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Unit 4 of 4 · MBA Sem 4

Unit 4: Portfolio analytics

Financial Analytics notes · PTU syllabus (MBA 965-26)

3 min read6 topics10 exam questions
On this page
  1. Unit summary
  2. Portfolio return and risk
  3. Performance metrics
  4. Markowitz mean–variance framework and efficient frontier
  5. Stress testing
  6. Backtesting
  7. Visualisation and reporting of financial insights
  8. Key terms
  9. Quick revision
  10. Important questions

Unit summary

Portfolio analytics measures returns and risks and tests strategies before money is committed. This unit covers portfolio returns, risk and performance metrics such as the Sharpe ratio, the Markowitz mean–variance framework and efficient frontier, stress testing and backtesting, and visualisation and reporting of financial insights.

After this unit you can

  • Compute portfolio returns, risk and performance metrics
  • Apply the Markowitz framework and efficient frontier
  • Conduct stress tests and backtests
  • Visualise and report financial insights

PTU syllabus topics

  • Portfolio returns
  • risk and performance metrics (Sharpe ratio)
  • Markowitz mean-variance framework and efficient frontier
  • stress testing and backtesting
  • visualization and reporting of financial insights
Key formulasPortfolio analytics

  • Portfolio return

    Σ wi Ri

  • Portfolio variance

    wᵀ Σ w

  • Sharpe ratio

    (Rp − Rf) / σp

  • Efficient frontier

    Highest return for each level of risk

1

Topic 1

Portfolio return and risk

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

Performance metrics

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.
  • Fama's decomposition: return due to selectivity and due to risk.
  • Information ratio: active return ÷ tracking error.
Key formulasAdditional risk metrics

  • Sortino ratio

    (Rp − Rf) ÷ downside deviation

  • Maximum drawdown

    Largest peak-to-trough fall

  • Information ratio

    Active return ÷ tracking error

3

Topic 3

Markowitz mean–variance framework and efficient frontier

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.
  • In practice: optimise with Excel Solver, R (PortfolioAnalytics) or Python (PyPortfolioOpt); add constraints (no short selling, weight limits); estimation error makes optimised weights unstable — use shrinkage or robust methods.
4

Topic 4

Stress testing

  • Stress testing: estimating portfolio losses under extreme but plausible scenarios.
  • Types: historical scenarios (2008 crisis, March 2020 COVID crash), hypothetical scenarios (rate shock of 200 basis points, rupee depreciation of 10%), reverse stress tests (what scenario causes failure?).
  • Regulation: RBI requires banks to conduct stress tests; SEBI requires stress testing for mutual fund liquidity and clearing corporations.
5

Topic 5

Backtesting

  • Backtesting: testing a strategy or model on historical data to see how it would have performed.
  • Pitfalls: look-ahead bias, survivorship bias, overfitting (data snooping), ignoring transaction costs and liquidity.
  • Good practice: out-of-sample and walk-forward testing, realistic costs, robustness checks.
6

Topic 6

Visualisation and reporting of financial insights

  • Charts: cumulative return lines vs benchmark, drawdown charts, rolling volatility and Sharpe, risk–return scatter with efficient frontier, allocation pie or treemaps, correlation heat maps.
  • Reporting: dashboards in Power BI or Tableau; clear explanation of risk, assumptions and limitations; regulatory and client reports.

Key terms

Sharpe ratio
Excess return per unit of total risk
Maximum drawdown
Largest fall from peak to trough
Efficient frontier
Portfolios with the best return for each risk level
Stress testing
Assessing losses under extreme scenarios
Look-ahead bias
Using information not available at the time

Quick revision

  • Portfolio return and SD; correlation and diversification.
  • Sharpe, Treynor, Jensen, Sortino, information ratio, drawdown.
  • Markowitz optimisation, efficient frontier, practical issues.
  • Historical, hypothetical, reverse stress tests; regulation.
  • Backtesting pitfalls; visualisation and reporting.

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.State the Sharpe ratio formula.
  2. Q2.What is maximum drawdown?
  3. Q3.What is the efficient frontier?
  4. Q4.Distinguish historical and hypothetical stress tests.
  5. Q5.Name two pitfalls in backtesting.
  6. Q6.Name two charts used in portfolio reporting.

Long-answer questions

  1. Q1.Explain the computation of portfolio return, risk and performance metrics.
  2. Q2.Explain the Markowitz mean–variance framework and the efficient frontier.
  3. Q3.Discuss stress testing and backtesting.
  4. Q4.Explain visualisation and reporting of financial insights.

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