Step 1 — Price = present value of future cash flows.
Why? A rupee tomorrow is worth less than a rupee today, because a safe rupee today can itself earn interest. So we discount every future payment.
For a bond paying coupon C each period, face value F, over n periods, discounted at rate y (the yield):
P=∑t=1n(1+y)tC+(1+y)nF
Why this step? Each cash flow at time t is divided by (1+y)t — that's exactly "undoing" t periods of compounding.
Step 2 — Where does credit risk enter?
For a risky bond, there's a probability the company defaults and you don't get paid. To be compensated, investors demand a higher discount rateycorp>ygov. Define:
Step 3 — A simple default-risk model (why spread ≈ expected loss).
Consider lending ₹1 for one year. The default probability is p. If the company survives (prob 1−p) you get back 1+ycorp. If it defaults (prob p) you recover only a fraction R of the principal — the recovery rate is conventionally defined on principal, so the defaulted payoff is R (not R(1+ycorp); you don't collect interest on a defaulted loan). For a fair deal, the risky bond's expected payoff must equal the safe payoff:
(1−p)(1+ycorp)+pR≈1+ygov
Why this step? We split into the two outcomes, weight each by its probability, and set the expected value equal to what the risk-free bond gives — otherwise no one would choose either bond over the other.
Expanding and using loss-given-default L=(1−R) (and dropping the tiny p⋅ycorp term for small p):
Spread=ycorp−ygov≈p⋅(1−R)=p⋅L
Why this step? The lender's extra yield just needs to cover the expected lossp×L. Higher default chance or lower recovery ⇒ bigger spread. This is the beating heart of why corporate > government yields.
Recall What single factor mainly explains why corporate bonds yield more than government bonds?
Higher default (credit) risk — quantified roughly as Spread ≈ p×L (default prob × loss given default). Investors demand extra yield to bear this risk.
Recall If coupon rate equals yield, what is the price?
Exactly the face value (par).
What is a bond?
A debt security (IOU): issuer pays periodic coupons + face value at maturity, in exchange for money lent today.
What mainly distinguishes government from corporate bonds?
Default/credit risk — governments are near risk-free in own currency; companies can default, so pay higher yield.
Define the credit spread.
Spread = y_corp − y_gov; the extra yield for taking default (and liquidity) risk.
Approximate formula for credit spread from default?
Spread ≈ p·(1−R) = p·L, where p = default probability, R = recovery on principal, and L = loss given default.
Why is the defaulted payoff R and not R(1+y_corp)?
Recovery is defined on principal only; a defaulted borrower stops paying interest.
Bond pricing formula from first principles?
P = Σ C/(1+y)^t + F/(1+y)^n — present value of all coupons plus face value.
Why do bond prices fall when yields rise?
Yield is in the denominator (1+y)^t; larger y shrinks the present value of every cash flow.
When does a bond trade at par?
When its coupon rate equals its yield to maturity.
What do credit ratings represent?
An agency's estimate of default probability (AAA safest → D default); lower rating ⇒ bigger spread ⇒ higher yield.
Are government bonds truly risk-free?
Only of default in their own currency; they still carry interest-rate and inflation risk.
What is a junk (high-yield) bond?
A bond rated below BBB− with high default probability, hence high yield.
Recall Feynman: explain to a 12-year-old
Imagine you lend your friend ₹100 and they promise ₹110 next year. If your friend is your responsible teacher (the government), you trust them and are happy with ₹105. But if your friend is a forgetful classmate (a company that might lose the money), you'd only lend if they promise ₹115 — extra money for the extra worry. That "extra worry money" is the spread. The riskier the borrower, the more extra they must promise you.
Bond ka matlab hai ek IOU — aap paisa aaj udhaar dete ho, aur badle mein aapko fixed interest (coupon) plus maturity par apna principal (face value) wapas milta hai. Ab sabse bada sawaal: paisa wapas milega ki nahi? Government bond (India mein G-Sec) mein risk kam hai, kyunki government tax laga sakti hai aur currency print kar sakti hai, isliye woh kam interest deti hai. Corporate bond mein company default kar sakti hai, isliye woh zyada interest — yaani zyada yield — offer karti hai taaki aap risk lene ko taiyaar ho.
Ye jo extra yield hai use credit spread kehte hain: Spread = corporate yield − government yield. Simple formula se samajh lo — agar default ki probability p hai aur default hone par aap principal ka R fraction recover karte ho (yaani loss L=1−R), toh Spread ≈ p×(1−R)=p×L. Dhyaan rakho: recovery sirf principal par hoti hai, interest par nahi — default hone par company interest dena band kar deti hai, isliye defaulted payoff R hota hai, R(1+ycorp) nahi. Jitni zyada default chance, utna bada spread. Rating agencies (AAA se D tak) basically isi p ka estimate deti hain.
Pricing ki key baat: bond ka price = future cash flows ka present value, P=∑C/(1+y)t+F/(1+y)n. Yahan yield y denominator mein hai, isliye jab yield badhti hai toh price girta hai — ye inverse relation hai, exam aur real trading dono mein bahut important. Aur ek myth tod do: "zyada yield = behtar bond" galat hai; zyada yield ka matlab market zyada risk price kar raha hai. Government bonds bhi 100% safe nahi — inme interest-rate aur inflation risk rehta hai, bas default risk near-zero hota hai (apni currency mein).
