NISM Series V-D adds derivatives and interest-rate instruments to the mutual fund syllabus, and both bring calculations: NAV and expenses, index levels, futures pricing, option payoffs and strategies, and bond price, yield and duration. Take one of the two free 20-question numerical tests below (you need a free account), then use the formula sheet to fix whatever you got wrong. Scoring copies the real exam: +1 for a correct answer, −0.10 for a wrong one.
Two free 20-question tests, 40 different calculation questions in all: NAV and expenses, returns, index and futures pricing, option payoffs and strategies, and bond yield and duration. Every answer comes with the formula, the working and the common mistake when you finish.
NISM does not publish how many questions in each paper are numerical, so use this table as a guide to where calculations appear in the V-D syllabus. The last two columns show how many numerical questions BullWiser has written for each chapter (200 in the full bank, 40 of them in the two free tests).
| Chapter | What gets calculated | Full bank | Free tests |
|---|---|---|---|
| 5. Scheme Related Information | SIP units, IDCW effect on NAV, allocation drift, merger swap and switch units | 6 | 3 |
| 7. Net Asset Value, Total Expense Ratio and Pricing of Units | NAV per unit, units for cut-off NAV, exit load, TER accrual, closed-end discount | 14 | 3 |
| 8. Taxation | STCG and LTCG tax, loss set-off, debt fund tax, TDS, STT, FIFO gains | 12 | 2 |
| 10. Risk, Return and Performance of Funds | HPR, CAGR, standard deviation, beta, CAPM, Sharpe, Treynor, Jensen alpha | 12 | 3 |
| 11. Mutual Fund Scheme Performance | Tracking error and difference, information ratio, geometric return, portfolio turnover | 8 | 4 |
| 12. Mutual Fund Scheme Selection | Age-based allocation, rebalancing, SIP and lump sum for goals, real and direct-plan returns | 8 | 3 |
| 13. Basics of Derivatives | Futures contract value, margin, forward P&L, hedge lots, imperfect hedge | 5 | 2 |
| 14. Understanding Index | Index level, divisor, base cap, free-float weights, impact cost, portfolio beta | 15 | 2 |
| 15. Introduction to Forwards and Futures | MTM, futures P&L, fair value, basis, cost of carry, arbitrage, calendar spread, hedge | 28 | 3 |
| 16. Introduction to Options | Premium paid, intrinsic and time value, breakeven, option P&L, put-call parity, delta | 30 | 2 |
| 17. Strategies using Equity Futures and Equity Options | Spread, straddle, strangle, butterfly, covered call, collar payoffs and limits | 25 | 3 |
| 18. Interest Rate Instruments and Fixed Income Markets | Bond price, YTM, duration, DV01, forward rate, T-bill price, accrued interest | 12 | 2 |
| 19. Interest Rate Derivatives | Swap payments and MTM, par swap rate, FRA settlement, implied FRA rate | 8 | 2 |
| 20. Exchange Traded Interest Rate Futures | IRF contract value, P&L, margin, notional bond price, PV01, basis with conversion factor | 6 | 2 |
| 21. Exchange Traded Interest Rate Options | IRF option premium, breakeven, call and put profit, protective put | 5 | 2 |
| 22. Strategies using Interest Rate Derivatives | Duration-based hedge lots, DV01 hedge, basis trade, curve spread P&L | 6 | 2 |
Chapters 1, 2, 3, 4, 6, 9 are mostly theory, so they have no numerical set here.
