📊 NISM Series X-A Chapter 14 of 20 ⚖ 6 marks weightage Case-Based ✓

Ch.14: Introduction to Modern Portfolio Theory

Q: Who laid the foundation of Modern Portfolio Theory with the 1952 article 'Portfolio Selection'?

Harry Markowitz. Markowitz's 1952 paper in The Journal of Finance started MPT. He later received the 1990 Nobel Prize in Economics for this work.

Q: Under MPT, which measure is used for the risk of a portfolio?

Variance (or standard deviation) of returns. Markowitz showed that the variance of returns is a meaningful measure of portfolio risk and derived a formula for portfolio variance.

Q: Two assets offer the same expected return. Under MPT assumptions, which will an investor choose?

The one with lower risk. MPT assumes investors want the most return for a given risk. With equal returns they pick the less risky asset.

Q: MPT assumes investors base their decisions on which two things only?

Expected return and expected variance of returns. Utility curves in MPT depend only on expected return and the expected variance (or standard deviation) of returns.

Q: What does 'diminishing marginal utility of wealth' mean?

Each extra rupee adds less satisfaction as wealth grows. Investors differ in how fast utility falls, but the principle is that the utility gained per extra rupee declines as wealth increases.

Q: Over how many periods do investors maximise expected utility under MPT?

One period. MPT is a single-period model: investors choose the action that gives the maximum expected utility over one holding period.

Q: What is a 'fair game' in investment terms?

A prospect with zero risk premium. A fair game offers no extra return for the risk taken. Risk-averse investors reject it.

Q: A risk-neutral investor judges investments on the basis of:

Expected return alone, ignoring risk. A risk-neutral investor puts no penalty on risk. For them the certainty equivalent rate equals the portfolio's expected return.

Practice questions for NISM-Series-X-A: Investment Adviser (Level 1) Certification Examination (mandated by SEBI under the Investment Advisers Regulations, 2013). Chapter 14 carries 6 out of 150 marks in the final examination. The exam has 90 MCQs + 9 case-based sets (5 sub-questions each, mixed 1-mark and 2-mark weighting), 180-minute duration, 60% passing score, and 25% negative marking on the marks of each wrong answer.

MCQ

Case Sets

Total Qs

Exam Marks

60%

Pass Score

−25%

Neg. Marking

What You Will Learn in This Chapter

Understand diversification and the efficient frontier concept
Know CAPM, beta and the distinction between systematic and unsystematic risk
Apply Modern Portfolio Theory principles to portfolio construction

Key Terms:Modern Portfolio Theoryefficient frontierCAPMbetasystematic riskunsystematic riskSharpe ratio

Chapter 14 in 10 minutes: Modern Portfolio Theory

This is a short chapter, but it is heavy on numericals. The X-A exam asks you to calculate expected returns, portfolio return and two-asset portfolio risk, and to know the vocabulary of risk attitudes and the efficient frontier. Work through the four formulas below until you can do them without notes.

1. Where MPT comes from

Harry Markowitz's 1952 paper "Portfolio Selection" turned the old advice of not putting all your eggs in one basket into maths. By using covariance and correlation between assets, he showed how much diversification actually reduces risk, and he used the variance of returns as the measure of risk. He received the Nobel Prize in Economics in 1990.

2. Key assumptions

Investors want the most return for a given risk. Faced with equal returns, they pick the lower-risk asset.
They maximise expected utility over one period.
Utility shows diminishing marginal utility of wealth: each extra rupee adds less.
Decisions depend only on expected return and variance.

3. Attitudes to risk

Investor	Fair game (zero risk premium)	Certainty Equivalent Rate
Risk-averse	Rejects it; wants a premium for risk	Below expected return; may even be below the risk-free rate
Risk-neutral	Indifferent; risk carries no penalty	Equal to the expected return
Risk-seeking	Accepts it	Utility adjusted upward for risk

The CER is the risk-free return that would be exactly as attractive as the risky portfolio.

