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MPT and efficient frontier

In this chapter: Diversification benefit · Efficient frontier construction

~3 min readLayer 4 · Professional CertificationsFree

Modern Portfolio Theory (Markowitz 1952): combining assets with low correlation reduces portfolio volatility without sacrificing return. Efficient frontier: highest-return portfolio for each risk level.

Foundation

Two-asset portfolio variance: σ²_p = w_A² σ_A² + w_B² σ_B² + 2 w_A w_B σ_A σ_B ρ_{AB} Diversification benefit: when ρ < 1, portfolio σ < weighted average σ. Efficient frontier: locus of portfolios offering maximum return for each risk level. Tangent portfolio: highest Sharpe portfolio on frontier (where Capital Market Line touches). Capital Allocation Line (CAL): risk-free + tangent portfolio combinations. Optimal portfolios on CAL.

Deep Dive

Indian asset class correlations (approximate): • Equity (NIFTY) vs G-Sec: 0.0 to 0.3 • Equity vs Gold: -0.1 to +0.1 (often near zero) • Equity vs Real Estate: 0.4-0.6 (longer measurement) • Indian equity vs US S&P: 0.4-0.6 (rising) Diversification implications: • Equity-debt mix: foundational diversification • Adding gold: marginal volatility reduction + crisis hedge • International equity: modest diversification + currency risk • Real estate: limited liquidity For most retail Indians, simple rules approximate efficient frontier: • 60/40 (equity/debt) • Age-based equity allocation • Lifecycle glide paths

Advanced

Practitioner traps with MPT: 1. Correlations rise during crises — exactly when diversification needed, it disappears. 2. Backward-looking correlations don't predict forward. 3. Optimisation produces concentrated portfolios sensitive to input assumptions. 4. Most retail can't implement multi-asset optimal portfolios. What works in practice: • Simple allocation rules (60/40 + 5-10% gold) • Lifecycle glide paths • Low-correlation diversifiers as opportunistic additions • Periodic rebalancing Black-Litterman model addresses optimisation issues by combining market-equilibrium with subjective views. Risk-parity allocates by risk contribution rather than capital. For CFP and CFA candidates: understand MPT principles, but use simplified rules for client implementation.

Regulatory references
  • CFA Institute curriculum on MPT
  • Markowitz 1952 paper
  • CFP-FPSB syllabus
Common mistakes & pitfalls
  • Confusing stock count with diversification.
  • Assuming correlations stable.
  • Static asset allocation despite market changes.
  • Random rebalancing.

Frequently asked

When does diversification disappoint?
In crises: correlations rise toward 1. 2008 GFC: equity, real estate, commodities crashed together. Diversification benefit reduced when most needed.
Best simple rule for retail?
60/40 equity/debt + 5-10% gold + automatic rebalancing. Approximates efficient frontier; manageable; reliable. Adjust based on age and risk tolerance.

Practice questions

Click each question to reveal the answer and explanation.

Q 1
Diversification benefit requires:
  1. (a)Correlation = 1
  2. (b)Correlation < 1
  3. (c)Many stocks
  4. (d)Same sector
Correct: (b) Correlation < 1
Diversification benefit when ρ < 1. Lower ρ = more benefit. ρ = 1: no benefit; ρ = -1: maximum benefit (theoretical).
Q 2
Capital Allocation Line:
  1. (a)Random portfolios
  2. (b)Risk-free + tangent portfolio combinations; optimal portfolios are on CAL
  3. (c)All possible portfolios
  4. (d)Only efficient frontier
Correct: (b) Risk-free + tangent portfolio combinations; optimal portfolios are on CAL
CAL: risk-free combined with tangent portfolio. Optimal portfolios all lie on CAL. Different risk levels chosen by mix.
Q 3
Indian equity-debt correlation typically:
  1. (a)0.9
  2. (b)0.0 to 0.3
  3. (c)-0.5
  4. (d)1.0
Correct: (b) 0.0 to 0.3
Indian equity-debt: low correlation (0.0-0.3). Foundation of diversification. Low correlation = real diversification benefit.
Q 4
Pre-committed rebalancing rule:
  1. (a)Always sell winners
  2. (b)Bring portfolio back to target allocation when drift exceeds threshold
  3. (c)Random rebalancing
  4. (d)No rebalancing
Correct: (b) Bring portfolio back to target allocation when drift exceeds threshold
Rebalancing rule: bring back to target when drift exceeds threshold (typically 5%). Eliminates emotional decisions; works through cycles.
Q 5
During 2020 March crash:
  1. (a)Stay in cash
  2. (b)Pre-committed rebalancing means buy more equity at lower prices
  3. (c)Sell everything
  4. (d)Wait until recovery
Correct: (b) Pre-committed rebalancing means buy more equity at lower prices
Pre-committed rebalancing: buy more equity in crash (low prices). Mechanical, not emotional. Performance benefit follows recovery.
Educational purposes only. The numbers, returns, and examples used in this lesson are illustrative. Past performance does not guarantee future results. Mutual fund and securities investments are subject to market risks. This lesson is not investment advice; for advice tailored to your circumstances, consult a SEBI-registered Investment Adviser. Read our full disclaimer.