Every formula below is used in the practice questions. Read the note column for conventions such as compounding period and sign.
| Measure | Formula | Note |
|---|---|---|
| NAV and total assets | NAV = (Investments + Receivables + Cash − Liabilities) ÷ Units ; Net assets = NAV × Units | |
| Units, exit load and switches | Units = Amount ÷ NAV ; Redemption amount = Units × NAV × (1 − Exit load %) ; Units of B = Units of A × NAV(A) × (1 − load) ÷ NAV(B) | |
| Expenses and net growth | Daily expense = Net assets × Annual rate ÷ 365 ; Year-end NAV = Opening NAV × (1 + Gross return − TER) | |
| IDCW, closed-end price and merger | Ex-IDCW NAV = Cum-IDCW NAV − IDCW ; Market price = NAV × (1 − Discount %) ; Swap: Units of Y = Units of X × NAV(X) ÷ NAV(Y) | |
| Turnover and SIP units | Turnover = min(Purchases, Sales) ÷ Average net assets ; SIP units = Σ (Amount ÷ NAV each month) |
| Measure | Formula | Note |
|---|---|---|
| Equity fund capital gains tax | STCG tax = 20% × STCG ; LTCG tax = 12.5% × (LTCG − Rs. 1,25,000) ; Set-off: net gains after losses | |
| Debt fund and cess | Tax = Gain × Slab rate × (1 + Cess rate) | Cess = 4% of tax |
| Gain, FIFO, TDS and STT | Gain = Redemption value − FIFO cost of units sold ; STT = Value × STT rate ; IDCW TDS applies only above the threshold ; NRI TDS = Rate × Capital gain |
| Measure | Formula | Note |
|---|---|---|
| Holding period and annualised return | HPR = (Ending NAV − Beginning NAV + IDCW) ÷ Beginning NAV ; Annualised = (1 + HPR)^(365/days) − 1 | |
| CAGR and geometric mean | CAGR = (End ÷ Begin)^(1/n) − 1 ; Geometric = [(1 + r1)(1 + r2)…(1 + rn)]^(1/n) − 1 | |
| Expected return and standard deviation | E(R) = Σ p × R ; SD = √[Σ (x − mean)² ÷ n] ; Range = Mean ± k × SD | k = 1: about 68%; k = 2: about 95%; k = 3: about 99.7% |
| Beta and portfolio risk | Beta = ρ × σfund ÷ σmarket ; Var = w1²σ1² + w2²σ2² + 2 w1 w2 ρ σ1 σ2 ; Portfolio beta = Σ w × β | |
| CAPM, Sharpe, Treynor and Jensen | CAPM: E(R) = Rf + β × (Rm − Rf) ; Sharpe = (Rp − Rf) ÷ σp ; Treynor = (Rp − Rf) ÷ β ; Alpha = Rp − [Rf + β(Rm − Rf)] | |
| Index fund tracking | Tracking difference = Fund return − Index return ; Tracking error = SD of (Fund − Index) ; IR = (Fund − Benchmark) ÷ Tracking error |
| Measure | Formula | Note |
|---|---|---|
| SIP maturity and SIP needed | FV = P × [(1 + i)^n − 1] ÷ i ; SIP = FV × i ÷ [(1 + i)^n − 1] | i = annual rate ÷ 12, n = months, end-of-month investing |
| Lump sum and real return | PV = FV ÷ (1 + r)^n ; Real = (1 + nominal) ÷ (1 + inflation) − 1 | |
| Allocation and rebalancing | Equity amount = Corpus × (100 − Age) ÷ 100 ; Shift = Current equity − Target weight × Portfolio ; Portfolio return = Σ w × R | |
| Direct vs regular plan | Difference = P × [(1 + g − TERdirect)^n − (1 + g − TERregular)^n] |
| Measure | Formula | Note |
|---|---|---|
| Index levels | Market-cap index = Current cap ÷ Base cap × Base value ; Free-float: use Price × Shares × Free-float factor ; Price-weighted = Σ prices ÷ Divisor | |
| Divisor and base capitalisation | New divisor = New Σ prices ÷ Old index value ; New base cap = Old base cap × New total cap ÷ Old total cap | |
