NISM Series XXI-A (PMS Distributors) has more arithmetic than most candidates expect: valuation ratios and bond maths in the markets chapters, then PMS fees, high water mark and hurdle rate, holding period return, TWRR, Sharpe and Treynor ratios and capital gains tax. 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, covering every one of the 12 chapters: returns and time value, valuation ratios, bonds, derivatives, PMS fees and loads, performance measures and tax. 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 XXI-A 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 |
|---|---|---|---|
| 1. Investments | Real and nominal rates, present and future value, required return | 15 | 3 |
| 2. Introduction to Securities Markets | Rights and bonus entitlements, MTM margin | 5 | 3 |
| 3. Investing in Stocks | P/E, P/B, P/S, PEG, EV/EBITDA, Gordon growth model, CAPM cost of equity | 24 | 3 |
| 4. Investing in Fixed Income Securities | Coupon amount, bond value, zero-coupon price, YTM direction, duration and price change | 15 | 4 |
| 5. Derivatives | Futures and option P&L, margins, zero-sum outcomes | 13 | 4 |
| 6. Collective Investment Vehicles | Units allotted at NAV, gain from NAV change | 2 | 2 |
| 7. Role of Portfolio Managers | Minimum investment, exit load caps, audit deadlines | 11 | 3 |
| 8. Operational Aspects of Portfolio Managers | Exit loads, operating-expense cap, high water mark and hurdle fees, minimum investment | 19 | 3 |
| 9. Portfolio Management Process | Allocation drift, rebalancing, surplus and net worth, relative performance | 24 | 3 |
| 10. Performance Measurement and Evaluation of Portfolio Managers | HPR, TWRR, gross vs net return, fees, portfolio return and beta, Sharpe and Treynor, attribution | 48 | 4 |
| 11. Taxation | STCG and LTCG tax, ₹1.25 lakh exemption, dividend TDS, non-deductible PMS fees | 11 | 4 |
| 12. Regulatory, Governance and Ethical Aspects of Portfolio Managers | Cash transaction reporting, unlisted-security limits, report frequency and deadlines | 13 | 4 |
Chapters 2, 6 and 7 are mostly theory, so they have only a few numerical questions.
Every formula below is used in the practice questions. Read the note column for conventions.
| Measure | Formula | Note |
|---|---|---|
| Nominal risk-free rate | NRR = (1 + real rate) × (1 + expected inflation) − 1 ; Shortcut: NRR ≈ real rate + inflation | Shortcut only for small values |
| Required return | Required return = Nominal risk-free rate + Risk premium | |
| Present and future value | FV = PV × (1 + r)^n ; PV = FV ÷ (1 + r)^n |
| Measure | Formula | Note |
|---|---|---|
| Dividend discount (Gordon) | P0 = D1 ÷ (r − g) ; D1 = D0 × (1 + g) | Use next year's dividend, not last year's |
| Cost of equity (CAPM) | re = Rf + β × (Rm − Rf) | |
| Price multiples | P/E = Price ÷ EPS ; P/BV = Price ÷ Book value per share ; P/S = Market cap ÷ Sales ; PEG = P/E ÷ EPS growth | |
| Enterprise value | EV = Market cap + Debt − Cash ; EV/EBITDA: lower suggests cheaper | |
| Free cash flow | FCFF = EBIT × (1 − t) + Depreciation − Capex − ΔWorking capital ; FCFE = Net income + Depreciation − Capex − ΔWorking capital + Net borrowing |
| Measure | Formula | Note |
|---|---|---|
| Coupon and value | Coupon = Face × Rate ÷ Payments per year ; Value = Σ C ÷ (1 + r)^t + Face ÷ (1 + r)^n ; Zero coupon = Face ÷ (1 + r)^n | Buy if value > price |
| Price and YTM | Discount bond: YTM > coupon ; Premium bond: YTM < coupon ; Par: YTM = coupon | |
| Duration | Modified duration = Macaulay duration ÷ (1 + periodic yield) ; %ΔPrice ≈ −Modified duration × Δyield | Δyield in decimals |
| Measure | Formula | Note |
