curve sirf ek chart hai ki "kitna bada shukriya" tumhe milta hai alag-alag time wait karne ke liye. Usually zyada wait = bada shukriya (upar jaati line). Lekin agar achanak sab sochne lage ki future scary lagta hai, toh woh abhi long term ke liye lend karne ki rush karte hain, aur long-term shukriya actually chhota ho jaata hai short-term wale se — woh ulti line ("inversion") ek weather warning ki tarah hai ki ek toofan (recession) aa sakta hai.

Recall flashcards

Yield curve har axis par kya plot karta hai?

Yield to maturity (y-axis) vs time to maturity (x-axis), same credit quality ke bonds ke liye.

Curve par saare bonds credit quality kyun share karte hain?

Default-risk differences hatakar sirf maturity (time) ke effect ko isolate karne ke liye.

Zero-coupon bond ki yield ka formula?

y = (F / P)^{1/ n} - 1

Bond price aur yield ka kya relationship hai?

Inverse — zyada price matlab kam yield (fixed cash flows).

Normal (upward-sloping) curve kya hota hai aur kyun hota hai?

Long yields > short yields; term/liquidity premium aur expected growth ki wajah se hota hai.

Inverted yield curve kya signal karta hai?

Market future rate cuts / slowing economy expect karti hai → classic recession warning (6–18 month lag ke saath).

Flat yield curve kya hota hai?

Short ≈ long yields; normal aur inverted ke beech ek transition state.

Mechanically, darr ke waqt long yields kyun girte hain?

Investors long bonds khareedte hain → prices badhte hain → yields girte hain (price–yield seesaw).

Connections

Bond Pricing and Present Value — woh discounting jo har yield produce karta hai.
Yield to Maturity — woh single rate jo har curve point define karta hai.
Interest Rate Risk and Duration — kyun long bonds zyada swing karte hain.
Central Bank Monetary Policy — curve ka short end set karta hai.
Inflation and Real vs Nominal Rates — long end ka ek key driver.
Recession Indicators — inversion ek leading signal ke roop mein.