| Impact cost | Impact cost = (Average execution price − Ideal price) ÷ Ideal price × 100 ; Ideal = (Best bid + Best ask) ÷ 2 | |
| Futures value, P&L and MTM | Contract value = Price × Lot × Lots ; Long P&L = (Exit − Entry) × Lot × Lots ; Short P&L = (Entry − Exit) × Lot × Lots ; MTM = (Today's settlement − Previous) × Lot × Lots | |
| Fair value and basis | F = S × (1 + r × t) ; F = S × e^(rT) ; With dividend yield: F = S × e^((r − q)T) ; Basis = Spot − Futures | |
| Hedge lots and margin | Lots = β × Portfolio value ÷ (Index level × Lot size) ; Initial margin = Contract value × Margin % |
| Measure | Formula | Note |
|---|---|---|
| Payoff and intrinsic value | Call payoff = max(S − K, 0) ; Put payoff = max(K − S, 0) ; Time value = Premium − Intrinsic value | |
| Option P&L and breakeven | Buyer P&L = (Payoff − Premium) × Lot × Lots ; Writer P&L = opposite ; Call BE = K + Premium ; Put BE = K − Premium | |
| Put-call parity | C − P = S − K × e^(−rT) | European options, no dividends |
| Delta | New premium ≈ Old premium + Delta × Change in underlying ; Shares to hold = Delta × Lot × Lots |
| Measure | Formula | Note |
|---|---|---|
| Spreads | Bull call max loss = Net debit × Lot ; Bull call / bear put max profit = (K2 − K1 − Net debit) × Lot ; Credit spread max loss = (Strike gap − Net credit) × Lot | |
| Straddle, strangle and butterfly | Long straddle P&L = (|S − K| − Total premium) × Lot ; Strangle max loss = Total premium × Lot ; Butterfly max profit = (Wing width − Net debit) × Lot | |
| Covered call, protective put and collar | Covered call return if exercised = (K − Purchase + Premium) ÷ Purchase ; Protective put BE = Purchase + Premium ; Collar max loss = (Purchase − Put strike + Net premium) × Lot |
| Measure | Formula | Note |
|---|---|---|
| Bond price and yields | P = Σ C ÷ (1 + y)^t + Face ÷ (1 + y)^n ; CY = Coupon ÷ Price ; YTM ≈ [C + (F − P)/n] ÷ [(F + P)/2] | |
| Duration and DV01 | Mac. duration = Σ t × PV(CFt) ÷ Price ; ModD = MacD ÷ (1 + y) ; %ΔP ≈ −ModD × Δy ; DV01 = ModD × Price × 0.0001 | |
| Forward rate | f = (1 + s2)² ÷ (1 + s1) − 1 | |
| Zero-coupon, T-bill and repo | Zero price = Face ÷ (1 + y)^n ; T-bill price = Face ÷ (1 + y × days/365) ; Repo interest = Amount × r × days/365 ; Clean = Dirty − Accrued interest |
| Measure | Formula | Note |
|---|---|---|
| Swap payments and par rate | Fixed payer (semi-annual) = N × (Floating − Fixed) ÷ 2 ; Par rate = (1 − DFn) ÷ Σ DF ; MTM = N × (Market rate − Fixed) × Annuity factor | |
| FRA | Buyer settlement = N × (Rref − Rfra) × (d/360) ÷ (1 + Rref × d/360) | Seller receives the negative |
| IRF value, P&L and margin | Contract value = Price × 2,000 × Lots ; Long P&L = (Exit − Entry) × 2,000 × Lots ; Margin = Contract value × Margin % ; Basis = Cash − CF × Futures | |
| IRF options | Call P&L = [max(F − K, 0) − Premium] × 2,000 × Lots ; Put P&L = [max(K − F, 0) − Premium] × 2,000 × Lots | |
| Hedge and duration lots | Lots = MDp × V ÷ (MDf × Contract value) ; Change duration: Lots = (MDtarget − MDcurrent) × V ÷ (MDf × CV) |
Spoiler warning: if you want to test yourself first, take the tests above before reading the tables.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 5 | SIP average cost per unit | 1966.667 | 666.667 + 800.000 + 500.000 = 1966.667. |
