Bonds

Part 1 gave a timeline of signed cash flows, rate quotes with their compounding, discount factors, and present value as a sum of discounted dated amounts. A fixed-rate bond is the first contract the course values with these tools: its contract terms fix the promised payments, and its price is their present value. The last chapter, on bond forwards, also uses the forward contract of Part 4.

This part values a simplified fixed-rate bond with deterministic promised payments. The first chapter turns face value, coupon rate, payment frequency, and maturity into the payment schedule. The next two chapters price the bond, first from one discount factor per payment and then from a single yield to maturity. The fourth chapter explains why the price decreases when the yield increases and why the price-yield curve is not linear. The last two chapters add trading details: accrued interest and the clean and dirty price at settlement, and the delivery price of a bond forward.

Part 2 of 76 chapters4 numbered equations6 knowledge checks

1. Fixed-rate bond contract and cash flows

   Translate face value, coupon rate, frequency, and maturity into promised payments.

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2. Bond price from discount factors

   Apply one discount factor to each promised payment before adding.

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3. Yield to maturity as a single-rate summary

   Interpret the rate that reproduces a toy bond price, then calculate the price from an input yield.

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4. The bond price-yield relationship

   Explain why the price of fixed positive cash flows decreases when the yield increases, and why the price-yield curve is not linear.

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5. Settlement, accrued interest, and clean versus dirty price

   Calculate actual/actual coupon-period accrual and keep quoted and cash bond prices on one basis.

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6. Bond forwards

   Apply cash-and-carry to a coupon bond while keeping coupon ownership and dirty-price units explicit.

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The argument

1. The contract terms fix every promised payment
2. The price is the present value of those payments
3. A yield to maturity summarizes the discounting in one rate
4. A higher yield gives a lower price, along a curve
5. Accrued interest separates the quoted clean price from the cash dirty price
6. Cash-and-carry gives a bond forward delivery price on the dirty-price basis

After this part you can

• Identify face value, annual coupon rate, coupon frequency, maturity, and principal redemption in a simplified fixed-rate bond description.
• Calculate each level coupon as face value times annual coupon rate divided by payments per year.
• Construct the coupon and principal cash-flow schedule of a simplified fixed-rate bond.
• Price a simplified fixed-rate bond by multiplying each promised cash flow by its stated discount factor and summing the results.
• Interpret yield to maturity as the single nominal annual rate, compounded at coupon frequency, that reproduces price from promised cash flows in the simplified model.
• Price a simplified fixed-coupon bond from a nominal annual yield compounded at the coupon frequency.
• Explain why the price of positive fixed cash flows moves inversely to yield while discounting denominators remain positive.
• Recognize that equal yield changes generally produce unequal price changes in the simplified fixed-cash-flow model.
• Calculate actual/actual coupon-period accrued interest and convert consistently between clean quoted price and dirty invoice price.
• Calculate a no-arbitrage bond forward delivery price from the current dirty bond price, the present value of pre-delivery coupons, and the delivery-date discount factor.

Builds on

• Foundations
• Derivative foundations

Leads to

• Bond options