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CFA Level I · CFA Level I Exam

Fixed-Income Bond Valuation: Prices and Yields

Bond valuation means pricing a bond as the present value of its coupons and principal, discounted at the market yield. Price and yield move in opposite directions. To solve questions, list the cash flows, pick the right discount rate and period count, then compute with your calculator's TVM keys or spot rates.

What this chapter covers

This chapter teaches you how a bond's price is built from its cash flows and how that price relates to yield. You start with the pricing equation, then see how price changes when yield changes (the price-yield curve and convexity), and how price drifts toward par as time passes.

The second half widens the lens. You price bonds with spot rates and matrix pricing, then learn the yield measures used for fixed-rate bonds, floating-rate notes and money market instruments. You finish with yield spreads and the term structure, which show how bonds are compared with benchmarks and with each other.

This chapter is the base for the rest of Fixed Income. Duration, credit analysis, securitised products and derivatives on rates all assume you can price a bond and read a yield. It also links to Quantitative Methods through time value of money, and to Portfolio Construction through the way rates drive portfolio returns.

Fixed Income carries a topic weight of 11-14% on the Level I exam, and this chapter feeds almost every later question in it. Questions are standalone three-option MCQs, so a clean calculation earns a mark quickly. There is no penalty for wrong answers, but you will still lose marks to avoidable errors such as wrong period counts or mixed-up yield definitions. Mastering the pricing mechanics here also speeds up duration and credit questions later, and the numerical options are listed smallest to largest, which helps you sanity-check your answer.

Fixed-Income Bond Valuation: Prices and Yields: topics in the order to study them

  1. 1Bond Prices and the Pricing EquationEverything else depends on pricing a bond as the present value of coupons and principal.
  2. 2Price-Yield Relationship and ConvexityOnce you can price a bond, you see how price reacts to yield changes and why the curve bends.
  3. 3Pull to Par and Constant-Yield Price TrajectoryIt extends the pricing equation across time, showing how premium and discount bonds move toward par.
  4. 4Spot Rates and Matrix PricingIt replaces one flat yield with a set of discount rates, and uses comparable bonds to estimate prices.
  5. 5Yield Measures for Fixed-Rate BondsWith pricing clear, you can learn the different yields quoted on the same bond and when each applies.
  6. 6Yield Measures for Floating-Rate Notes and Money MarketFloating-rate and short-term instruments use different conventions, so learn them after the fixed-rate basics.
  7. 7Yield Spreads and the Term StructureIt ties the chapter together by comparing yields across benchmarks, credit risk and maturity.

How to prepare Fixed-Income Bond Valuation: Prices and Yields

Treat this chapter as a calculation skill first and a vocabulary list second. Practise by hand with your approved calculator until the steps are automatic.

  1. Set up your TI BA II Plus or HP 12C for bond pricing. On the TI, set P/Y = 1 or 2 to match the compounding, then enter N, I/Y, PMT and FV and compute CPT PV. Drill until you never mis-set the periods.
  2. Price at least ten bonds: annual and semiannual, premium, par and discount. Always write N, the periodic rate and the periodic coupon before you press any keys.
  3. Change the yield in each example and note the new price. Check that the price rises when yield falls, and that a fall in yield raises price by more than an equal rise in yield lowers it.
  4. Practise pull to par by recomputing the price one period later at the same yield. Confirm that the discount bond's price rises and the premium bond's price falls.
  5. Build a one-page table of yield measures, with the formula, the cash flow assumptions and the bond type each one suits. Test yourself until you can say which yield fits which question.
  6. Do timed sets of standalone MCQs at about 90 seconds each. Eliminate options that go in the wrong direction before you calculate.
  7. Review every wrong answer and tag the cause: wrong formula, wrong period count or misread wording. Redo the tagged questions after two days.

Common mistakes in Fixed-Income Bond Valuation: Prices and Yields

  • Using annual inputs for a semiannual bond.

    Fix: Write N, periodic rate and periodic coupon on paper first. For semiannual pay, halve the rate and coupon and double the years.

  • Mixing up the direction of price change when yield moves.

    Fix: Remember that a higher discount rate shrinks present value. Use this to rule out options that move the wrong way.

  • Forgetting that the price-yield relationship is curved, not linear.

    Fix: Treat convexity as the reason gains from falling yields exceed losses from rising yields of the same size.

  • Confusing the bond price at a later date with the price today at a different yield.

    Fix: Separate the two effects. Change only time for the constant-yield path, and change only yield for the price-yield curve.

  • Applying one yield measure to every bond.

    Fix: Check the bond type and the question wording, then match the yield measure to its assumptions before you calculate.

  • Discounting all cash flows at a single rate when spot rates are given.

    Fix: When a question gives spot rates, discount each cash flow at the spot rate for its own maturity and add them up.

Last-day revision: Fixed-Income Bond Valuation: Prices and Yields

  • Bond price = Σ cash flows discounted at the yield per period, plus principal discounted at the same rate.
  • Price and yield move in opposite directions.
  • Coupon rate above yield gives a premium price; below yield gives a discount; equal gives par.
  • For a semiannual bond, halve the annual yield and coupon and double the years to get N.
  • The price-yield curve is convex, so a given yield fall raises price more than the same yield rise lowers it.
  • With a constant yield, a discount bond's price rises toward par and a premium bond's price falls toward par.
  • A spot rate is the yield on a zero-coupon bond for a given maturity; price a bond by discounting each cash flow at its own spot rate.
  • Matrix pricing estimates the yield of an illiquid bond from comparable bonds with similar credit quality and maturity.
  • Know which yield is which: yield to maturity, current yield, yield to call and yield to worst each have different assumptions.
  • A yield spread is a bond's yield minus a benchmark yield, and it compensates for credit, liquidity and other risks.
  • Always check whether a question gives a quoted annual rate with periodic compounding before you set N and the rate.
  • Use the direction of change to remove one or two options before you calculate.

Fixed-Income Bond Valuation: Prices and Yields practice questions

Fixed-Income Bond Valuation: Prices and Yields in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Fixed-Income Bond Valuation: Prices and Yields: frequently asked questions

How do I calculate a bond's price on the TI BA II Plus?

Enter N as the number of periods, I/Y as the periodic yield in percent, PMT as the periodic coupon and FV as the par value, then press CPT PV. The result is negative because the calculator treats it as a cash outflow, so read its absolute value as the price.

Why does a bond trade at a premium or a discount?

A bond trades at a premium when its coupon rate is above the market yield, because its cash flows are worth more than required. It trades at a discount when the coupon is below the market yield. At equal rates, the price is par.

What is the difference between a spot rate and a yield to maturity?

A spot rate is the yield on a zero-coupon bond for a specific maturity. Yield to maturity is a single rate that equates the present value of all of a bond's cash flows to its price. Using spot rates discounts each cash flow separately.

Do I need to memorise every yield formula for the exam?

You need to know the main ones well enough to apply them and to know their assumptions. Focus on when each measure applies and on setting up the calculation correctly. The exam asks standalone questions, so clear understanding is more useful than rote recall.