Synetic College Logo
Unit 4 of 4 · B.Com Sem 6

Unit 4: Portfolio management

Security Analysis & Portfolio Management notes · PTU syllabus (BCOP 611-18)

3 min read5 topics10 exam questions
On this page
  1. Unit summary
  2. Markowitz model
  3. CAPM, CML and SML
  4. Arbitrage Pricing Theory (APT)
  5. Portfolio performance evaluation
  6. Portfolio revision, formula plans and global investing
  7. Key terms
  8. Quick revision
  9. Important questions

Unit summary

Portfolio management combines securities to get the best return for a given level of risk. This unit covers the Markowitz model, the Capital Market Line and Security Market Line, CAPM and Arbitrage Pricing Theory, portfolio performance evaluation (Sharpe, Treynor and Jensen), techniques of portfolio revision, formula plans and global investing.

After this unit you can

  • Explain the Markowitz model and the efficient frontier
  • Explain CAPM, CML, SML and APT
  • Evaluate portfolio performance using Sharpe, Treynor and Jensen measures
  • Explain portfolio revision, formula plans and global investing

PTU syllabus topics

  • Capital Asset Pricing Model
  • Arbitrage Pricing Theory
  • Markowitz Model
  • Capital Market Line
  • Security Market Line
  • portfolio performance evaluation (Sharpe, Jensen, Treynor models)
  • techniques of portfolio revision
  • formula plans
  • global investing
Key formulasPortfolio formulas

  • CAPM

    E(R) = Rf + β (Rm − Rf)

  • Sharpe ratio

    (Rp − Rf) / σp

  • Treynor ratio

    (Rp − Rf) / βp

  • Jensen's alpha

    Rp − [Rf + βp (Rm − Rf)]

1

Topic 1

Markowitz model

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.
2

Topic 2

CAPM, CML and SML

  • Adding a risk-free asset gives the Capital Market Line (CML) — a straight line from Rf tangent to the efficient frontier at the market portfolio (M).
Key formulasCapital market theory

  • Capital Market Line

    E(Rp) = Rf + [(E(Rm) − Rf) ÷ σm] × σp

  • CAPM / Security Market Line

    E(Ri) = Rf + βi [E(Rm) − Rf]

ComparisonCML vs SML
CML
SML

Measures risk by

Standard deviation (total risk)

Beta (systematic risk)

Applies to

Efficient portfolios only

All securities and portfolios

Slope

Market price of risk (Rm − Rf) ÷ σm

Market risk premium (Rm − Rf)

Example

Rf = 6%, Rm = 13%, β = 1.2 → required return = 6 + 1.2 × 7 = 14.4%. If the stock is expected to return 16%, it plots above the SML — undervalued (buy).

  • CAPM assumptions: perfect markets, homogeneous expectations, borrowing and lending at Rf, no taxes, single period.
3

Topic 3

Arbitrage Pricing Theory (APT)

  • Stephen Ross (1976): expected return depends on several systematic factors, not just the market.
Key formulasAPT

  • Expected return

    E(Ri) = Rf + βi1 λ1 + βi2 λ2 + … + βik λk — λ factor risk premiums, β factor sensitivities

  • Factors: inflation, industrial production, interest rate term structure, default risk premium, oil prices, exchange rates.
  • Based on no-arbitrage — two portfolios with the same factor exposures must offer the same return.
  • Vs CAPM: fewer assumptions, multiple factors, no need for the market portfolio; but factors are not specified by theory.
4

Topic 4

Portfolio performance evaluation

Key formulasPerformance measures

  • Sharpe ratio

    (Rp − Rf) ÷ σp — reward per unit of total risk

  • Treynor ratio

    (Rp − Rf) ÷ βp — reward per unit of systematic risk

  • Jensen's alpha

    αp = Rp − [Rf + βp (Rm − Rf)]

FundReturnσβSharpeTreynor
A15%18%1.10.508.18
B13%12%0.80.588.75
Market12%14%1.00.436.00

Example

With Rf = 6%: Fund B ranks higher on both Sharpe and Treynor. Jensen's alpha for A = 15 − [6 + 1.1 × 6] = 2.4%; for B = 13 − [6 + 0.8 × 6] = 2.2% — both beat the market on a risk-adjusted basis.

  • Sharpe for undiversified portfolios (total risk matters); Treynor and Jensen for well-diversified portfolios.
5

Topic 5

Portfolio revision, formula plans and global investing

  • 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.

Key terms

Efficient frontier
Set of portfolios with maximum return for each level of risk
Market portfolio
Portfolio of all risky assets weighted by market value
Security Market Line
Graph of CAPM relating expected return to beta
Jensen's alpha
Excess return above that predicted by CAPM
Formula plan
Mechanical rule for portfolio revision

Quick revision

  • Markowitz: diversification benefit depends on correlation.
  • CML uses σ; SML uses β; CAPM E(R) = Rf + β(Rm − Rf).
  • APT: multiple factors, no-arbitrage.
  • Sharpe (σ), Treynor (β), Jensen (alpha).
  • Revision: active vs passive; formula plans; global investing via LRS.

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 efficient frontier?
  2. Q2.State the CAPM equation.
  3. Q3.Distinguish CML and SML.
  4. Q4.What is APT?
  5. Q5.Define the Sharpe ratio.
  6. Q6.What is a constant ratio plan?

Long-answer questions

  1. Q1.Explain the Markowitz portfolio model with an illustration.
  2. Q2.Explain the Capital Asset Pricing Model and the CML and SML.
  3. Q3.Explain the Arbitrage Pricing Theory and compare it with CAPM.
  4. Q4.Explain portfolio performance evaluation using Sharpe, Treynor and Jensen measures, and portfolio revision techniques.

Stuck on this unit?

Message SBS on WhatsApp for help with Security Analysis & Portfolio Management, or to ask about studying B.Com at Synetic.

WhatsApp us