NP

NISM Series X-A

Investment Adviser (Level 1)

NISM-Series-X-A Formula Sheet

Every formula with one worked ₹ example, the Excel function to use at the exam workstation, and the trap that question-setters use to reword it.

Compiled from the NISM-Series-X-A formula sheet (based on the NISM X-A workbook), with every worked example recomputed and tax figures updated to current rules.

78 formulas across 9 chapters

Chapter 2. Time Value of Money

Open chapter →

Present Value: single sum

Ch 2.2

PV = FV ÷ (1 + r)ⁿ

Excel: PV(rate, nper, 0, −FV)

Example →
₹50,000 receivable after 5 years at 6% → 50,000 ÷ 1.06⁵ = ₹37,362.91.
Trap →
The rate is stated 'quarterly' but the term is in years. Convert first: r = 6% ÷ 4 = 1.5%, n = 5 × 4 = 20.

Present Value: regular annuity

Ch 2.2

PV = C × [1 − (1 + r)⁻ⁿ] ÷ r

Excel: PV(rate, nper, −C)

Example →
Shyam gets ₹6,500 a year for 8 years at 7% → 6,500 × 5.9713 = ₹38,813.44.
Trap →
'Payments at the start of each year' makes it an annuity due: multiply the result by (1 + r), or use type = 1 in Excel.

Future Value: single sum

Ch 2.3

FV = PV × (1 + r)ⁿ

Excel: FV(rate, nper, 0, −PV)

Example →
Krishna invests ₹5,00,000 at 8% for 5 years, compounded annually → ₹7,34,664 (interest ₹2,34,664).
Trap →
The same problem compounded quarterly (r = 2%, n = 20) gives ₹7,42,974. Watch for the compounding frequency hidden in the question.

CAGR (Compounded Annual Growth Rate)

Ch 2.4

CAGR = (End value ÷ Begin value)^(1/n) − 1

Excel: RATE(n, 0, −Begin, End)

Example →
NAV grows from ₹10.50 to ₹12.25 in 3 years → (12.25 ÷ 10.50)^(1/3) − 1 = 5.27%.
Trap →
For periods under one year CAGR isn't appropriate; use the simple (absolute) return. Fractional years are fine, e.g. n = 450/365.

EMI: Equated Monthly Instalment

Ch 2.5

EMI = P × r × (1 + r)ⁿ ÷ [(1 + r)ⁿ − 1] (r monthly, n months)

Excel: PMT(rate/12, years×12, −loan)

Example →
₹30 lakh loan at 6.5% for 20 years → PMT(0.065/12, 240, −30,00,000) = ₹22,367 a month.
Trap →
If the rate is already given as a monthly rate (e.g. 0.6% a month), don't divide by 12 again. Enter the loan as negative to get a positive EMI.

NPER: loan tenure

Ch 2.5

Number of periods needed to repay a loan at a given EMI

Excel: NPER(rate/12, −EMI, loan)

Example →
₹5,00,000 loan, EMI ₹12,000, rate 8% → NPER(0.08/12, −12000, 500000) = 48.98 months.
Trap →
The answer comes out in months; if the question asks for years, convert (48.98 ÷ 12 ≈ 4.08 years).

PPMT / IPMT: principal and interest split

Ch 2.5

Principal part = PPMT(rate, period, nper, pv) · Interest part = IPMT(rate, period, nper, pv)

Excel: PPMT(0.07/12, 1, 120, −1000000) · IPMT(0.07/12, 1, 120, −1000000)

Example →
₹10 lakh at 7% for 10 years, month 1 → EMI ₹11,611 = interest ₹5,833 + principal ₹5,778. Interest dominates early EMIs.
Trap →
'A higher rate means more of the EMI goes to principal early' is wrong. A higher rate raises the interest share of early EMIs.

Ordinary annuity vs annuity due

Ch 2.6

PV(due) = PV(ordinary) × (1 + r)

Excel: type = 0 (end of period) vs type = 1 (start of period)

Example →
₹5,000 a year for 4 years at 10% → ordinary ₹15,849.33; annuity due ₹17,434.26.
Trap →
Rent paid at the start of the month is an annuity due (higher PV); salary received at month-end is an ordinary annuity.