|---|---|---|
| Futures | Long P&L = (Exit − Entry) × Quantity ; Short P&L = (Entry − Exit) × Quantity ; Margin = Contract value × Margin % | Both buyer and seller post margin |
| Options | Call buyer = [max(S − K, 0) − Premium] × Quantity ; Put buyer = [max(K − S, 0) − Premium] × Quantity | Writer's P&L is the opposite (zero-sum) |
| Measure | Formula | Note |
|---|---|---|
| Minimum investment | Shortfall = ₹50,00,000 − (Cash + Market value of securities brought in) | |
| Exit load caps | Year 1: up to 3% of amount redeemed ; Year 2: up to 2% ; Year 3: up to 1% ; After 3 years: nil | |
| Operating expense cap | Other expenses ≤ 0.50% p.a. × Average daily AUM | Excludes brokerage and the PMS fee |
| High water mark | Performance fee only on value above the highest value on which a fee was earlier charged | |
| Hurdle | Hurdle value = Capital × (1 + hurdle)^n ; Fee = Fee % × (Value − Hurdle value) | Compound, not simple |
| Measure | Formula | Note |
|---|---|---|
| Allocation drift | New weight = Asset value after move ÷ Total value after move | |
| Holding period return | HPR = [Income + (Ending − Beginning)] ÷ Beginning | |
| TWRR | TWRR = (1 + R1)(1 + R2)…(1 + Rn) − 1 ; Annual = (1 + TWRR)^(1/n) − 1 | Split at each external cash flow |
| Gross and net return | Return = (Portfolio value − Capital) ÷ Capital ; Post-tax = Pre-tax × (1 − Tax rate) | |
| Portfolio return and beta | Rp = Σ w × R ; βp = Σ w × β | Cash has beta 0 |
| Sharpe and Treynor | Sharpe = (Rp − Rf) ÷ σp ; Treynor = (Rp − Rf) ÷ βp | Higher is better |
| Attribution | Allocation = Σ (Wp − Wb) × Rb ; Selection = Σ Wb × (Rp − Rb) ; Interaction = Σ (Wp − Wb) × (Rp − Rb) |
| Measure | Formula | Note |
|---|---|---|
| Listed equity gains | STCG (≤ 12 months) = 20% × Gain ; LTCG = 12.5% × (Gain − ₹1,25,000) | Surcharge and cess extra |
| PMS fees | Gain = Sale price − Cost of acquisition | Management and performance fees are not deductible from capital gains |
| Dividend TDS | TDS = 10% of dividend if it exceeds ₹10,000 in the year |
Spoiler warning: if you want to test yourself first, take the tests above before reading the tables.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Additive nominal rate | 7.00% | For small values, nominal risk-free rate ≈ real risk-free rate + inflation = 2.5% + 4.5% = 7.00%. |
| 1 | Exact versus additive nominal rate | 0.21 percentage points | Exact NRR = 1.035 × 1.06 − 1 = 9.71%; additive NRR = 3.5% + 6% = 9.50%. The difference is the cross term 3.5% × 6% = 0.21 percentage points, which is why the additive form is used only for small values. |
| 2 | Rights entitlement | 500 | Rights are offered in proportion to existing holdings: 1,250 x 2/5 = 500 shares. |
| 3 | EV/EBITDA comparison | A looks cheaper: 10.0x against 11.2x for B | EV = market cap + debt − cash: A = ₹14,000 crore, B = ₹14,000 crore. EV/EBITDA: A = 10.0x, B = 11.2x; the lower multiple (A) suggests relative undervaluation. Using market cap alone ignores B's heavier debt. |
| 4 | Semi-annual coupon amount | ₹42.50 | Each coupon = face value × coupon rate ÷ 2 = ₹1,000 × 8.5% ÷ 2 = ₹42.50. |
| 4 | Modified duration rupee price change | A fall of about ₹78,400 | % change in price ≈ −MD × change in yield = −5.6 × 0.0035 = −1.96%. On ₹40,00,000 that is a fall of about ₹78,400; prices move opposite to yields. |
| 5 | Speculation P&L | a loss of ₹3,500 | Loss = (247 − 254) × 500 = −₹3,500. The view did not come true, so the speculator loses. |
| 6 | Units allotted at NAV | 2,500 units | Units allotted = amount invested ÷ NAV = ₹60,000 ÷ ₹24 = 2,500 units. |