4. The four calculations

Expected return of a security = Σ (probability × return). Example: 0.3×15 + 0.5×10 + 0.2×2 = 9.9%.
Standard deviation: find the mean, square each deviation, add them, divide by n − 1, then take the square root.
Portfolio return = Σ (weight × expected return). Example: 0.2×9 + 0.1×12 + 0.3×15 + 0.4×18 = 14.7%.
Two-asset variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂. Example: 50/50 weights, σ = 5% each, ρ = 0.5 → variance 0.001875, σ ≈ 4.33%.

Number of covariance terms = (n² − n) ÷ 2: 1 for two assets, 3 for three, 1,225 for fifty.

5. Correlation and the efficient frontier

With correlation of +1 there is no diversification benefit. Risk and return both move along a straight line between the two assets.
Correlation below +1 makes portfolio risk lower than the weighted average of the individual risks.
The efficient frontier is the umbrella-shaped set of portfolios with the highest return for each level of risk. Portfolios below it, or to its right, are sub-optimal.

6. Optimisation and estimation risk

To use MPT, a manager estimates expected returns, standard deviations and correlations for every asset, then adds the investor's constraints and picks the feasible portfolio that fits the objectives. Because the output depends on these estimates, errors in them create estimation risk, which grows quickly as more securities are added. Large portfolios are handled with a variance-covariance matrix.

Summary written by BullWiser from the NISM Series X-A workbook (March 2026 edition), Chapter 14. Always refer to the current NISM workbook before your exam.

Multiple Choice Questions (38)

Q1 MCQ · 1 mark EasyMPT origins

Who laid the foundation of Modern Portfolio Theory with the 1952 article 'Portfolio Selection'?

AEugene Fama

BHarry Markowitz

CBenjamin Graham

DWilliam Sharpe

Q2 MCQ · 1 mark MediumMPT origins

What did Markowitz add that investors before the 1950s could not do?

AShow that risk can be removed completely

BInvent the idea of diversification

CProve that equity always beats debt

DQuantify the benefit of diversification using covariance or correlation

Q3 MCQ · 1 mark MediumMPT origins

Under MPT, which measure is used for the risk of a portfolio?

AThe highest price in the last year

BThe number of stocks held

CVariance (or standard deviation) of returns

DThe average of past returns

Q4 MCQ · 1 mark EasyAssumptions

Two assets offer the same expected return. Under MPT assumptions, which will an investor choose?

AThe one with lower risk

BThe one with higher risk

CEither, since only return matters

DNeither, they will hold cash

Q5 MCQ · 1 mark MediumAssumptions

MPT assumes investors base their decisions on which two things only?

AExpected return and expected variance of returns

BPast returns and brokerage costs

CDividend yield and P/E ratio

DTax rate and liquidity

Q6 MCQ · 1 mark MediumAssumptions

What does 'diminishing marginal utility of wealth' mean?

AInvestors become more risk-seeking as they get richer

BEach extra rupee adds less satisfaction as wealth grows

CWealth loses value over time due to inflation

DEach extra rupee adds more satisfaction than the last

Q7 MCQ · 1 mark MediumAssumptions

Over how many periods do investors maximise expected utility under MPT?

ATwo periods

BTheir full lifetime, period by period

CAn infinite number of periods

DOne period

Q8 MCQ · 1 mark EasyRisk attitudes

What is a 'fair game' in investment terms?

AA game regulated by SEBI

BA prospect with a guaranteed positive return

CA prospect with zero risk premium

DA risk-free investment

Q9 MCQ · 1 mark MediumRisk attitudes

How does a risk-averse investor treat a fair game?

AAlways accepts it

BRejects it and invests only in risk-free assets or those with a positive risk premium

CAccepts it only if it is short-term

DIs indifferent to it

Q10 MCQ · 1 mark MediumRisk attitudes

A risk-neutral investor judges investments on the basis of:

AExpected return alone, ignoring risk

BThe certainty equivalent rate being below the risk-free rate

CRisk alone, ignoring return

DPast performance only

Q11 MCQ · 1 mark EasyRisk attitudes

Which type of investor is willing to take part in a fair game?

ARisk-averse

BNone of them

CRisk-neutral only if it is risk-free

DRisk-seeking

Q12 MCQ · 1 mark HardCertainty equivalent

What is the Certainty Equivalent Rate (CER) of a risky portfolio?