Perpetuity

Ch 2.7

PV = C ÷ r

Example →
A perpetual bond paying ₹10,000 a year at an 8% discount rate → 10,000 ÷ 0.08 = ₹1,25,000.
Trap →
A 'very long-term 50-year bond' is still an annuity, not a perpetuity. A perpetuity has no n.

Chapter 3. Evaluating the Financial Position of Clients

Open chapter →

Net worth

Ch 3.5

Net worth = Total assets − Total liabilities

Example →
Lakshmi: assets ₹36.22 lakh − liabilities ₹12.07 lakh = ₹24.15 lakh.
Trap →
'Gross assets of ₹50 lakh means a strong position' is wrong. Subtract liabilities; net worth is the right measure.

Savings ratio

Ch 3.2

Savings ratio = Total savings ÷ Total income × 100

Example →
ABC family: savings ₹34,000 (surplus ₹7,000 + PF ₹9,000 + investments ₹18,000) on income ₹1,37,000 → 24.8%.
Trap →
Savings isn't just the monthly surplus in hand (₹7,000). PF contributions and other investments are added back.

Leverage ratio

Ch 3.7

Leverage ratio = Total liabilities ÷ Total assets

Example →
Liabilities ₹13 lakh, assets ₹65 lakh → 20%. Higher is riskier; above 1 means assets can't cover liabilities.
Trap →
Not the same as debt-to-equity or DSCR. Here the denominator is total assets.

Solvency ratio

Ch 3.7

Solvency ratio = Net worth ÷ Total assets = 1 − Leverage ratio

Example →
Net worth ₹52 lakh, assets ₹65 lakh → 80% (check: 1 − 0.20 = 0.80).
Trap →
An insurance company's solvency ratio is a different concept; don't mix them up.

Liquidity ratio

Ch 3.7

Liquidity ratio = Liquid assets ÷ Monthly expenses (benchmark 4–6)

Example →
Liquid assets ₹13 lakh (savings ₹7L + short-term FD ₹2L + liquid MF ₹4L); monthly expenses ₹1.5 lakh → 8.67, comfortable.
Trap →
Equity shares, long-term FDs and closed-end funds are not liquid assets; they're excluded because of value uncertainty or lock-in.

Liquid assets to net worth

Ch 3.7

Liquid assets ÷ Net worth

Example →
A client with long-term goals should have a low ratio, since excess liquidity drags returns; near-term goals justify a higher one.
Trap →
'Higher is always better' is wrong. The right level depends on the client's goal horizon.

Financial assets ratio

Ch 3.7

Financial assets ÷ Total assets × 100

Example →
Shares ₹5L + FD ₹10L + MF ₹12L = ₹27L financial; land ₹9L + gold ₹14L physical; total ₹50L → 54%.
Trap →
Physical gold is not a financial asset. Gold, land and real estate are physical; shares, mutual funds and deposits are financial.

Debt-to-income (debt servicing) ratio

Ch 3.7 / 4.2

DTI = Monthly debt servicing (principal + interest) ÷ Monthly income (above 35–40% is excessive)

Example →
Salary ₹15,000, loan repayments ₹7,500 → DTI 50%, too high.
Trap →
Use the full EMI (principal + interest), not just one part. If figures are annual, convert to monthly first.

Emergency fund

Ch 3.6

Emergency fund ≈ 6 × Monthly expenses (laddered: some highly liquid, the rest slightly less liquid)

Example →
Monthly expenses ₹80,000 → target emergency corpus ₹4,80,000.
Trap →
The benchmark is months of expenses, not months of income. Review it yearly and whenever a new EMI is added.

Chapter 4. Debt Management and Loans

Open chapter →

Effective annual cost of revolving credit

Ch 4.3

Effective annual cost = (1 + monthly rate)¹² − 1

Example →
A card charging 3% a month → 1.03¹² − 1 = 42.6% a year, well above the naive 36%.
Trap →
The option '36% p.a.' is simple annualisation; the compounded effective rate is 42.6%.