| 5 | Scheme merger swap ratio | 900.00 | 2000 x 18.00 / 40.00 = 900.00. |
| 7 | NAV after gain and expenses | Rs. 12.61 | 500 x 1.0250 = 512.50; - 8.00 = 504.50; / 40 = 12.61. |
| 7 | Units to redeem for a target amount | 3248.731 | 80000 / (25.00 x 0.985) = 3248.731. |
| 8 | NRI TDS on redemption | Rs. 76,250.00 | Gain = Rs. 30,000.00; TDS = Rs. 3,750.00; Rs. 80,000.00 - Rs. 3,750.00 = Rs. 76,250.00. |
| 10 | Annualising a short-period return | 12.67% | (1 + 0.0400)^(365/120) - 1 = 12.67%. |
| 11 | Arithmetic vs geometric return | 3.92% | (1.20 x 0.90)^(1/2) - 1 = 3.92%. |
| 11 | Portfolio turnover ratio | 20.00% | min(600, 400) / 2000 = 20.00%. |
| 12 | Portfolio rebalancing amount | Rs. 4,00,000 | Rs. 29,00,000 - 0.5 x 50,00,000 = Rs. 4,00,000. |
| 13 | Contract value of index futures | Rs. 44,00,000 | 22,000 x 50 x 4 = Rs. 44,00,000. |
| 14 | Divisor after a stock split | 2.700 | Old index = 1000/3 = 333.333; new sum = 900; divisor = 900/333.333 = 2.700. |
| 15 | Futures price - simple interest carry | Rs. 2040.00 | 2000 x (1 + 0.12 x 2/12) = 2040.00. |
| 15 | Implied cost of carry from futures price | 8.00% | ln(1040.24/1000) = 0.03945; / 0.4932 = 8.00% p.a. |
| 16 | Move needed to break even | +4.50% | Breakeven = 2090.00; (2090.00 - 2000.00) / 2000.00 = +4.50%. |
| 17 | Long strangle | Rs. 11,500 | (120 + 110) x 50 = Rs. 11,500. |
| 18 | Accrued interest and dirty price | Rs. 98.50 | 99.90 - 1.40 = 98.50. |
| 19 | Par swap rate from discount factors | 6.89% | (1 - 0.8163) / (0.9524 + 0.8985 + 0.8163) = 6.89%. |
| 20 | IRF profit or loss on price move | Loss of Rs. 9,000 | (102.10 - 101.20) x 2,000 x 5 x -1 = Loss of Rs. 9,000. |
| 21 | IRF option premium payable | Rs. 12,000 | 0.50 x 2,000 x 12 = Rs. 12,000. |
| 22 | Number of IRF lots to hedge using DV01 | 800 lots | DV01 = 4.0 x 30,00,00,000 x 0.0001 = Rs. 1,20,000; / 150 = 800 lots. |
The second free test covers different topics and numbers from Test 1. The same spoiler warning applies.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 5 | Asset allocation drift after market move | 52.38% | Equity = 500 x 1.10 = 550.0; total = 550.0 + 500 = 1050.0; weight = 52.38%. |
| 7 | Applicable NAV and cut-off time | 1785.714 | Received at 3:40 pm on Tuesday, so applicable NAV is Wednesday's Rs. 28.00; 50000 / 28.00 = 1785.714. |
| 8 | Debt fund gains at slab rate with cess | Rs. 11,700.00 | Gain = Rs. 37,500.00; tax = Rs. 37,500.00 x 30% x 1.04 = Rs. 11,700.00. |
| 10 | Expected return from scenarios | 11.50% | 0.3 x 25 + 0.5 x 12 + 0.2 x -10 = 11.50%. |
| 10 | Standard deviation of returns | 3.57% | Mean = 12.50; Sum sq dev = 51.00; /4 = 12.75; sqrt = 3.57%. |
| 11 | Tracking difference | -0.80% | 11.2 - 12.0 = -0.80%. |
| 11 | Tracking error of an index fund | 0.316% | Mean difference = 0; sum of squares = 0.40; /4 = 0.1000; sqrt = 0.316%. |
| 12 | Future value of a monthly SIP | Rs. 8,16,697 | i = 0.0100, n = 60; FV = 10,000 x 81.6697 = Rs. 8,16,697. |
| 12 | Lump sum needed for a goal | Rs. 3,85,543 | 10,00,000 / 2.5937 = Rs. 3,85,543. |
| 13 | Imperfect hedge outcome | Rs. 40,000 | Portfolio loss = Rs. 1,60,000; futures gain = Rs. 1,20,000; net loss = Rs. 40,000. |
