Introduction to Modern Portfolio Theory
6 questions. Each answer is explained.
Question 1 of 6Practice · Series XXI-B — Portfolio Managers
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Learn these topics
More units in NISM Series XXI-B
- Investment Landscape and Required Return4
- Introduction to Securities Markets and Participants3
- Investing in Stocks and Equity Research7
- Investing in Fixed Income Securities and Bond Valuation6
- Derivatives in Portfolio Management6
- Mutual Fund6
- Role of Portfolio Managers in India8
- Operational Aspects of Portfolio Managers (Onboarding and Fees)8
- Portfolio Management Process and Asset Allocation8
- Taxation6
- Regulatory, Governance and Ethical Aspects of Portfolio Managers8
- Introduction to Indices6
- Concept of Informational Efficiency6
- Behavioral Finance6
- Introduction to Capital Market Theory6
- Risk8
- Equity Portfolio Management Strategies14
- Fixed Income Portfolio Management Strategies14
- Performance measurement and evaluation of Portfolio Managers8
- Portfolio Rebalancing6
Exam format
| Questions | 120 · 1 or 2 marks each |
|---|---|
| Duration | 180 min · 3 hours |
| Pass mark | 60% · 90 of 150 marks |
| Negative marking | 25% · 0.25 or 0.5 marks off per wrong answer |
| Certificate validity | 3 years · from the date of the examination |
| Marks for this unit | Not published by NISM |
NISM Series XXI-B Portfolio Managers
Exam rules read on NISM's site on 30 October 2026. Check the current rules on NISM's site (opens in a new tab)
What these answers assume, and when it was last checked
Each question uses the rules listed below. We last checked them on 5 September 2026. A Budget or SEBI circular can change a rate, lot size or expiry day. If a rule changes before your exam, treat the linked questions as out of date and check NISM's current workbook.
- NSE uses Tuesday expiry and BSE uses Thursday expiry. This applies from 1 September 2025.
- The January 2026 index lot sizes are NIFTY 65, BANKNIFTY 30, FINNIFTY 60, MIDCPNIFTY 120 and NIFTYNXT50 25.
- The October 2024 SEBI framework sets a minimum index contract value of Rs 15–20 lakh. Each exchange may list one weekly benchmark index.
- Option buyers pay the premium upfront from 1 February 2025. A short index option has an extra 2% Extreme Loss Margin on expiry day from 20 November 2024.
- Equity short-term capital gains are taxed at 20%. Long-term gains are taxed at 12.5% above Rs 1.25 lakh. Both rates apply from 23 July 2024.
- F&O income is non-speculative business income in ITR-3. NSE equity derivatives trade from 9:15 a.m. to 3:40 p.m.
- The final ten-minute session began on 3 August 2026. It aligns with the cash market Closing Auction Session.
- Most Securities Transaction Tax questions test the base and who pays. On an option sale, it is the premium and the seller pays. On a futures sale, it is the traded value and the seller pays.
- On exercise, Securities Transaction Tax uses intrinsic value: settlement price minus strike price. The buyer pays it.
- Two questions test the current rate. From 1 April 2026, option sales carry 0.15% on the premium and futures sales carry 0.05% on traded price. The earlier rates were 0.10% and 0.02% from 1 October 2024.
- This section uses the T+1 rolling settlement cycle. Obligations are fixed on T+1. A short delivery goes to buy-in auction on T+1 and settles on T+2.
- The trade-for-trade surveillance segment uses direct close-out. Funds pay in by 10:30 a.m. and pay out on or after 1:30 p.m. on settlement day.
- Securities pay in to the settlement pool by 10:30 a.m. They pay out directly to the client’s demat account by 3:30 p.m.
- The 3:30 p.m. deadline replaced 1:30 p.m. under SEBI’s 10 October 2024 circular. Direct client credit was required by SEBI’s 5 June 2024 circular.
- The optional T+0 cycle trades until 1:30 p.m. Obligations are fixed by 2:30 p.m. on the trade day. An early pay-in shortage is closed out directly.
- Cash-market Value at Risk margin is six times exponentially weighted moving-average volatility. It has a 9% floor for Group I, a 21.5% floor for Group II, and a fixed 50% or 75% level for Group III.
- Extreme Loss Margin is 3.5% for a share and 2% for a broad-market-index exchange traded fund. Mark-to-market margin is collected before the next day’s trading. The trade-for-trade segment has 100% upfront margin.
- Close-out uses the higher of the highest price from trade day to auction day and 20% above the auction day’s official close.
- A funds shortage costs 0.07% a day. The trading facility is withdrawn at a shortage of Rs 5 lakh or more.
- SCORES allows 21 calendar days, then two 15-day review levels. Online Dispute Resolution moves from conciliation to arbitration after the market participant and SCORES steps.