Floating rate: internal vs external benchmark

Ch 4.7 / 4.12

Floating rate = Benchmark ± Spread · Internal benchmark: MCLR · External benchmark: e.g. repo rate (EBLR)

Example →
When the repo rate is cut, a repo-linked loan reprices at its next reset; an MCLR loan adjusts more slowly.
Trap →
Don't swap them: changes in the policy rate pass through faster to external-benchmark (repo-linked) loans than to MCLR loans.

Debt repayment strategies

Ch 4.15

Avalanche = highest interest rate first · Snowball = smallest balance first · Blizzard = snowball, then avalanche

Example →
Credit card ₹30k at 42%, personal loan ₹1.2L at 21%, car ₹1L at 12%, home ₹15L at 8%. Avalanche: CC → PL → Car → Home. Snowball: CC → Car → PL → Home.
Trap →
Definitions get swapped ('snowball = highest interest first'). Learn the general rule, not one example where both orders start the same way.

Chapter 8. Investing in Stocks

Open chapter →

Earnings per share (EPS)

Ch 8.5

EPS = Profit after tax ÷ Number of outstanding equity shares

Example →
PAT ₹100 crore, 20 crore shares → EPS ₹5.
Trap →
Use profit after tax and outstanding shares, not profit before tax or authorised shares.

P/E ratio

Ch 8.5

P/E = Market price per share ÷ EPS

Example →
Price ₹100, EPS ₹5 → P/E 20. With an industry average of 22, the stock looks relatively cheap.
Trap →
Trailing P/E uses the last 4 quarters' actual EPS; forward P/E uses the next 4 quarters' estimates. Questions mix the two.

P/B ratio (price to book)

Ch 8.5

P/B = Market price per share ÷ Book value per share · Book value per share = Shareholders' equity ÷ Shares outstanding

Example →
Price ₹200, book value ₹100 a share → P/B 2. Widely used for banks and financials.
Trap →
'A low P/B always means undervalued' is wrong; it can reflect impaired or overstated book assets.

P/S ratio (price to sales)

Ch 8.5

P/S = Market capitalisation ÷ Trailing 12-month sales

Example →
Useful for loss-making companies; sales are harder to manipulate than earnings.
Trap →
For a heavily leveraged firm, use EV/Sales instead, because P/S ignores debt.

PEG ratio

Ch 8.5

PEG = P/E ÷ Expected annual EPS growth rate (as a number, e.g. 25 for 25%)

Example →
P/E 20, expected growth 25% → PEG = 20 ÷ 25 = 0.8, undervalued relative to growth.
Trap →
PEG below 1 = undervalued, 1 = fair, above 1 = overvalued. Questions reverse this.

Enterprise value (EV)

Ch 8.5

EV = Market cap + Market value of debt − Excess cash and equivalents

Example →
Market cap ₹800 crore + debt ₹300 crore − cash ₹50 crore = ₹1,050 crore.
Trap →
Cash is subtracted, not added. Use the market value of debt where it's given.

Dividend yield

Ch 8.5

Dividend yield = Dividend per share ÷ Market price per share × 100

Example →
Price ₹40, dividend ₹2 a share → 5%.
Trap →
Use the current market price, not the face value. 'Dividend of 50% on face value' isn't the yield.

Earnings yield

Ch 8.5

Earnings yield = EPS ÷ Market price × 100 = 1 ÷ (P/E)

Example →
EPS ₹25, price ₹500 → 5% (the inverse of a P/E of 20).
Trap →
Don't confuse it with dividend yield; earnings yield uses EPS, not DPS.

Market capitalisation

Ch 8.5

Market cap = Current market price × Total outstanding shares

Example →
Price ₹500 × 10 crore shares = ₹5,000 crore.
Trap →
Use the market price, not the face value, and total outstanding shares.

Chapter 9. Investing in Fixed Income Securities

Open chapter →

Bond price (discounted cash flow)

Ch 9.4

Price = Σ Coupon ÷ (1 + y)ᵗ + Face value ÷ (1 + y)ⁿ

Excel: PV(ytm, n, −coupon, −face)

Example →
10% annual coupon, face ₹100, 5 years, YTM 8% → 10 × 3.9927 + 100 × 0.6806 = ₹107.99 (premium, since coupon > YTM).
Trap →
With semi-annual coupons use n = 10, y = 4%, coupon ₹5 → ₹108.11. Questions forget to halve the rate and coupon.

