Learn about the yield curve and its shapes — Stock-Market notes

WHAT is the yield curve?

WHY hold credit quality constant? Because a bond's yield reflects both how risky the borrower is and how long you lend. To study "the price of time," we must remove the "price of default risk." Government bonds are treated as (nearly) risk-free, so what's left is pure time.

HOW is a single point on the curve built? (Derive the yield)

A bond promises fixed cash flows. Its price today is the present value of those cash flows. The yield to maturity ( $y$ ) is the single discount rate that makes present value equal to the market price.

For a zero-coupon bond paying face value $F$ in $n$ years at price $P$ :

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

Why this form? If $1 today grows to$ (1+y)^n $in$ n $years, then$ F $received in$ n $years is worth only$ F/(1+y)^n$ today. We invert to find the rate the market is charging:

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

Why this step? We divide $F$ by $P$ to get the total growth factor, take the $n$ -th root to get the per-year growth factor, then subtract 1 to convert a factor into a rate.

The three shapes

Figure — Learn about the yield curve and its shapes

WHY is "normal" upward-sloping?

Two forces push long yields higher:

Term (liquidity) premium: locking money away for 30 years is riskier (inflation surprises, opportunity cost), so investors demand extra reward. WHY: you can't easily grab your cash back, so you charge for the inconvenience.
Growth/inflation expectations: a healthy economy expects future rates to rise, so long bonds must offer more to compete.

WHY does inversion signal recession?

An inverted curve means the market expects the central bank to cut short-term rates in the future — and the only reason to cut is a slowing economy. Investors, fearing recession, rush to lock in today's long rates, bidding long-bond prices up and long yields down below short yields.

Worked examples

Common mistakes

Recall Feynman: explain to a 12-year-old

Imagine lending your friend money. If they pay it back tomorrow, you want a tiny thank-you. If they keep it for 10 years, you want a bigger thank-you because you waited longer and anything could happen. The yield curve is just a chart of "how big a thank-you" you get for waiting different amounts of time. Usually longer wait = bigger thank-you (upward line). But if everyone suddenly thinks the future looks scary, they rush to lend for the long term now, and the long-term thank-you actually gets smaller than the short-term one — that upside-down line ("inversion") is like a weather warning that a storm (recession) might be coming.

Recall flashcards

What does the yield curve plot on each axis?

Yield to maturity (y-axis) vs time to maturity (x-axis), for bonds of the same credit quality.

Why must all bonds on the curve share credit quality?

To isolate the effect of maturity (time) alone by removing default-risk differences.

Formula for a zero-coupon bond's yield?

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

Relationship between bond price and yield?

Inverse — higher price means lower yield (fixed cash flows).

What is a normal (upward-sloping) curve and why does it occur?

Long yields > short yields; caused by term/liquidity premium and expected growth.

What does an inverted yield curve signal?

Market expects future rate cuts / slowing economy → classic recession warning (with a 6–18 month lag).

What is a flat yield curve?

Short ≈ long yields; a transition state between normal and inverted.

Mechanically, why do long yields fall during fear?

Investors buy long bonds → prices rise → yields fall (price–yield seesaw).

Connections

Bond Pricing and Present Value — the discounting that produces each yield.
Yield to Maturity — the single rate defining each curve point.
Interest Rate Risk and Duration — why long bonds swing more.
Central Bank Monetary Policy — sets the short end of the curve.
Inflation and Real vs Nominal Rates — a key driver of the long end.
Recession Indicators — inversion as a leading signal.

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Yield curve ek simple picture hai jo batata hai ki paisa "time" ke hisaab se kitna interest deta hai. X-axis pe maturity hoti hai (kitne time baad paisa wapas milega — 1 saal, 5 saal, 10 saal, 30 saal) aur Y-axis pe yield (interest rate). Hum hamesha same credit quality ke bonds lete hain — jaise government bonds — taaki sirf "time ka effect" dikhe, default risk beech mein na aaye.

Ek zero-coupon bond ki yield nikalna easy hai: $y=(F/P)^{1/n}-1$ . Yaani face value ko price se divide karo, $n$ -th root lo, aur 1 minus kar do. Yaad rakho — price aur yield ulte chalte hain. Agar tum same fixed paise ke liye zyada price doge, to tumhara return (yield) kam ho jaayega. Yeh point exam aur real trading dono mein bahut important hai.

Curve ke teen shapes hote hain. Normal (upar ki taraf) — long yields short se zyada, kyunki lambe time tak paisa lock karne ka extra reward (term premium) milta hai; yeh healthy economy ka sign hai. Inverted (neeche ki taraf) — jab market ko lagta hai future mein interest rates girenge (recession aane wali hai), sab log long bonds khareedte hain, unka price badhta hai aur yield gir jaati hai short se bhi neeche. Flat — short aur long lagbhag barabar, ek transition state.

Bottom line: inverted yield curve ek strong recession warning hai, lekin turant nahi — historically 6 se 18 mahine ka lag hota hai. Isliye traders aur economists yield curve ko roz dhyaan se dekhte hain.

Test yourself — Equity & Fixed Income

Connections