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Module 1.5CFP IPSFull chapter

Portfolio theory

In this chapter: Diversification and correlation · Modern Portfolio Theory and the efficient frontier

~6 min readLayer 4 · Professional CertificationsFree

Diversification reduces risk without sacrificing return — Markowitz's 1952 insight. By combining assets with low correlation, the portfolio's volatility falls below any individual asset's. The Efficient Frontier maps the highest-return portfolio for each risk level. CFPs use this framework as the conceptual basis for asset allocation, even if practical implementation uses simplified rules.

Foundation

Modern Portfolio Theory (MPT) core insights: 1. Diversification: combining assets with correlation < 1 reduces portfolio σ below weighted-average individual σ. 2. Efficient frontier: set of portfolios offering maximum return for each risk level. 3. Tangent portfolio: highest-Sharpe portfolio on the frontier. 4. Capital Allocation Line (CAL): risk-free asset + tangent portfolio. Optimal portfolios all lie on CAL. Formulas: Portfolio variance (2 assets): σ²_p = w_A² σ_A² + w_B² σ_B² + 2 w_A w_B σ_A σ_B ρ_{AB} With more assets, generalize using covariance matrix. Key insight: when ρ < 1, portfolio σ < weighted average σ. Diversification benefit grows as ρ falls. ρ = −1 (perfect negative): can construct zero-risk portfolio.

Deep Dive

Practitioner-grade analysis of correlation: Indian asset class correlations (approximate, long-term): • 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 period) • Equity (large-cap) vs Equity (small-cap): 0.7-0.85 • Indian equity vs US S&P 500: 0.4-0.6 (rising over time as integration grows) Diversification implications: • Equity-debt mix is the foundational diversification — adds debt to equity, σ falls noticeably. • Adding gold to equity-debt: marginal volatility reduction + crisis hedge. • International equity adds modest diversification at the cost of currency risk. • Within equity (large + mid + small): diversification but high correlation limits benefit. Frontier construction in practice: most planners don't solve mean-variance optimisation explicitly. They use simple rules (60/40, age-based equity %, lifecycle glide paths) that approximate the efficient frontier. The math is the principle; the practice uses heuristics.

Advanced

Practitioner traps with MPT: 1. Correlations rise during crises — exactly when you need diversification, it disappears. 2008 saw equity, real estate, commodities all correlate near 1. International equity offered limited protection. 2. Backward-looking correlations don't predict forward. Correlation matrices change regime; mean-variance optimisation that assumes stability produces fragile portfolios. 3. Optimisation algorithms produce concentrated portfolios sensitive to input assumptions ("optimisation error"). Tiny changes in expected returns shift weights dramatically. 4. Most retail investors can't implement multi-asset optimal portfolios — too many constraints (lock-ins, taxation, vehicle availability). What works in practice: • Simple allocation rules (60/40 + 5-10% gold) • Lifecycle glide paths (target-date funds) • Low-correlation diversifiers as opportunistic additions (REITs, gold, international) • Periodic rebalancing The Black-Litterman model addresses some optimisation issues by combining market-equilibrium with subjective views. Risk-parity allocates by risk contribution rather than capital — used by some institutional managers. For CFPs: understand MPT principles, but use simplified rules for client implementation.

Regulatory references
  • CFA Institute curriculum on Modern Portfolio Theory
  • AMFI Best Practices on diversification
  • FPSB India syllabus on portfolio theory
Common mistakes & pitfalls
  • Confusing stock count with diversification — high correlation defeats the count.
  • Assuming correlations are stable — they rise in crises.
  • Over-relying on mean-variance optimisation in client portfolios — fragile to input assumptions.
  • Forgetting that international diversification adds currency risk.
  • Using historical correlations without considering regime changes.

Frequently asked

Is 30 stocks enough for diversification?
For idiosyncratic risk: yes, 30+ stocks across sectors largely diversify firm-specific risk. For systematic risk: no — market-wide moves still apply. Asset-class diversification (equity + debt + gold) addresses systematic risk; stock count addresses firm risk.
Should I add international equity?
For genuine diversification, yes — moderate allocation (10-15%). But: tax treatment changed in 2024 (now treated as debt for tax), currency risk, and rising integration with India reduce diversification benefit over time. Consider but don't overweight.
How often should I rebalance?
Annual rebalancing or when allocation drifts >5% from target — whichever first. Avoid frequent rebalancing (monthly) — tax and transaction costs eat the benefit. CFPs document rebalancing rules in IPS to avoid emotion-driven decisions.

Practice questions

Click each question to reveal the answer and explanation.

Q 1
Two assets with σ 20% and 10%, correlation 0.5, equal-weighted portfolio σ:
  1. (a)8.7%
  2. (b)13.0%
  3. (c)15.0%
  4. (d)20.0%
Correct: (b) 13.0%
σ²_p = 0.25(0.04) + 0.25(0.01) + 2(0.5)(0.5)(0.20)(0.10)(0.5) = 0.01 + 0.0025 + 0.005 = 0.0175. σ_p = 13.2% ≈ 13%.
Q 2
Diversification benefit is largest when:
  1. (a)ρ = +1 (perfect positive correlation)
  2. (b)ρ = 0 (no correlation)
  3. (c)ρ = −1 (perfect negative correlation)
  4. (d)σ is high
Correct: (c) ρ = −1 (perfect negative correlation)
ρ = −1: assets move opposite. Can construct zero-risk portfolio (in theory). Real assets rarely have ρ = −1, but lower ρ means more diversification benefit.
Q 3
Modern Portfolio Theory was developed by:
  1. (a)Sharpe
  2. (b)Markowitz
  3. (c)Black & Litterman
  4. (d)Fama & French
Correct: (b) Markowitz
Harry Markowitz, 1952, "Portfolio Selection". Won Nobel Prize 1990. Sharpe extended with CAPM (1964); Black-Litterman is a refinement; Fama-French is a multi-factor extension.
Q 4
During crisis, asset correlations typically:
  1. (a)Stay constant
  2. (b)Decrease
  3. (c)Increase toward 1
  4. (d)Become negative
Correct: (c) Increase toward 1
Correlations rise during crises — diversification benefit disappears exactly when needed. Empirical regularity. Practitioners account for "stress correlations" in stress testing.
Q 5
A risk-parity portfolio:
  1. (a)Equal-weights all assets
  2. (b)Allocates equal capital across assets
  3. (c)Allocates so each asset contributes equally to portfolio risk
  4. (d)Uses only risk-free asset
Correct: (c) Allocates so each asset contributes equally to portfolio risk
Risk-parity allocates so each asset contributes equally to portfolio risk. High-volatility assets get less capital; low-volatility assets get more. Bridgewater's All-Weather is a famous example.
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.