Coupon (nominal) yield

Ch 9.5

Coupon yield = Annual coupon ÷ Face value

Example →
Coupon ₹8.24 on face ₹100 → 8.24%.
Trap →
Using the market price in the denominator gives the current yield, not the coupon yield.

Current yield

Ch 9.5

Current yield = Annual coupon ÷ Current market price

Example →
Coupon ₹8.24, price ₹103 → 8.00%.
Trap →
Current yield ignores the capital gain or loss to maturity; that's why YTM differs from it.

Yield to maturity (YTM)

Ch 9.5

Solve Price = Σ CFₜ ÷ (1 + YTM)ᵗ

Excel: RATE(n, coupon, −price, face) · YIELD(settle, maturity, rate, price, redemption, freq, basis)

Example →
G-Secs pay semi-annually: freq = 2. YTM is the bond's IRR.
Trap →
YTM assumes every coupon is reinvested at the YTM, which rarely happens. Don't use annual frequency for a semi-annual bond.

Price, yield and coupon relationship

Ch 9.4

Par: Coupon = CY = YTM · Discount: Coupon < CY < YTM · Premium: Coupon > CY > YTM

Example →
Market rate 9%, coupon 8% → bond sells at a discount, with YTM 9% > current yield > 8% coupon.
Trap →
Questions reverse the ordering. Remember: price and yield move in opposite directions.

Macaulay duration

Ch 9.7

Macaulay duration = Σ [t × PV(CFₜ)] ÷ Bond price

Example →
A 5-year zero-coupon bond has a Macaulay duration of exactly 5 years.
Trap →
'Duration equals maturity for all bonds' is wrong; only for zero-coupon bonds. Coupon bonds have duration below maturity.

Modified duration

Ch 9.7

Modified duration = Macaulay duration ÷ (1 + periodic yield) · % price change ≈ −ModDur × Δy

Example →
Macaulay duration 6.50, YTM 8% → 6.50 ÷ 1.08 = 6.02, so the price falls about 6.02% if yield rises 1%.
Trap →
With semi-annual compounding divide by (1 + y/2), not (1 + y).

Clean vs dirty price

Ch 9.5

Dirty (invoice) price = Clean price + Accrued interest

Example →
Clean price ₹102 + accrued interest ₹1.50 → dirty price ₹103.50. Markets quote clean; trades settle at dirty.
Trap →
Yield formulas use the clean price, not the dirty price.

Chapter 10. Understanding Derivatives

Open chapter →

Futures price: cost of carry

Ch 10

F = S + Cost of carry · Basis = Spot − Futures · At expiry F = S (basis = 0)

Example →
Spot ₹3,984, 27-day futures ₹4,032 → annualised return (48 ÷ 3,984) × (365 ÷ 27) = 16.29%. If it beats the funding cost, cash-and-carry arbitrage exists.
Trap →
'At expiry futures stay above spot because of interest' is wrong; the carry shrinks to zero and futures converge to spot.

Long call payoff (buyer)

Ch 10.3

Payoff = Max(Spot − Strike, 0) − Premium

Example →
Strike ₹100, premium ₹5: spot ₹112 → +₹7; spot ₹95 → −₹5 (maximum loss = premium).
Trap →
Forgetting to subtract the premium overstates profit. The buyer's maximum loss is the premium.

Short call payoff (writer)

Ch 10.3

Payoff = Premium − Max(Spot − Strike, 0)

Example →
Strike ₹100, premium ₹5, spot ₹120 → 5 − 20 = −₹15. Maximum loss is unlimited.
Trap →
'The call writer's maximum loss is the premium' describes the buyer. The writer's loss is unlimited.

Long put payoff (buyer)

Ch 10.3

Payoff = Max(Strike − Spot, 0) − Premium

Example →
Strike ₹200, premium ₹8, spot ₹180 → 20 − 8 = +₹12. Maximum gain = strike − premium.
Trap →
A long put's gain is not unlimited; it's capped because the price can't fall below zero.

