NISM Series XIII Formula Sheet
Ten formulas, what each one is for, and a worked example.
Series XIII combines equity, currency and interest rate derivatives in one paper. The good news is that most of the formulas are shared: cost of carry, payoffs, mark-to-market and hedging look the same whatever the underlying.
These ten formulas cover all three segments, with a worked mark-to-market example.
The 10 Formulas
1
Formula
Equity futures fair price
Expression
F = S × (1 + r × t) − Dividends
Use it for
Stock and index futures.
2
Formula
Currency futures fair price
Expression
F = S × (1 + r_INR × t) ÷ (1 + r_foreign × t)
Use it for
USD/INR and other currency pairs.
3
Formula
Basis
Expression
Futures price − Spot price
Use it for
Premium of futures over spot in any segment.
4
Formula
Mark-to-market
Expression
(Today's settlement − Previous settlement) × Lot size × Contracts
Use it for
Daily cash settlement on futures.
5
Formula
Long call payoff
Expression
max(S_T − K, 0) − Premium
Use it for
Buying the right to buy.
6
Formula
Long put payoff
Expression
max(K − S_T, 0) − Premium
Use it for
Buying the right to sell.
7
Formula
Put-call parity
Expression
C + K ÷ (1 + r)ᵗ = P + S
Use it for
Linking call and put prices.
8
Formula
Hedge ratio (beta)
Expression
Portfolio value × β ÷ Contract value
Use it for
Equity index futures needed to hedge a portfolio.
9
Formula
Bond price sensitivity
Expression
ΔP% ≈ −Modified duration × Δy
Use it for
Effect of a rate change on an interest rate futures position.
10
Formula
Contract value
Expression
Futures price × Lot size
Use it for
Exposure per contract in any segment.
| # | Formula | Expression | Use it for |
|---|---|---|---|
| 1 | Equity futures fair price | F = S × (1 + r × t) − Dividends | Stock and index futures. |
| 2 | Currency futures fair price | F = S × (1 + r_INR × t) ÷ (1 + r_foreign × t) | USD/INR and other currency pairs. |
| 3 | Basis | Futures price − Spot price | Premium of futures over spot in any segment. |
| 4 | Mark-to-market | (Today's settlement − Previous settlement) × Lot size × Contracts | Daily cash settlement on futures. |
| 5 | Long call payoff | max(S_T − K, 0) − Premium | Buying the right to buy. |
| 6 | Long put payoff | max(K − S_T, 0) − Premium | Buying the right to sell. |
| 7 | Put-call parity | C + K ÷ (1 + r)ᵗ = P + S | Linking call and put prices. |
| 8 | Hedge ratio (beta) | Portfolio value × β ÷ Contract value | Equity index futures needed to hedge a portfolio. |
| 9 | Bond price sensitivity | ΔP% ≈ −Modified duration × Δy | Effect of a rate change on an interest rate futures position. |
| 10 | Contract value | Futures price × Lot size | Exposure per contract in any segment. |
Worked Example: Mark-to-Market on Currency Futures
A trader is long 10 USD/INR futures contracts (lot size USD 1,000). Yesterday's settlement price was ₹84.30 and today's is ₹84.42.
- 1
Price change
84.42 − 84.30 = ₹0.12 per dollar.
- 2
Per contract
0.12 × 1,000 = ₹120.
- 3
For the position
120 × 10 = ₹1,200 credited to the long position today.
Free account, this exam preselected.
One Structure, Three Segments
Once you know the cost-of-carry idea, the only difference between segments is what is carried: interest less dividends for equity, the interest differential for currency, and coupon against financing for bonds.
FAQs
Is Series XIII harder than VIII or I?expand_more
It covers more ground, because it combines segments, but each formula is the same as in the single-segment exams.
Does mark-to-market apply to options?expand_more
Option buyers pay the premium upfront. Daily mark-to-market settlement applies to futures.
Why is currency futures pricing a ratio?expand_more
Because both currencies earn interest. The forward rate reflects the difference between the two rates.
Next steps
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