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FRM Part I · FRM Exam Part I

Properties of Interest Rates for FRM Part I

Properties of interest rates covers how rates are quoted, compounded and converted, how zero rates and forward rates come from bond prices, and how duration and convexity measure price sensitivity. To solve questions, identify the compounding basis, discount cash flows at the right rate, then apply the formula step by step.

What this chapter covers

This chapter is the base of fixed income and rate-based valuation in FRM Part I. It starts with how a rate is stated: the compounding frequency, the day count and the reference rate behind it. It then moves to zero rates, bond prices and bootstrapping, followed by forward rates and forward rate agreements. It ends with duration, convexity and the theories that explain why the yield curve slopes the way it does.

The maths is not hard, but the questions are multi-step. You may need to convert a rate from annual to continuous compounding, discount a bond's cash flows, back out a forward rate, and then estimate a price change. One slip in the first step carries through to the final answer.

The chapter connects to the rest of the paper in several ways. Valuation and Risk Models uses duration, convexity and DV01 when it covers market risk measurement. Financial Markets and Products uses forward rates for futures, swaps and FRAs. Quantitative Analysis supplies the tools for the risk work built on top of these rates. If you learn this chapter well, much of that later material becomes easier.

Questions on rates are calculation-heavy, and they test whether you can follow a method without slipping. That makes them reliable marks for a prepared candidate. With 100 questions in 4 hours, you need to solve a compounding conversion or a duration estimate in a couple of minutes. The ideas also recur in other chapters, so time spent here pays off beyond this one. GARP does not publish a pass mark, so you cannot afford to leave easy-to-practise topics weak.

Properties of Interest Rates: topics in the order to study them

  1. 1Interest Rate Measurement and CompoundingEvery later formula assumes you can state a rate on the right compounding basis and convert between bases.
  2. 2Types of Interest Rates and Reference RatesLearn the vocabulary of treasury, repo and overnight reference rates before using rates in pricing, so the terms in questions are clear.
  3. 3Zero Rates, Bond Pricing and BootstrappingBond prices are discounted cash flows at zero rates, and bootstrapping builds the curve you need for forwards.
  4. 4Forward Rates and Forward Rate AgreementsForward rates are derived from the zero curve, so they come once you are comfortable with zero rates.
  5. 5Duration and ConvexityThese measure how bond prices respond to yield changes and rely on your bond pricing skills.
  6. 6Theories of the Term StructureThis is mostly conceptual, so it works best last, when you can link each theory to the curves you have already built.

How to prepare Properties of Interest Rates

Treat this as a calculation chapter. Learn each method, then drill it until the steps are automatic.

  1. Read the topics in the order above and write each formula on one page, with the conditions under which it applies.
  2. Practise compounding conversions until you can switch between annual, semiannual and continuous rates without looking at notes.
  3. Solve bond pricing and bootstrapping problems by hand, writing out each cash flow and discount factor, then check them with your financial calculator's cash flow and time value functions.
  4. Work forward rate and FRA questions in both directions: from zero rates to forwards, and from forwards back to a price or payoff.
  5. For duration and convexity, practise the price-change estimate and note the sign and size of each term.
  6. Do the theories of the term structure as short written summaries: what each theory predicts for the curve and what it assumes.
  7. Finish with timed mixed sets, and log every error by cause: wrong compounding basis, wrong period count, or formula slip.

Common mistakes in Properties of Interest Rates

  • Using a rate on the wrong compounding basis

    Fix: Write the compounding frequency next to every rate before you start, and convert first if the formula needs a different one.

  • Miscounting periods and cash flows in bond pricing

    Fix: Set up a small table of time, cash flow and discount factor, and check the number of rows against the maturity.

  • Mixing up zero rates, par yields and forward rates

    Fix: Remember what each represents: a zero rate is a spot rate for one maturity, a par yield prices a coupon bond at par, and a forward rate covers a future period.

  • Forgetting the sign and units in duration estimates

    Fix: Convert yield changes to decimals first and state the expected direction of the price change before you calculate.

  • Treating convexity as a small correction that can be skipped

    Fix: Include the convexity term when it is given or the move is large, and know that it always helps the holder of a bond with positive convexity.

  • Learning the term structure theories as lists of names

    Fix: For each theory, write what it says about the curve's shape and why, so you can match a description to the theory.

Last-day revision: Properties of Interest Rates

  • Continuous rate: Rc = m × ln(1 + Rm ÷ m), and Rm = m × (e^(Rc ÷ m) − 1).
  • Value with continuous compounding: A × e^(R × T).
  • A bond price is the sum of its cash flows discounted at the matching zero rates.
  • Par yield is the coupon rate that prices the bond at par.
  • Bootstrapping solves for each new zero rate using the earlier ones, working from short to long maturities.
  • Forward rate with continuous compounding: F = (R2 × T2 − R1 × T1) ÷ (T2 − T1).
  • With an upward-sloping zero curve, forward rates sit above zero rates for the same maturity.
  • Modified duration ≈ Macaulay duration ÷ (1 + y ÷ m).
  • ΔP ÷ P ≈ −D × Δy + ½ × C × (Δy)².
  • Convexity adds to price gains when yields fall and reduces losses when yields rise.
  • DV01 is the price change for a one basis point move in yield.
  • Expectations theory ties the long rate to expected future short rates; liquidity preference and market segmentation add other explanations.

Properties of Interest Rates practice questions

Properties of Interest Rates in other exams

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

Properties of Interest Rates: frequently asked questions

How much calculation is in the Properties of Interest Rates chapter?

A large part of it is numerical: compounding conversions, bond prices, forward rates, and duration and convexity estimates. The term structure theories are conceptual. Prepare for both, but give most practice time to the calculations.

Do I need a financial calculator for this chapter?

It helps for bond pricing and time value steps, and it saves time on longer cash flow problems. You still need to understand the formula so you can set up the inputs correctly. Practise with your approved calculator before exam day.

Which topic should I start with?

Start with interest rate measurement and compounding. Every other topic uses rates stated on a specific basis, so errors here carry through everything that follows.

How does this chapter link to the rest of FRM Part I?

Duration, convexity and DV01 feed into market risk measurement, and forward rates support the study of futures, swaps and FRAs. The compounding and discounting skills you build here are used across valuation questions.