Short put payoff (writer)

Ch 10.3

Payoff = Premium − Max(Strike − Spot, 0)

Example →
Strike ₹200, premium ₹8: spot ₹180 → 8 − 20 = −₹12; spot ₹210 → keeps the ₹8 premium.
Trap →
The put writer profits when the price stays above the strike, because the buyer won't exercise.

Intrinsic and time value

Ch 10.3

Call IV = Max(Spot − Strike, 0) · Put IV = Max(Strike − Spot, 0) · Time value = Premium − IV

Example →
Spot ₹110, strike ₹100 → call IV ₹10 (in the money); put IV 0 (out of the money).
Trap →
Intrinsic value can't be negative; it's floored at zero.

Initial margin

Ch 10.2

Initial margin = SPAN margin + Extreme loss margin (ELM) · Premium margin (option buyers) = Premium × Quantity

Example →
Higher volatility → higher SPAN margin → bigger margin requirement.
Trap →
Premium margin is collected from option buyers, not sellers.

Chapter 11. Mutual Funds

Open chapter →

Net asset value (NAV) per unit

Ch 11.2

NAV = (Total assets − Liabilities and expenses) ÷ Units outstanding

Example →
Net assets ₹500 crore, 50 crore units → NAV ₹10.
Trap →
Purchases and redemptions don't change NAV by themselves; units are issued or cancelled in proportion. NAV moves with the portfolio's market value and expenses.

Units allotted

Ch 11.2

Units = Amount invested ÷ Applicable NAV (fractions allowed)

Example →
₹10,000 at NAV ₹12.50 → 800 units.
Trap →
The applicable NAV depends on cut-off timing and when the fund receives clear funds, not when the order is placed.

Instant access facility (liquid funds)

Ch 11.7

IAF limit = lower of ₹50,000 or 90% of the investment value (per day, per scheme, per investor)

Example →
₹40,000 invested → min(₹50,000, ₹36,000) = ₹36,000.
Trap →
It's the lower of the two, and only for liquid funds, not all open-ended schemes.

ELSS tax benefit

Ch 11.4 / 11.10

Deduction up to ₹1,50,000 a year (old tax regime only) · Lock-in 3 years · Tax saved = Amount × marginal rate

Example →
₹1.5 lakh invested by someone in the 30% slab (old regime) → about ₹45,000 tax saved, before cess.
Trap →
The lock-in is 3 years, not 5 (5 years applies to solution-oriented retirement and children's funds). No deduction under the new regime.
Update:
The Income-tax Act, 2025 replaced the 1961 Act from 1 Apr 2026, so the old section number (80C) no longer applies; the deduction is described by what it does.

Equity fund taxation (from 23 July 2024)

Ch 11.10

Short-term (held ≤ 12 months): 20% · Long-term (> 12 months): 12.5% on gains above ₹1.25 lakh a year

Example →
Long-term gain ₹3 lakh → (3 − 1.25) lakh × 12.5% = ₹21,875.
Trap →
Don't use the old rates (15% short-term; 10% above ₹1 lakh long-term). Both the rates and the exemption changed in July 2024.

Debt fund taxation

Ch 11.10

Units of 'specified mutual funds' bought on or after 1 Apr 2023: gains taxed at the investor's slab rate, regardless of holding period, with no indexation

Example →
30% slab, ₹1 lakh gain on a debt fund held 4 years → ₹30,000 tax.
Trap →
Applying 20% with indexation is wrong for these units; that treatment ended for purchases from 1 Apr 2023.
Update:
From 1 Apr 2025 a 'specified mutual fund' means a fund with more than 65% in debt and money market instruments, so international funds and fund-of-funds aren't automatically taxed at slab rates any more.

Large, mid and small cap scheme rules

Ch 11.4

Large cap ≥ 80% in companies ranked 1–100 · Mid cap ≥ 65% in 101–250 · Small cap ≥ 65% in 251+ · Multi cap ≥ 75% equity with ≥ 25% each in large, mid and small · Flexi cap ≥ 65% equity, no segment rule

Example →
Rankings follow the official AMFI list by full market capitalisation, not the fund's own view.
Trap →
Multi cap and flexi cap definitions get swapped; only multi cap has the 25/25/25 rule.

