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Unit 3 of 4 · M.Com Sem 4

Unit 3: Efficient markets and portfolio management

Security Analysis and Portfolio Management notes · PTU syllabus (MCOP402-18)

3 min read5 topics10 exam questions
On this page
  1. Unit summary
  2. Random walk theory and forms of efficiency
  3. Random walk vs technical and fundamental analysis
  4. Portfolio management: objectives and construction
  5. Portfolio revision
  6. Portfolio return, standard deviation and Markowitz optimisation
  7. Key terms
  8. Quick revision
  9. Important questions

Unit summary

If markets are efficient, beating them is hard — so portfolios must be built carefully. This unit covers the random walk theory and its weak, semi-strong and strong forms, comparison with technical and fundamental analysis, portfolio management objectives and construction issues, portfolio revision and evaluation, estimating portfolio return and standard deviation, and Markowitz risk–return optimisation.

After this unit you can

  • Explain the random walk theory and the three forms of market efficiency
  • Compare random walk with technical and fundamental analysis
  • Explain portfolio objectives, construction, revision and evaluation
  • Compute portfolio return and risk and explain Markowitz optimisation

PTU syllabus topics

  • Random walk theory (weak/semi-strong/strong forms)
  • comparison of random walk with technical and fundamental analysis
  • portfolio management objectives and construction issues
  • portfolio revision and evaluation
  • estimating return and standard deviation
  • Markowitz risk-return optimization
Key formulasPortfolio theory

  • Portfolio return

    Rp = Σ wi Ri

  • Two-asset risk

    σp² = wA²σA² + wB²σB² + 2wAwBρσAσB

  • CAPM

    E(R) = Rf + β (Rm − Rf)

  • Total risk

    Systematic + unsystematic

1

Topic 1

Random walk theory and forms of efficiency

Efficient Market Hypothesis (Eugene Fama, 1970): security prices fully reflect all available information; hence consistently earning above-normal returns is not possible.

HierarchyForms of market efficiency
  1. Strong form

    Prices reflect all information, public and private (insider) — even insiders cannot earn excess returns

  2. Semi-strong form

    Prices reflect all public information — fundamental analysis cannot beat the market

  3. Weak form

    Prices reflect all past prices and volumes — technical analysis cannot beat the market

  • Tests: weak form — serial correlation, runs tests, filter rules; semi-strong — event studies (earnings, splits, bonus); strong form — performance of insiders and fund managers.
  • Random Walk Theory (Malkiel): successive price changes are independent and random, so past prices cannot predict future prices — consistent with weak-form efficiency.
  • Evidence and anomalies: January effect, small-firm effect, momentum, value premium, bubbles — and behavioural finance explanations (overconfidence, herding).
  • Implications: passive investing (index funds), diversification, low-cost strategies.
2

Topic 2

Random walk vs technical and fundamental analysis

ComparisonImplications of efficiency
Technical analysis
Fundamental analysis

Weak-form efficiency

Useless — past prices already reflected

Can still add value

Semi-strong efficiency

Useless

Useless for public information

Strong-form efficiency

Useless

Useless even with private information

Practical view

Anomalies and momentum suggest partial inefficiency

Skilled analysts may add value in less efficient segments (small caps)

3

Topic 3

Portfolio management: objectives and construction

  • Objectives: maximise return for a given risk, safety of principal, liquidity, regular income, capital growth, tax efficiency, marketability.
ProcessPortfolio management process
  1. 1

    Specify objectives and constraints

    Return, risk, horizon, liquidity, taxes, legal

  2. 2

    Asset allocation

    Strategic and tactical

  3. 3

    Security selection

  4. 4

    Portfolio construction

    Diversification, weights

  5. 5

    Monitoring and revision

  6. 6

    Performance evaluation

  • Construction issues: number of securities (diversification benefits level off after 15–25 stocks), correlations, transaction costs, taxes, liquidity, investor constraints; active vs passive management.
4

Topic 4

Portfolio revision

  • Portfolio revision: changing the mix of securities as conditions, objectives or relative values change.
  • Active revision (market timing, sector rotation) vs passive revision (rebalancing to a target allocation, indexing).
ClassificationFormula plans
Formula plans

  • Constant rupee value plan

    Keep a fixed rupee amount in equities; sell when it rises, buy when it falls

  • Constant ratio plan

    Keep a fixed ratio between equity and debt (e.g., 60:40)

  • Variable ratio plan

    Equity proportion falls as prices rise and rises as prices fall

  • Rupee cost averaging

    Invest a fixed amount at regular intervals (SIP)

  • Formula plans remove emotion and force "buy low, sell high", but may underperform in strong trends.

Global investing

  • Benefits: further diversification (low correlation between markets), access to global leaders and sectors, currency diversification.
  • Risks: exchange rate risk, political and regulatory risk, information gaps, higher costs, taxation.
  • Routes for Indian investors: RBI's Liberalised Remittance Scheme (US$ 2,50,000 a year), international mutual funds and fund-of-funds, ETFs, GIFT City IFSC platforms; TCS on remittances above ₹10 lakh.
5

Topic 5

Portfolio return, standard deviation and Markowitz optimisation

Harry Markowitz (1952) showed that portfolio risk depends on the covariance between securities, not just their individual risks.

Key formulasTwo-asset portfolio

  • Portfolio return

    Rp = wA RA + wB RB

  • Portfolio variance

    σp² = wA² σA² + wB² σB² + 2 wA wB ρAB σA σB

  • Minimum-variance weight of A

    wA = (σB² − ρ σA σB) ÷ (σA² + σB² − 2ρ σA σB)

Example

A: return 12%, σ 15%; B: return 18%, σ 25%; ρ = 0.2; equal weights. Rp = 15%. σp² = 0.25(225) + 0.25(625) + 2(0.25)(0.2)(15)(25) = 56.25 + 156.25 + 37.5 = 250 → σp ≈ 15.8% — less than the weighted average SD of 20%.

  • Efficient frontier: the set of portfolios offering the highest return for each level of risk; rational investors choose a point on it based on their indifference curves.
  • Assumptions: investors are risk-averse, decisions based on mean and variance, single-period horizon.

Key terms

Random walk
Price changes are independent and unpredictable
Semi-strong efficiency
Prices reflect all public information
Asset allocation
Distribution of funds across asset classes
Portfolio revision
Changing the portfolio to maintain its objectives
Efficient frontier
Portfolios with maximum return for each level of risk

Quick revision

  • Random walk; weak, semi-strong, strong forms and tests.
  • Efficiency undermines technical (weak) and fundamental (semi-strong) analysis.
  • Portfolio process: objectives → allocation → selection → construction → revision → evaluation.
  • Formula plans for revision.
  • Portfolio variance depends on correlation; Markowitz efficient frontier.

Important exam questions

Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).

Short-answer questions

  1. Q1.What is the random walk theory?
  2. Q2.State the three forms of market efficiency.
  3. Q3.What are the objectives of portfolio management?
  4. Q4.What is a constant ratio plan?
  5. Q5.Write the formula for the variance of a two-asset portfolio.
  6. Q6.What is the efficient frontier?

Long-answer questions

  1. Q1.Explain the random walk theory and the forms of market efficiency.
  2. Q2.Compare random walk theory with technical and fundamental analysis.
  3. Q3.Explain portfolio objectives, construction and revision.
  4. Q4.Explain the Markowitz model of portfolio optimisation.

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