| 6 | Change in value with NAV | ₹8,800 | Gain = units × change in NAV = 3,200 × (₹18.25 − ₹15.50) = 3,200 × ₹2.75 = ₹8,800. ₹58,400 is the current value of the holding, not the increase. |
| 7 | Exit load calc year 2 partial | ₹50,000 | Eighteen months falls in the second year, where the cap is 2% of the amount redeemed: 2% × ₹25,00,000 = ₹50,000. The load applies only to the amount redeemed, not the whole portfolio. |
| 7 | Audit certificate deadline date | 30 September 2026 | The certificate is due within six months of the close of the accounting period: six months after 31 March 2026 is 30 September 2026. |
| 8 | Exit load on two partial redemptions | ₹90,000 | First year: up to 3% of the amount redeemed = ₹60,000. At 26 months the client is in the third year: up to 1% = ₹30,000. Total = ₹90,000. |
| 8 | Minimum investment shortfall | ₹5,00,000 | Cash and securities can be combined. Total = ₹20,00,000 + ₹25,00,000 = ₹45,00,000; shortfall = ₹50,00,000 - ₹45,00,000 = ₹5,00,000. |
| 9 | Drift after market move | 64.10% | Equity = 60 × 1.25 = ₹75 lakh; debt = 40 × 1.05 = ₹42 lakh; total = ₹117 lakh; equity weight = 75 ÷ 117 = 64.10%. |
| 10 | Sharpe ratio ranking | Fund Y, with a Sharpe ratio of about 0.83 | Sharpe = (Rp − Rf) ÷ σp: X = 10.5 ÷ 15 = 0.70, Y = 7.5 ÷ 9 = 0.83, Z = 13.5 ÷ 22 = 0.61. Y earns the most excess return per unit of total risk, even though Z has the highest raw return. |
| 10 | Portfolio beta with cash | 1.02 | Portfolio beta is the value-weighted average beta, with cash at zero: (24 × 1.35 + 18 × 0.85 + 12 × 1.10 + 6 × 0) ÷ 60 = 1.015 ≈ 1.02. Leaving cash out of the weights overstates beta at 1.13. |
| 11 | STCG with PMS fees not deductible | ₹33,000 | Both holdings were held 12 months or less, so gains are short-term: ₹90,000 + ₹75,000 = ₹1,65,000. PMS fees are not deductible from capital gains, so tax = 20% × ₹1,65,000 = ₹33,000. |
| 11 | STCG tax calculation | ₹48,000 | Shares held for 12 months or less give STCG, taxed at 20% with no exemption: 20% × ₹2,40,000 = ₹48,000. |
| 12 | Periodic reports | 4 | Reports must be sent at least once every 3 months, so at least 12 ÷ 3 = 4 reports a year, plus whenever the client asks. |
| 12 | Unlisted securities limits | ₹15.60 crore | For non-discretionary or advisory clients the cap is 25% of AUM: 25% × ₹2.40 crore = ₹0.60 crore. For a large value accredited investor it can go up to 100%: ₹15 crore. Combined maximum = ₹15.60 crore. |
The second free test covers different topics and numbers from Test 1. The same spoiler warning applies.
| Ch. | Topic | Correct answer | Working |
|---|---|---|---|
| 1 | Present value | ₹50,000 | Present value = 54,000 ÷ (1 + 0.08) = ₹50,000. Multiplying by 0.92 is a common mistake that understates the value. |
| 2 | Bonus calculation | 1,200 | A 1:3 bonus gives 1 bonus share for every 3 held: 900/3 = 300 bonus shares, so total = 900 + 300 = 1,200. |
| 2 | MTM margin | ₹12,000 | MTM margin is the notional loss on the open position: 500 x (₹820 - ₹796) = ₹12,000. |
| 3 | Price to sales | 1.50 times | Market capitalisation = 10 crore × ₹240 = ₹2,400 crore. P/S = 2,400/1,600 = 1.50 times. |
| 3 | Gordon Growth Model with D0 | ₹72.00 | D1 = 4 × 1.08 = ₹4.32. P0 = D1/(r − g) = 4.32/0.06 = ₹72.00. Using ₹4 (last year's dividend) directly gives ₹66.67. |
| 4 | Zero coupon bond value | ₹680.58 | Value = 1,000 ÷ (1.08)^5 = ₹680.58. Discounting with simple interest (1,000 ÷ 1.40 = ₹714.29) understates the effect of compounding. |
| 4 | Bond buy/sell decision | Intrinsic value is about ₹951.93, below the price, so avoid it (or sell if held) | Intrinsic value = Σ 80 ÷ 1.095^t (t = 1 to 4) + 1,000 ÷ 1.095⁴ = ₹951.93. When intrinsic value is below the market price of ₹960, the bond is overvalued for this investor, so it should not be bought and could be sold if held. |