| 14 | Base cap adjustment for constituent change | Rs. 1100.00 crore | New cap = 2000 - 100 + 300 = 2200; 1000 x 2200/2000 = 1100.00. |
| 15 | Profit or loss on futures position | Loss of Rs. 24,000 | (24920.0 - 25000.0) x 100 x 3 = Loss of Rs. 24,000. |
| 16 | Put-call parity arbitrage profit | Rs. 599.68 | K x e^(-rT) = 1200.99; (C - P) = 5.01; S - PV(K) = -0.99; difference 6.00 x 100 = Rs. 599.68. |
| 17 | Covered call | Rs. 7,40,000 | (1500 - 20) x 500 = Rs. 7,40,000. |
| 17 | Long or short straddle | Profit of Rs. 2,250 | (|22500 - 22000| - 470) x 75 = Profit of Rs. 2,250. |
| 18 | Zero-coupon bond price | Rs. 712.99 | 1000 / 1.4026 = Rs. 712.99. |
| 19 | Effective borrowing cost after a swap | Rs. 17.00 crore | (7.5% + 1.0%) x 200 = Rs. 17.00 crore, whatever MIBOR turns out to be. |
| 20 | Initial margin on IRF | Rs. 81,800 | 102.25 x 2,000 x 20 = Rs. 40,90,000; x 2.0% = Rs. 81,800. |
| 21 | Protective put on IRF long | Loss of Rs. 36,000 | (98.10 - 99.80) + (99.30 - 98.10) - 0.40 = -0.90; x 2,000 x 20 = Loss of Rs. 36,000. |
| 22 | Changing portfolio duration with futures | Sell 938 lots | (4.0 - 7.0) x 50,00,00,000 / (8.0 x 2,00,000) = -937.5 => Sell 938 lots. |
Yes. Besides the mutual fund calculations (NAV, expenses, taxation, returns), the derivatives chapters need index, futures pricing, option payoff and strategy break-even arithmetic, and the interest-rate chapters need bond price, yield and duration calculations. NISM does not publish how many questions are numerical.
NISM's general candidate instructions say candidates may bring their own physical calculator, which must be silent and have no connectivity, and that rough sheets are provided by the invigilator. Confirm the rules in your registration or admit instructions before exam day.
The exam has 150 MCQs of 1 mark each over 180 minutes. The pass mark is 90 out of 150 (60%). Each wrong answer costs 10% of the question's marks, so 0.10 for a 1-mark question. Unanswered questions score zero.
You get 1 mark for each correct answer and lose 0.10 for each wrong answer, the same 10% scheme as the exam for a 1-mark question. Skipped questions score zero.
Yes. Two 20-question numerical tests (40 solved questions) are free with a free BullWiser account, which takes a few seconds to create. The full bank of 200 numerical questions, served 25 at a time and favouring questions you have not seen, comes with BullWiser V-D mock access, a one-time payment of Rs 199 per series.
Yes. Every question in the two free tests shows the correct answer, the formula, the step-by-step working and the common mistake when you finish. The solutions are also published on this page, so you can read them without taking the test.
No. BullWiser prepared them from the standard formulas taught in the NISM workbook, and each has a worked explanation. Names of people, companies and funds are fictional. BullWiser is not affiliated with NISM.
Take the full-length V-D mock, read the V-D notes and question bank, or start with the chapters that have the most numericals: Introduction to Options, Introduction to Forwards and Futures, Strategies using Equity Futures and Equity Options.
Preparing for another paper? Numerical practice is also available for: