Learn about government vs corporate bonds — Hinglish notes

2.1.3 · Stock-Market › Equity & Fixed Income

WHAT is a bond?

WHY yields differ hain — "spread" ko first principles se derive karo

Chalte hain pricing ko scratch se build karte hain.

Step 1 — Price = future cash flows ki present value. Kyun? Kal ka ek rupaya aaj ke ek rupaye se kam worth hai, kyunki aaj ka safe rupaya khud interest earn kar sakta hai. Toh hum har future payment ko discount karte hain.

Ek bond ke liye jo har period coupon $C$ deta hai, face value $F$ , $n$ periods mein, rate $y$ (the yield) par discount kiya:

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

Yeh step kyun? Time $t$ par har cash flow ko $(1 + y)^{t}$ se divide kiya jaata hai — exactly $t$ periods ki compounding ko "undo" karna.

Step 2 — Credit risk kahan enter karta hai? Ek risky bond ke liye, ek probability hai ki company default kar de aur tumhe payment na mile. Compensated hone ke liye, investors ek higher discount rate $y_{cor p} > y_{g o v}$ demand karte hain. Define karo:

Step 3 — Ek simple default-risk model (kyun spread ≈ expected loss). Consider karo ₹1 ek saal ke liye lending. Default probability $p$ hai. Agar company survive karti hai (prob $1 - p$ ) toh tumhe $1 + y_{cor p}$ milta hai. Agar default karti hai (prob $p$ ) toh tumhe sirf principal ka ek fraction $R$ milta hai — recovery rate conventionally principal par define hoti hai, isliye defaulted payoff $R$ hai (na ki $R (1 + y_{cor p})$ ; defaulted loan par tum interest collect nahi karte). Fair deal ke liye, risky bond ka expected payoff safe payoff ke barabar hona chahiye:

$(1 - p) (1 + y_{cor p}) + p R \approx 1 + y_{g o v}$

Yeh step kyun? Hum dono outcomes mein split karte hain, har ek ko uski probability se weight karte hain, aur expected value ko risk-free bond ke barabar set karte hain — warna koi bhi dono bonds mein se kisi ek ko doosre par prefer nahi karta.

Expand karke aur loss-given-default $L = (1 - R)$ use karke (aur chote $p$ ke liye tiny $p \cdot y_{cor p}$ term drop karke):

$Spread = y_{cor p} - y_{g o v} \approx p \cdot (1 - R) = p \cdot L$

Yeh step kyun? Lender ki extra yield sirf expected loss $p \times L$ cover karne ke liye chahiye. Higher default chance ya lower recovery ⇒ bigger spread. Yahi beating heart hai ki corporate > government yields kyun hoti hain.

Figure — Learn about government vs corporate bonds

HOW compare karte hain — poori picture

Feature	Government bond	Corporate bond
Issuer	National government	Ek company
Default (credit) risk	Bahut kam	Higher (rating ke hisaab se vary karta hai)
Yield	Kam	Zyada (= gov yield + spread)
Rated by	(sovereign rating)	Agencies: AAA…D (S&P/Moody's/CRISIL)
Taxation (India)	Interest taxable; kuch tax-free	Fully taxable
Liquidity	Usually high	Aksar lower
Purpose	Public spending fund karna	Business fund karna

Worked examples

Common mistakes (steel-manned)

Active recall

Recall Woh kaun sa single factor hai jo mainly explain karta hai ki corporate bonds government bonds se zyada yield kyun karte hain?

Higher default (credit) risk — roughly quantified as Spread ≈ $p \times L$ (default prob × loss given default). Investors is risk ko bear karne ke liye extra yield demand karte hain.

Recall Agar coupon rate yield ke barabar ho, toh price kya hogi?

Exactly face value (par).

What is a bond?

Ek debt security (IOU): issuer periodic coupons + face value at maturity pay karta hai, aaj udhar liye gaye paison ke badle.

Government aur corporate bonds mein mainly kya fark hai?

Default/credit risk — governments apni currency mein near risk-free hain; companies default kar sakti hain, isliye higher yield deti hain.

Credit spread define karo.

Spread = y_corp − y_gov; default (aur liquidity) risk lene ke liye extra yield.

Default se credit spread ka approximate formula?

Spread ≈ p·(1−R) = p·L, jahan p = default probability, R = principal par recovery, aur L = loss given default.

Defaulted payoff R kyun hai na ki R(1+y_corp)?

Recovery sirf principal par define hoti hai; ek defaulted borrower interest dena band kar deta hai.

First principles se bond pricing formula?

P = Σ C/(1+y)^t + F/(1+y)^n — saare coupons aur face value ki present value.

Yields badhne par bond prices kyun girti hain?

Yield denominator mein hai (1+y)^t; bada y har cash flow ki present value ko shrink karta hai.

Bond par value par kab trade karta hai?

Jab uska coupon rate yield to maturity ke barabar hota hai.

Credit ratings kya represent karti hain?

Ek agency ka default probability ka estimate (AAA safest → D default); lower rating ⇒ bigger spread ⇒ higher yield.

Kya government bonds truly risk-free hain?

Sirf apni currency mein default se; unpar abhi bhi interest-rate aur inflation risk rehta hai.

Junk (high-yield) bond kya hota hai?

BBB− se neeche rated bond jisme high default probability hoti hai, isliye high yield hoti hai.

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

Socho tum apne dost ko ₹100 udhar dete ho aur woh ₹110 agale saal dene ka promise karta hai. Agar tumhara dost tumhara zimmedar teacher hai (government), tum trust karte ho aur ₹105 par khush ho. Lekin agar tumhara dost ek bhulakkad classmate hai (ek company jo paisa khho sakti hai), toh tum tabhi udhar doge jab woh ₹115 promise kare — extra worry ke liye extra paisa. Woh "extra worry money" spread hai. Jitna risky borrower, utna extra promise karna padta hai.

Connections

Bond pricing and present value
Yield to maturity
Interest-rate risk and duration
Credit ratings and default probability
Inflation risk and real returns
Equity vs debt in the capital structure