AThe return guaranteed by the fund manager

BThe expected return of the risky portfolio for every investor

CThe risk-free return that would be just as attractive as the risky portfolio

DThe average return of the market index

Q13 MCQ · 1 mark MediumUtility

Which portfolio would an investor assign a higher utility score to, other things being equal?

AOne with higher expected return and lower risk

BOne with lower expected return and higher risk

COne with returns equal to the risk-free rate but higher risk

DOne with the highest risk

Q14 MCQ · 1 mark MediumExpected return

A stock returns 15% in a boom (probability 0.3), 10% in a normal year (0.5) and 2% in a recession (0.2). What is its expected return?

A9.0%

B10.0%

C9.9%

D11.3%

Q15 MCQ · 1 mark HardExpected return

A stock returns 25% in a boom (0.3), 20% in a normal year (0.5) and 1% in a recession (0.2). What is its expected return?

A20.0%

B17.7%

C22.5%

D15.3%

Q16 MCQ · 1 mark MediumExpected return

How is the expected return of a single security calculated from scenarios?

AMedian of the possible returns

BHighest possible return times its probability

CSimple average of the best and worst returns

DSum of each possible return multiplied by its probability

Q17 MCQ · 1 mark MediumPortfolio return

Weights of 0.2, 0.1, 0.3 and 0.4 are held in assets expected to return 9%, 12%, 15% and 18%. What is the portfolio's expected return?

A16.2%

B13.5%

C14.7%

D15.0%

Q18 MCQ · 1 mark EasyPortfolio return

A portfolio's expected return is the:

AWeighted average of the expected returns of its assets

BHighest return among its assets

CReturn of its largest holding only

DSimple average of the assets' returns

Q19 MCQ · 1 mark EasyVariance

What does a larger standard deviation of returns indicate?

AHigher guaranteed returns

BGreater dispersion of returns and therefore higher risk

CLower risk

DBetter liquidity

Q20 MCQ · 1 mark MediumVariance

What is the relationship between variance and standard deviation?

AThey are always equal

BStandard deviation is variance divided by n

CVariance is the square root of standard deviation

DStandard deviation is the square root of variance

Q21 MCQ · 1 mark HardVariance

When calculating the variance of a sample of yearly returns, the sum of squared deviations is divided by:

Bn²

Cn + 1

Dn − 1

Q22 MCQ · 1 mark MediumPortfolio variance

How many terms does the variance formula for a two-asset portfolio have?

AFour

BThree

CTwo

DSix

Q23 MCQ · 1 mark MediumPortfolio variance

What makes up the variance of a two-asset portfolio?

AEach asset's variance times its squared weight, plus twice the weighted covariance

BThe simple average of the two variances

CThe product of the two standard deviations

DThe sum of the two variances with no weights

Q24 MCQ · 1 mark HardPortfolio variance

Two assets each have a standard deviation of 5%, weights of 50% each and a correlation of 0.5. What is the portfolio standard deviation?

A5.00%

B3.54%

CAbout 4.33%

D2.50%

Q25 MCQ · 1 mark HardPortfolio variance

In the same two-asset example, why is the portfolio standard deviation (4.33%) lower than each asset's 5%?

ACorrelation below +1 gives a diversification benefit

BThe weights add up to more than 1

CStandard deviations always fall when added

DReturns are higher in the portfolio

Q26 MCQ · 1 mark MediumCovariance terms

How many weighted variance and covariance terms are in a three-asset portfolio's variance formula?

AThree: one per asset

BFour: three variances and one covariance

CNine: three variances and six covariances

DSix: three variances and three covariances

Q27 MCQ · 1 mark HardCovariance terms

How many covariance (correlation) estimates are needed for a portfolio of 50 securities?

A2,450

B1,225

C2,500

D50

Q28 MCQ · 1 mark MediumCorrelation

What happens when two securities are perfectly positively correlated?

APortfolio risk falls to zero

BPortfolio risk is always higher than either security

CThere is no diversification benefit; risk and return are both weighted averages

DPortfolio return doubles

Q29 MCQ · 1 mark MediumEfficient frontier

What is the efficient frontier?