Focused fund

Ch 11.4

Focused fund: at most 30 stocks

Example →
A fund holding 45 stocks can't be categorised as a focused fund.
Trap →
The SEBI limit is 30, not 25 or 50.

Minimum investment: SIF vs PMS vs AIF

Ch 11.6

Specialised Investment Fund (SIF) ₹10 lakh · PMS ₹50 lakh · AIF ₹1 crore

Example →
A client with ₹15 lakh and a sophisticated risk profile can invest in a SIF but not in PMS.
Trap →
The three thresholds are commonly swapped in question stems.

Chapter 14. Introduction to Modern Portfolio Theory

Open chapter →

Expected return (probability-weighted)

Ch 14.4

E(R) = Σ (Probabilityᵢ × Returnᵢ)

Excel: SUMPRODUCT(probabilities, returns)

Example →
Boom 0.3 × 15% + normal 0.5 × 10% + recession 0.2 × 2% = 9.9%.
Trap →
Check that the probabilities add up to 1 first.

Sample variance and standard deviation

Ch 14.4

σ² = Σ (Xᵢ − X̄)² ÷ (n − 1) · σ = √σ²

Excel: VAR.S(range) · STDEV.S(range)

Example →
Returns 10%, 14%, 8%, 12%: mean 11%, squared deviations sum to 20 → σ² = 20 ÷ 3 = 6.67, σ = 2.58%.
Trap →
Dividing by n instead of n − 1. Even 'all past data available to the adviser' is still a sample.

Covariance

Ch 14.5

Cov(A,B) = ρ(A,B) × σA × σB

Example →
σA 5%, σB 8%, ρ 0.4 → 0.4 × 5 × 8 = 16 (%²).
Trap →
Covariance has no fixed range; −1 to +1 is the range of the correlation coefficient.

Correlation coefficient

Ch 14.5

ρ(A,B) = Cov(A,B) ÷ (σA × σB) (range −1 to +1)

Example →
ρ = +1 → no diversification benefit; ρ = −1 → maximum benefit (risk can in theory fall to zero).
Trap →
Zero correlation doesn't eliminate risk; both variance terms remain.

Portfolio return

Ch 14.6

E(Rp) = Σ wᵢ × Rᵢ

Excel: SUMPRODUCT(weights, returns)

Example →
A 0.2 × 9% + B 0.1 × 12% + C 0.3 × 15% + D 0.4 × 18% = 14.7%.
Trap →
Expected portfolio return is the weighted arithmetic mean, not a geometric average.

Two-asset portfolio variance

Ch 14.6

σp² = w₁²σ₁² + w₂²σ₂² + 2 w₁ w₂ ρ₁₂ σ₁ σ₂

Example →
Weights 0.5/0.5, σ₁ = σ₂ = 5%, ρ = 0.5 → 0.000625 × 3 = 0.001875 → σp = 4.33%.
Trap →
If covariance is given instead of ρ, don't multiply by σ₁σ₂ again. Portfolio SD is not the weighted average of SDs.

Number of covariance terms

Ch 14.11

Covariance terms = (n² − n) ÷ 2 (plus n variance terms)

Example →
50 securities → (2,500 − 50) ÷ 2 = 1,225 covariances plus 50 variances.
Trap →
Not n² or n(n + 1) ÷ 2; the correct count is n(n − 1) ÷ 2.

Chapter 16. Portfolio Performance Measurement and Evaluation

Open chapter →

Holding period return (HPR)

Ch 16.2.1

HPR = [Income + (End value − Begin value)] ÷ Begin value

Example →
₹1 lakh grows to ₹1.2 lakh plus ₹5,000 dividend → (5,000 + 20,000) ÷ 1,00,000 = 25%.
Trap →
Leaving out the income shows 20% instead of 25%. Annualise HPRs for periods longer than a year.

Time-weighted rate of return (TWRR)

Ch 16.2.2

TWRR = [Π (1 + HPRᵢ)]^(1/n) − 1 (chain-linked sub-period returns)

Example →
Yearly returns −5%, −15.2%, 8.1%, 30.75%, 17.65% → product 1.3396 → 6.02% a year.
Trap →
Taking the arithmetic mean (7.26%) overstates it. TWRR removes the effect of client cash flows; SEBI mandates TWRR for PMS performance disclosure.

