NISM Series XXI-B Short Notes – Part 7: Modern Portfolio Theory & Capital Market Theory

NISM Series XXI-B Short Notes – Part 7: Modern Portfolio Theory & Capital Market Theory

This is Part 7 of our 10-part NISM XXI-B short notes series on PassNISM.in. This part covers Chapters 15 and 16 — Modern Portfolio Theory (MPT) and Capital Market Theory including the Capital Asset Pricing Model (CAPM). These are among the most calculation-heavy and concept-rich chapters in the NISM XXI-B syllabus.

👉 Also Read: Part 6: Indices, Market Efficiency & Behavioural Finance | Free Mock Test

Chapter 15: Introduction to Modern Portfolio Theory (MPT) What is Modern Portfolio Theory?

MPT, developed by Harry Markowitz, provides a framework for constructing and selecting portfolios based on expected performance and investor risk appetite. It quantified the concept of diversification by introducing statistical tools like covariance and correlation between investment assets.

The central insight of MPT: You can reduce overall portfolio risk without necessarily reducing expected return, simply by combining assets that are not perfectly correlated.

Assumptions of MPT

• An investor wants to maximize return for a given level of risk (mean-variance optimization).
• Each investment is represented by a probability distribution of expected returns over a holding period.
• Investors maximize one-period expected utility.
• Investors base decisions solely on expected return and risk (standard deviation).
• All investors have the same expectations about risk, return, and correlations (homogeneous expectations).

Risk Attitudes of Investors

Measuring Risk for Individual Assets

• Standard Deviation (σ): Square root of variance; measures dispersion of returns around the expected value. Higher σ = higher risk.
• Variance (σ²): Average of squared deviations from the mean return.

Covariance and Correlation

• Covariance: Measures the degree to which two assets move together relative to their individual means.
• Correlation Coefficient (ρ): Standardized measure of covariance, ranging from -1 to +1.

ρ = +1 → perfect positive correlation → no diversification benefit
ρ = -1 → perfect negative correlation → maximum diversification benefit
ρ < 1 → some diversification benefit exists

Portfolio Risk for Two Securities

Portfolio risk is NOT simply the weighted average of individual risks. It also depends on how the assets move together (covariance):

Portfolio Variance (two assets) = w₁²σ₁² + w₂²σ₂² + 2·w₁·w₂·σ₁·σ₂·ρ₁₂

Where w₁, w₂ = weights; σ₁, σ₂ = standard deviations; ρ₁₂ = correlation coefficient

Key insight: As long as ρ < +1, combining two assets produces a portfolio with lower risk than the weighted average risk of the two assets. The lower the correlation, the greater the diversification benefit.

The Efficient Frontier

When we plot all possible combinations of two or more assets (varying the weights), we get a risk-return opportunity set. Of all these combinations, those offering:

• the highest return for a given level of risk, or
• the lowest risk for a given level of return

…form a curve called the Efficient Frontier. This curve has an umbrella-like shape. Rational investors will only choose portfolios on the efficient frontier — portfolios below it are suboptimal.

Portfolio Optimization

An optimal portfolio is a combination of investments with desirable individual risk-return characteristics for a given set of constraints. To use the MPT framework, the portfolio manager must estimate:

• Expected return for each asset
• Standard deviation for each asset
• Correlation coefficients between all pairs of assets

Chapter 16: Introduction to Capital Market Theory From MPT to Capital Market Theory

Capital Market Theory extends MPT by introducing the concept of a risk-free asset. This has a profound impact on how investors construct efficient portfolios. CAPM (Capital Asset Pricing Model) emerged from this framework to answer the fundamental question: How should the risk of an investment affect its expected return?

Risk-Free Asset Characteristics

• Certain (known) return
• Standard deviation = Zero
• Covariance with any risky asset = Zero

Combining Risk-Free Asset with Risky Portfolio

When a risk-free asset is combined with a risky portfolio, the resulting risk-return combinations lie on a straight line (unlike the curve we get with only risky assets).

The optimal straight line is the one that is tangent to the efficient frontier of risky assets. This tangent portfolio is called the Market Portfolio (M) — every rational investor wants exposure to it, combined with the risk-free asset in proportions dictated by their risk appetite.

Capital Market Line (CML)

The Capital Market Line is the efficient frontier when a risk-free asset is available. It is a straight line connecting the risk-free rate to the market portfolio M.

CML Formula: E(Rp) = Rf + [(E(Rm) – Rf) / σm] × σp

Where: E(Rp) = Expected portfolio return, Rf = Risk-free rate, E(Rm) = Market return, σm = Market standard deviation, σp = Portfolio standard deviation

All risky portfolios below the CML are inefficient — rational investors prefer CML combinations.

Market Portfolio and Full Diversification

The market portfolio (M) is a portfolio that contains all risky assets in proportion to their market capitalization. Because it includes everything, it is perfectly diversified — all unsystematic (company-specific) risk is eliminated. Only systematic (market) risk remains.

Types of Risk in Capital Market Theory

Capital Asset Pricing Model (CAPM)

CAPM provides a way to determine the expected return on any risky asset based on its systematic risk relative to the market, measured by Beta (β).

E(Ri) = Rf + βi × (E(Rm) – Rf)

• E(Ri) = Expected return on asset i
• Rf = Risk-free rate
• βi = Beta of asset i (sensitivity of asset's return to market return)
• (E(Rm) – Rf) = Market risk premium

Understanding Beta (β)

• β = 1 → Asset moves exactly with the market
• β > 1 → Asset is more volatile than the market (aggressive)
• β < 1 → Asset is less volatile than the market (defensive)
• β = 0 → Asset's return is uncorrelated with market returns (like a risk-free asset)

Security Market Line (SML)

The Security Market Line is the graphical representation of CAPM. It plots the expected return of assets against their Beta. All fairly priced assets lie on the SML:

• Assets above the SML → underpriced (offering excess return for given risk) → Buy signal
• Assets below the SML → overpriced (offering insufficient return for given risk) → Sell signal

CML vs SML — Key Difference

Multi-Factor Models

CAPM is a single-factor model (uses only market risk/beta). In practice, multiple factors drive returns. Extensions include:

• Fama-French Three-Factor Model: Adds size (small-cap premium) and value (value stock premium) factors to market risk.
• Macro-Economic Factor Models: Use factors like GDP growth, inflation, interest rate changes.
• Fundamental Factor Models: Use company-level financial factors.

Quick Revision Box – Part 7

• MPT = diversification reduces risk if assets are not perfectly correlated
• Efficient Frontier = best risk-return combinations from all possible portfolios
• Risk-free asset has σ = 0 and covariance with risky assets = 0
• CML = efficient frontier when risk-free asset is available (uses total risk)
• Market portfolio = all risky assets; fully diversified; only systematic risk remains
• CAPM: E(Ri) = Rf + β × (Rm – Rf)
• β > 1 = aggressive; β < 1 = defensive
• SML = graphical form of CAPM (uses beta on x-axis)
• CML uses total risk (σ); SML uses systematic risk (β)

👉 Continue Reading: Part 8: Risk Management in Portfolio Management

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