AThe highest-returning single stock in each sector

BThe set of all portfolios with positive returns

CThe set of portfolios with the highest return for each level of risk, or lowest risk for each return

DThe line joining the risk-free asset and the market index

Q30 MCQ · 1 mark MediumEfficient frontier

How should a portfolio lying below the efficient frontier be viewed?

AOptimal for risk-averse investors

BBetter than any portfolio on the frontier

CRisk-free

DSub-optimal, because it does not give enough return for its risk

Q31 MCQ · 1 mark EasyEfficient frontier

When many risky securities are combined and the best combinations plotted, what shape does the efficient frontier take?

AAn umbrella-shaped curve

BA downward-sloping straight line

CA circle

DA straight horizontal line

Q32 MCQ · 1 mark MediumOptimisation

Which three inputs must a portfolio manager estimate to use the MPT framework?

AP/E ratios, dividends and book values

BExpected returns, standard deviations and correlations of the assets

CBrokerage, taxes and exit loads

DCredit ratings, durations and yields only

Q33 MCQ · 1 mark MediumOptimisation

After the feasible portfolios are identified, which one is selected for the investor?

AAlways the one with the highest return

BAlways the one with the lowest risk

CThe one with the most securities

DThe one that meets the investor's objectives and constraints

Q34 MCQ · 1 mark MediumEstimation risk

What is estimation risk in portfolio construction?

AThe risk of a change in tax laws

BThe risk of fraud by the custodian

CThe chance of error because the inputs (returns, risks, correlations) are estimates

DThe risk that the market will be closed

Q35 MCQ · 1 mark MediumEstimation risk

Why does estimation risk grow sharply as the number of securities rises?

AThe number of correlation estimates grows roughly with the square of the number of securities

BLarger portfolios pay higher taxes

CEach security needs a SEBI approval

DPrices of more securities are harder to find

Q36 MCQ · 1 mark HardVariance-covariance

For portfolios with many securities, what is usually built to calculate portfolio risk?

AA trial balance

BA variance-covariance matrix

CA decision tree

DA cash flow statement

Q37 MCQ · 1 mark EasyDiversification

What is diversification?

APutting all money in the best-performing asset

BTrading frequently to capture short-term gains

CInvesting only in government bonds

DSpreading investments across different assets so that their different behaviour reduces risk

Q38 MCQ · 1 mark HardRisk attitudes

A highly risk-averse investor sets the CER of a risky portfolio below the risk-free rate. What will they do?

AInvest all their money in the risky portfolio

BReject the risky portfolio and prefer the risk-free investment

CBe indifferent between the two

DBorrow to invest more in the risky portfolio

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Case-Based Questions (1 set)

Case 1 Case-Based · 2 marks each Portfolio risk and return

Ms. Rao, an investment adviser, is building a two-fund portfolio for a client. Fund P has an expected return of 12% and a standard deviation of 10%. Fund Q has an expected return of 8% and a standard deviation of 6%. The correlation between their returns is 0.2. The client will invest 60% in Fund P and 40% in Fund Q. The client asks why adding a lower-return fund makes sense, and whether a 10-fund portfolio would be harder to model.

Easy Sub-question 1

What is the expected return of the client's portfolio?

A9.6%

B11.2%

C10.0%

D10.4%

Hard Sub-question 2

What is the approximate standard deviation of the portfolio?

A4.87%

B7.60%

CAbout 6.9%

D8.40%

Medium Sub-question 3

Why is the portfolio's risk lower than the weighted average of the two funds' standard deviations?

AThe correlation of 0.2 is well below +1, so part of each fund's volatility offsets the other

BThe weights add up to more than 100%

CFund Q has a negative expected return

DStandard deviations are always added directly

Medium Sub-question 4

If the adviser models a 10-fund portfolio instead, how many correlation estimates are needed?

A10

B45

C90

D100

About this content: These practice questions are based on the NISM-Series-X-A: Investment Adviser (Level 1) Certification Examination Workbook published by the National Institute of Securities Markets (NISM), Mumbai. NISM is a SEBI-established institution. Questions cover Introduction to Modern Portfolio Theory with verified answers and explanations. BullWiser is an independent exam preparation platform — not affiliated with NISM or SEBI. Last updated: October 02, 2026.

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