Money-weighted rate of return (MWRR)

Ch 16.2.2

MWRR = IRR of all client cash flows (contributions, withdrawals and ending value)

Excel: IRR(values) · XIRR(values, dates)

Example →
Answers 'how much did this client actually earn?', so it's sensitive to the timing and size of contributions.
Trap →
Don't confuse it with TWRR. MWRR suits client-level reports; manager comparison and PMS disclosure use TWRR.

Arithmetic vs geometric mean return

Ch 16.2.3

AMR = ΣR ÷ n · GMR = [Π (1 + Rᵢ)]^(1/n) − 1 · GMR ≤ AMR

Example →
Returns −50% then +100% → AMR 25%, but GMR 0% (the money is flat).
Trap →
AMR presented as the actual long-run return is wrong; GMR (CAGR) reflects what the investor earned.

CAGR

Ch 16.2.6

CAGR = (End ÷ Begin)^(1/t) − 1

Example →
₹1,00,000 → ₹1,33,960 in 5 years → 1.3396^0.2 − 1 = 6.02%.
Trap →
Not appropriate for periods under one year.

Post-tax and pre-tax return

Ch 16.2.5

Post-tax = Pre-tax × (1 − t) · Pre-tax = Post-tax ÷ (1 − t)

Example →
Pre-tax 5% at a 15% tax rate → 4.25% post-tax. Needing 8.4% post-tax in the 30% slab → 12% pre-tax.
Trap →
Multiply by (1 − t); don't subtract the tax rate from the return.

Cash-drag adjusted return

Ch 16.2.8

Adjusted return = (w_equity × R_equity + w_cash × R_cash) ÷ Total capital

Example →
₹100 lakh: ₹75 lakh in equity at 10%, ₹25 lakh in liquid funds at 4% → (7.5 + 1) ÷ 100 = 8.5%, not 10%.
Trap →
Reporting the return only on the invested ₹75 lakh inflates it. Measure on total capital.

Portfolio beta

Ch 16.3

βp = Σ wᵢ × βᵢ (weighted average)

Example →
A: β 1.2 at 60%, B: β 1.1 at 40% → 0.72 + 0.44 = 1.16.
Trap →
Beta is linear in weights, but portfolio SD isn't; SD needs the correlations.

CAPM required return

Ch 16.2.9

Required return = Rf + β × (Rm − Rf)

Example →
Rf 5%, β 1.5, Rm 15% → 5 + 1.5 × 10 = 20%.
Trap →
If the equity risk premium (Rm − Rf) is given directly, don't subtract Rf from it again.

Jensen's alpha

Ch 16.2.9

α = Rp − [Rf + β × (Rm − Rf)]

Example →
Rp 25%, Rf 5%, β 1.5, Rm 15% → 25 − 20 = +5%.
Trap →
Alpha isn't 'return over the benchmark' (25 − 15 = 10%); it's return over the CAPM-required return.

Sharpe ratio

Ch 16.4.1

Sharpe = (Rp − Rf) ÷ σp (total risk)

Example →
Rp 10.50%, Rf 5.50%, σ 6.50% → 5 ÷ 6.50 = 0.769.
Trap →
Using β in the denominator gives Treynor. Sharpe suits a standalone (only) portfolio.

Treynor ratio

Ch 16.4.2

Treynor = (Rp − Rf) ÷ βp (systematic risk only)

Example →
Rp 10.50%, Rf 5.50%, β 1 → 5.0 (percentage points of excess return per unit of beta).
Trap →
Treynor suits a holding within an already well-diversified portfolio, not an under-diversified one.

Sortino ratio

Ch 16.4.4

Sortino = (Rp − Rf) ÷ Downside (semi) standard deviation

Example →
Only downside volatility is penalised, which suits investors who define risk as the chance of losing money.
Trap →
Using total SD in the denominator gives Sharpe, not Sortino.

