calculation-reference

CFA Level I Fixed Income Calculations

Bond pricing, yield, duration, convexity, spot rates, and forward rates for CFA Level I.

TL;DR

Fixed income calculations reduce to discounting promised cash flows and measuring sensitivity to yield changes. The core tools are bond price, YTM, spot rates, Macaulay duration, modified duration, and convexity.

Formula Reference

Bond price

Price = sum[Coupon_t / (1 + y)^t] + Par / (1 + y)^n

Discount each coupon and principal payment at the required yield.

Modified duration

ModDur = MacDur / (1 + y / m)

Use periodic yield based on coupon frequency.

Price change

Approx % price change = -ModDur x change in yield

Add convexity for larger yield changes.

BA II Plus Keystrokes

  1. 2nd CLR TVM
  2. N = years x coupon frequency
  3. I/Y = annual YTM / coupon frequency
  4. PMT = coupon rate x par / coupon frequency
  5. FV = par
  6. CPT PV

Worked Example

  • Problem: 5-year annual-pay bond, 6 percent coupon, 8 percent YTM, $1,000 par.
  • Keystrokes: 2nd CLR TVM; 5 N; 8 I/Y; 60 PMT; 1000 FV; CPT PV.
  • Result: PV is about -920.15, so price is $920.15.

Common Mistakes

  • For semiannual bonds, forgetting to double N and halve I/Y and PMT.
  • Interpreting the negative PV sign as a negative bond value.
  • Using Macaulay duration directly for a price-change estimate.

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