- At NSE, the Investor Protection Fund limit is Rs 35 lakh per investor for each defaulting or expelled member. This applies to claims arising after 13 August 2024.
- A Basic Services Demat Account has no annual maintenance charge up to Rs 4 lakh of holdings. It costs up to Rs 100 above that, until the Rs 10 lakh eligibility ceiling. These slabs apply from 1 September 2024.
- The rupee pairs are USD-INR, EUR-INR, GBP-INR and JPY-INR. The cross-currency pairs are EUR-USD, GBP-USD and USD-JPY.
- Each contract covers 1,000 units of the foreign currency, except JPY-INR. JPY-INR covers 100,000 yen and is quoted in rupees per 100 yen.
- The tick is 0.25 paise, or Rs 0.0025. It equals Rs 2.50 a contract.
- Rupee pairs trade from 9:00 a.m. to 5:00 p.m. A monthly contract stops trading at 12:30 p.m. two working days before the expiry month’s last business day.
- Final settlement is in cash at the FBIL reference rate on expiry day. FBIL, Financial Benchmarks India, has published this rate in place of the Reserve Bank since 2018. Premium-style European options are quoted in rupees. The buyer pays the premium in cash on T+1.
- Daily settlement is on T+1 and final settlement is on T+2.
- NSE Clearing circular 026/2020 sets SPAN margin plus Extreme Loss Margin. The futures margin is 0.50% for USD-INR, 0.15% for EUR-INR, 0.25% for GBP-INR and 0.35% for JPY-INR. A short option has 0.75%. These figures apply from 1 June 2020.
- A USD-INR client may hold 6% of total open interest or USD 20 million, whichever is higher. A trading member may hold 15% or USD 100 million.
- A resident user has one USD 100 million equivalent limit across all rupee pairs and exchanges. No document is needed below that limit, but a valid underlying contracted exposure must still exist. This clarification applies from 3 May 2024.
- The currency segment has no Securities Transaction Tax.
The exam figures (questions, time, pass mark, negative marking and certificate validity) come from NISM's own pages, read on 30 October 2026. Timed practice uses the same figures. Study with the official workbook as well.
The written-out answers on this page are hidden while your timed set runs.
All 6 questions on Introduction to Modern Portfolio Theory, with answers
Q1What characterises a portfolio on the mean-variance efficient frontier?
Option A. The lowest return among portfolios with the same risk
Why it is wrong: A lower expected return at the same risk is dominated rather than efficient.
Option B. The highest possible return in every future scenario
Why it is wrong: Efficiency is based on expected return and risk, not winning in every realised outcome.
Option C. The highest expected return available for its level of risk — Correct answer
Option D. The absence of risk in every individual holding
Why it is wrong: Efficient portfolios can contain risky assets and have positive total risk.
Answer: C. An efficient-frontier portfolio offers the highest available expected return at its risk level. An alternative with equal risk and a higher expected return would dominate it. Remember: Efficiency is a comparison of expected risk and return, not a profit guarantee.
Hint, shown before you answer in practice mode: Compare portfolios at the same risk or the same expected return. Common mistake: Confusing an efficient portfolio with a risk-free or always-winning portfolio.
XXI-B-089easyconceptual
Q2A security returns −5%, 10% or 20% with probabilities 20%, 50% and 30%. What is its expected return?
Option A. 12.00%
Why it is wrong: This treats the negative scenario as a gain instead of a loss.
Option B. 8.33%
Why it is wrong: This gives equal weight to three outcomes that have unequal probabilities.
Option C. 25.00%
Why it is wrong: Adding scenario returns does not account for their probabilities.
Option D. 10.00% — Correct answer
Answer: D. Expected return is 10.00% because it is the probability-weighted average of outcomes. Working: 0.20 × (−5%) + 0.50 × 10% + 0.30 × 20% = −1% + 5% + 6% = 10%. Remember: Expected return uses probabilities and can differ from every simple unweighted average.
Hint, shown before you answer in practice mode: Give each possible return its stated probability weight. Common mistake: Ignoring outcome probabilities or dropping the sign of a possible loss.
XXI-B-090mediumnumerical
Q3A portfolio allocates 60% to an asset expecting 12% and 40% to an asset expecting 7%. What is expected portfolio return?
Option A. 8.00%
Why it is wrong: This does not follow the stated portfolio weights and expected returns.
Option B. 10.00% — Correct answer
Option C. 9.50%
Why it is wrong: This uses equal weights rather than the stated 60% and 40% allocations.
Option D. 19.00%
Why it is wrong: Adding both returns ignores that only part of the portfolio is in each asset.
