IIBF CTP Formula Sheet
Ten formulas, what each one is for, and a worked example.
A treasury desk spends its day pricing bonds, converting yields and quoting forward rates, and the CTP exam tests the same skills. These ten formulas cover the money market, bonds and forex.
A worked T-bill example follows the table.
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The 10 Formulas
1
Formula
Bond price
Expression
P = Σ C ÷ (1 + y)ᵗ + F ÷ (1 + y)ⁿ
Use it for
Price of a coupon bond for a given yield.
2
Formula
Current yield
Expression
Annual coupon ÷ Market price
Use it for
Running income return on a bond.
3
Formula
Approximate YTM
Expression
[C + (F − P) ÷ n] ÷ [(F + P) ÷ 2]
Use it for
Quick yield-to-maturity estimate without iteration.
4
Formula
T-bill yield
Expression
y = (100 − P) ÷ P × 365 ÷ Days to maturity × 100
Use it for
Annualised yield on a treasury bill bought at price P.
5
Formula
Macaulay duration
Expression
D = Σ[t × PV(CFₜ)] ÷ P
Use it for
Weighted average life of a bond's cash flows.
6
Formula
Modified duration and price change
Expression
MD = D ÷ (1 + y); ΔP% ≈ −MD × Δy
Use it for
Interest-rate sensitivity of a bond or portfolio.
7
Formula
Accrued interest (G-secs)
Expression
Coupon × Face value × Days since last coupon ÷ 360
Use it for
Interest the buyer pays the seller. G-secs use 30/360.
8
Formula
Implied forward rate
Expression
(1 + s₂)² = (1 + s₁) × (1 + f₁,₂)
Use it for
One-year rate one year from now, implied by spot rates.
9
Formula
Forward exchange rate (interest parity)
Expression
F = S × (1 + r_d × t) ÷ (1 + r_f × t)
Use it for
Theoretical forward rate from spot and the two interest rates.
10
Formula
Repo interest
Expression
Amount × Repo rate × Days ÷ 365
Use it for
Interest on a repo or TREPS borrowing.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Bond price | P = Σ C ÷ (1 + y)ᵗ + F ÷ (1 + y)ⁿ | Price of a coupon bond for a given yield. |
| 2 | Current yield | Annual coupon ÷ Market price | Running income return on a bond. |
| 3 | Approximate YTM | [C + (F − P) ÷ n] ÷ [(F + P) ÷ 2] | Quick yield-to-maturity estimate without iteration. |
| 4 | T-bill yield | y = (100 − P) ÷ P × 365 ÷ Days to maturity × 100 | Annualised yield on a treasury bill bought at price P. |
| 5 | Macaulay duration | D = Σ[t × PV(CFₜ)] ÷ P | Weighted average life of a bond's cash flows. |
| 6 | Modified duration and price change | MD = D ÷ (1 + y); ΔP% ≈ −MD × Δy | Interest-rate sensitivity of a bond or portfolio. |
| 7 | Accrued interest (G-secs) | Coupon × Face value × Days since last coupon ÷ 360 | Interest the buyer pays the seller. G-secs use 30/360. |
| 8 | Implied forward rate | (1 + s₂)² = (1 + s₁) × (1 + f₁,₂) | One-year rate one year from now, implied by spot rates. |
| 9 | Forward exchange rate (interest parity) | F = S × (1 + r_d × t) ÷ (1 + r_f × t) | Theoretical forward rate from spot and the two interest rates. |
| 10 | Repo interest | Amount × Repo rate × Days ÷ 365 | Interest on a repo or TREPS borrowing. |
What the Symbols Mean
- C, F, P
- Coupon per period, face value and price.
- y
- Yield per period.
- r_d, r_f
- Domestic and foreign interest rates for the period t, in years.
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Worked Example: 91-Day T-Bill Yield
A 91-day T-bill is bought at ₹98.25 per ₹100 face value.
- 1
Discount earned
100 − 98.25 = ₹1.75.
- 2
Return for the period
1.75 ÷ 98.25 = 1.781%.
- 3
Annualise on 365 days
1.781% × 365 ÷ 91 ≈ 7.14% a year.
Yield Up, Price Down
Every bond question rests on the inverse link between price and yield. Before you calculate, decide whether the price should rise or fall. That alone often rules out half the options.
FAQs
Why does the T-bill yield divide by price, not face value?expand_more
Because the return is earned on the amount you invest, which is the price. Dividing by face value gives the discount rate, which is lower.
Which day count do Indian G-secs use?expand_more
30/360 for accrued interest on G-secs. Money market instruments such as T-bills and repo use actual days over 365.
Is modified duration in years or percent?expand_more
It's quoted in years but read as a percentage: a modified duration of 4 means about a 4% price change for a 1 percentage point change in yield.
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