| 5 | Call option buyer payoff | ₹24,200 | The call is worth exercising because the price is above the strike: gain = (1,586 − 1,500) × 550 = ₹47,300; less premium 42 × 550 = ₹23,100; net profit = ₹24,200. |
| 5 | Zero-sum game | ₹6,000 | Seller gains (2,150 − 2,090) × 100 = ₹6,000 and the buyer loses the same amount, so the net position is zero – a zero-sum game. |
| 5 | Futures margin collected | ₹2,68,800 | Contract value = 750 × ₹1,280 = ₹9,60,000; margin per party = 14% × ₹9,60,000 = ₹1,34,400. Margins are paid by both parties, so the total is ₹2,68,800. |
| 7 | Minimum investment shortfall | ₹8,00,000 | The minimum is ₹50 lakh, so the shortfall is ₹50,00,000 − ₹42,00,000 = ₹8,00,000. |
| 8 | Operating expense ceiling | ₹60,000 | The ceiling is 0.50% p.a. of average daily AUM: 0.50% x ₹1,20,00,000 = ₹60,000. |
| 9 | Relative performance | 3 percentage points above | Relative performance = 14% − 11% = 3 percentage points above the benchmark. |
| 9 | Investable surplus | ₹4,20,000 | Monthly surplus = 1,20,000 − 85,000 = ₹35,000; annual = 35,000 × 12 = ₹4,20,000. |
| 10 | Hurdle value over multiple years | ₹94,47,840 | Required value at hurdle = Capital × (1 + hurdle)^n = ₹75,00,000 × 1.08³ = ₹94,47,840. Simple interest (8% × 3) gives only ₹93,00,000. |
| 10 | Comparing Sharpe ratios | Fund B is better, with a Sharpe ratio of 0.68 against 0.55 | Sharpe A = (18 − 6.5)/21 = 0.55; Sharpe B = (14 − 6.5)/11 = 0.68. The higher Sharpe ratio (Fund B) indicates more return per unit of total risk. |
| 11 | Dividend TDS threshold | Nil | TDS at 10% applies only where dividends exceed the threshold, which rose from ₹5,000 to ₹10,000 from FY 2025-26. At ₹8,000 the dividend is below ₹10,000, so no TDS is deducted. The ₹800 option uses the old ₹5,000 threshold. |
| 11 | LTCG tax calculation | ₹21,875 | Taxable LTCG = ₹3,00,000 − ₹1,25,000 exemption = ₹1,75,000. Tax = 12.5% × ₹1,75,000 = ₹21,875. Taxing the full ₹3,00,000 would give ₹37,500, which ignores the exemption. |
| 12 | Integrally connected cash transactions | Record them, as the total of ₹10.3 lakh exceeds ₹10 lakh | A series of integrally connected cash transactions each below ₹10 lakh within one calendar month must be recorded if the total exceeds ₹10 lakh; here 3.2 + 3.5 + 3.6 = ₹10.3 lakh. |
| 12 | Rectifying audit deficiencies | 15 July 2026 | Deficiencies in the auditor's report must be rectified within two months of the report date: 15 May 2026 + 2 months = 15 July 2026. |
Yes. The markets chapters test valuation ratios, bond value, yield and duration, and futures and option payoffs. The PMS chapters test fees (high water mark, hurdle rate, exit loads, the 0.50% expense cap), holding period return, TWRR, Sharpe and Treynor ratios, portfolio beta and capital gains tax. 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 100 MCQs of 1 mark each over 120 minutes. The pass mark is 60 out of 100 (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 XXI-A 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 wrote them from the formulas and rules in the NISM XXI-A syllabus, and each has a worked explanation. Names of people, companies and funds are fictional. BullWiser is not affiliated with NISM.
Take the full-length XXI-A mock, read the XXI-A notes and question bank, or start with the chapters that have the most numericals: Performance Measurement and Evaluation, Investing in Stocks, Portfolio Management Process.
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