Answer: B. Expected portfolio return is 10.00% because each asset contributes its weighted expected return. Working: 0.60 × 12% + 0.40 × 7% = 7.20% + 2.80% = 10.00%. Remember: Expected portfolio return is a weighted average of expected asset returns.
Hint, shown before you answer in practice mode: Combine expected returns using the amounts exposed to each asset. Common mistake: Using an unweighted average despite unequal portfolio allocations.
XXI-B-091mediumnumerical
Q4Two assets have return standard deviations of 20% and 10% and correlation 0.30. What is their covariance using decimal returns?
Option A. 0.300
Why it is wrong: This reports the correlation rather than the covariance.
Option B. 0.006 — Correct answer
Option C. 0.0006
Why it is wrong: This is one-tenth of the correctly scaled covariance.
Option D. 0.060
Why it is wrong: This is ten times the product of the stated decimal standard deviations and correlation.
Answer: B. Covariance is 0.006 when returns are expressed as decimals. Covariance = correlation × standard deviation of the first asset × standard deviation of the second. Working: 0.30 × 0.20 × 0.10 = 0.006. Remember: Correlation and covariance are related but not interchangeable.
Hint, shown before you answer in practice mode: Correlation is unitless, while covariance also reflects both assets’ volatility. Common mistake: Using percentage numbers as if they were decimal returns.
XXI-B-092mediumnumerical
Q5An equally weighted two-asset portfolio has standard deviations of 20% and 10% with zero correlation. What is its standard deviation, approximately?
Option A. 22.36%
Why it is wrong: This omits the effect of the 50% portfolio weights.
Option B. 15.00%
Why it is wrong: This averages standard deviations and ignores the portfolio-variance calculation.
Option C. 12.50%
Why it is wrong: This confuses the variance calculation with its square root and percentage conversion.
Option D. 11.18% — Correct answer
Answer: D. Portfolio standard deviation is approximately 11.18% because zero correlation reduces combined volatility. Variance = 0.50² × 0.20² + 0.50² × 0.10² + 2 × 0.50 × 0.50 × 0.20 × 0.10 × 0 = 0.0125. Standard deviation = √0.0125 = 0.111803, or 11.18%. Remember: Portfolio risk depends on covariance, not just average individual volatility.
Hint, shown before you answer in practice mode: Combine variances and co-movement before taking a square root. Common mistake: Calculating a weighted average of standard deviations as portfolio risk.
XXI-B-093hardnumerical
Q6Two assets have 30% and 10% standard deviations and perfect negative correlation. What first-asset weight produces zero variance under these exact assumptions?
Option A. 50%
Why it is wrong: Equal money weights do not offset unequal 30% and 10% volatilities.
Option B. 10%
Why it is wrong: This copies a standard deviation rather than solving for the balancing portfolio weight.
Option C. 25% — Correct answer
Option D. 75%
Why it is wrong: This is the required weight of the lower-volatility second asset.
Answer: C. A 25% weight in the first asset cancels the two volatility contributions under perfect negative correlation. Set 0.30w = 0.10(1 − w). Then 0.40w = 0.10 and w = 0.25. The remaining 75% is in the second asset. This exact cancellation depends on the stated model assumptions. Remember: With perfect negative correlation, unequal volatilities need unequal balancing weights.
Hint, shown before you answer in practice mode: Make the two weighted volatility contributions cancel. Common mistake: Assuming equal money weights always eliminate risk when correlation is minus one.
XXI-B-094hardnumerical
Introduction to Modern Portfolio Theory: common questions
How many practice questions are there on Introduction to Modern Portfolio Theory?
6 questions, all written out on this page with the correct answer and why each other option is wrong. This unit is one of the 21 practice topics for NISM Series XXI-B, which has 150 questions in total.
Are these real NISM Series XXI-B questions on Introduction to Modern Portfolio Theory?
No. LearnNifty wrote every question from NISM's public syllabus. NISM does not publish its question bank, so nobody can offer you the real paper. Use these questions to check that an idea has gone in. Use the official NISM workbook to see what is examined.
Does negative marking apply to NISM Series XXI-B?
Yes. NISM takes off 25% of a question's marks for a wrong answer. On a 1 or 2-mark question that is 0.25 or 0.5 marks off. A blank question earns nothing and loses nothing, so a wrong guess costs marks on this paper. Timed practice here uses the same rule.
Are these practice questions kept up to date?
Each question is written against the rules printed on this page, last checked on 5 September 2026. A Budget or a SEBI circular can change a rate, a lot size or an expiry day. If one of those rules changes before your exam, treat the questions that use it as out of date. Then check NISM's current workbook.
Introduction to Capital Market Theory
6 questions on Introduction to Capital Market Theory. Its quiz opens on that unit.
Open Introduction to Capital Market TheoryPaper Trading Try it on the practice trading desk