Information ratio

Ch 16.4.5

IR = (Rp − Rb) ÷ Tracking error · Tracking error = SD(Rp − Rb)

Example →
Active return 2%, tracking error 4% → IR 0.50. It shows whether alpha comes from skill or luck.
Trap →
The denominator is the SD of the return difference (tracking error), not the portfolio's total SD. Tracking error isn't the same as tracking difference.

M² (Modigliani–Modigliani)

Ch 16.4.6

w = σm ÷ σp · M² return = w × Rp + (1 − w) × Rf

Example →
Rp 35%, σp 42%; Rm 28%, σm 30%; Rf 6% → w = 0.714 → M² = 26.7%, below the market's 28%: underperformed on a risk-adjusted basis.
Trap →
Comparing raw returns (35% > 28%) is wrong; first scale the portfolio to market risk with T-bills.

Fama's net selectivity

Ch 16.4

Net selectivity = (Rp − Rf) − [(Rm − Rf) ÷ σm × σp]

Example →
Rp 18%, Rf 6%, Rm 14%, σm 15%, σp 20% → 12 − 10.67 = 1.33%. Positive means genuine selection skill.
Trap →
Not Jensen's alpha: Fama scales by total risk (σ), Jensen uses systematic risk (β).

Currency effect on foreign investments

Ch 16.6

₹ return ≈ Local-currency return + % change in the exchange rate (₹ per foreign unit)

Example →
₹50 lakh at ₹70/$ = $71,428.57; earns 15% → $82,142.86; rupee appreciates to ₹65/$ → ₹53.39 lakh, a ₹ return of 6.79%.
Trap →
Rupee appreciation reduces the ₹ return on foreign assets; depreciation adds to it.

Excel functions you'll use in the exam

The exam workstation provides Excel or OpenOffice Calc. Know each function's argument order and sign convention.

FunctionSyntaxTypical NISM useSign convention
PVPV(rate, nper, pmt, [fv], [type])Present value of a goal or annuitypmt / fv negative for outflows
FVFV(rate, nper, pmt, [pv], [type])Corpus after n periodspv negative for an outflow
PMTPMT(rate, nper, pv, [fv], [type])EMI on a loan, SIP needed for a goalpv negative → positive EMI
NPERNPER(rate, pmt, pv, [fv], [type])Tenure to repay a loan or reach a goalpmt negative, pv positive
RATERATE(nper, pmt, pv, [fv], [type])CAGR, implied yield, loan ratepv negative when solving for a return
PPMTPPMT(rate, per, nper, pv)Principal in a given EMISame as PMT
IPMTIPMT(rate, per, nper, pv)Interest in a given EMISame as PMT
NPVNPV(rate, values) + CF₀NPV of goal-based cash flowsNPV excludes CF₀; add it separately
IRRIRR(values, [guess])MWRR, project returnFirst cash flow usually negative
XIRRXIRR(values, dates)MWRR with irregular dates (e.g. SIPs)Same as IRR
YIELDYIELD(settle, maturity, rate, price, redemption, freq, [basis])Bond YTMG-Secs: freq = 2

Traps to know before the exam

  1. Always convert annual rates to the periodic rate (monthly ÷ 12, quarterly ÷ 4) and years to periods.
  2. Sample variance divides by n − 1, not n.
  3. SEBI mandates TWRR for PMS disclosure; MWRR is for client-level reports.
  4. Sharpe uses total risk (σ); Treynor and Jensen use systematic risk (β).
  5. Modified duration = Macaulay duration ÷ (1 + periodic yield).
  6. Discount bond: coupon < current yield < YTM. Premium bond: the reverse.
  7. Call buyer's maximum loss is the premium; call writer's loss is unlimited. A put buyer's gain is capped.
  8. Equity tax from July 2024: short-term 20%, long-term 12.5% above ₹1.25 lakh. Specified (debt) funds: slab rate.
  9. Multi cap needs 25% each in large, mid and small; flexi cap has no segment rule.
  10. Correlation ranges from −1 to +1; covariance has no fixed range.

Practice questions are based on the NISM Series X-A workbook (February 2025), updated for later SEBI/RBI changes up to November 2026. Always check the latest NISM syllabus before your exam. Video lessons on YouTube ↗