Modern Portfolio Theory in 6 Charts

Modern Portfolio Theory (MPT) is the conceptual backbone of ICWIM Chapter 6, CFA Level 1, and most portfolio-management content on CISI Diploma exams. The maths gets dense fast, but the intuition is visual: six diagrams cover the whole framework. Once you can sketch each chart from memory, the formulas slot in naturally.

Chart 1: The risk-return scatter

Every individual asset can be plotted as a single point in risk-return space — risk (σ, standard deviation of returns) on the x-axis, expected return on the y-axis. Higher up = more return; further right = more risk.

Key intuition: higher expected returns require accepting higher risk. There are no free lunches. The cluster of asset classes traces a rough upward-sloping pattern — this is the empirical version of the risk-return tradeoff.

Chart 2: The diversification benefit (correlation effect)

When you combine two assets into a portfolio, the portfolio's risk depends on their correlation. The two-asset portfolio variance formula:

The last term — the cross-term — is where diversification operates. When ρ < 1, the cross-term reduces overall portfolio risk below the weighted average of the individual standard deviations.

Key intuition:

• ρ = +1: no diversification benefit. Portfolio risk = weighted average. Straight line.
• ρ = 0: meaningful diversification benefit. Portfolio risk < weighted average. Curve bulges left.
• ρ = −1: maximum diversification. Risk can theoretically be reduced to zero at the right weights. Sharp left bulge.

Realistic correlations across asset classes typically sit between 0.2 and 0.7, so the diversification benefit is moderate. Negative correlations are rare and valuable (gold vs equities at times; cash vs equities).

Chart 3: The efficient frontier

Plotting EVERY possible combination of the available assets (varying weights across N assets) produces a CLOUD of portfolios. The upper edge of this cloud — for each risk level, the portfolio with the highest expected return — is the efficient frontier.

Every point BELOW the frontier is suboptimal — for the same risk, there's a higher-return portfolio on the frontier above it. Rational investors should only hold portfolios ON the frontier.

The minimum variance portfolio is the leftmost point of the frontier — the portfolio with the lowest possible risk regardless of return.

Chart 4: Adding a risk-free asset — the Capital Market Line

When you introduce a risk-free asset (e.g. T-bills), the picture changes dramatically. Combining the risk-free asset with any portfolio on the efficient frontier creates a STRAIGHT LINE in risk-return space (because the risk-free asset has σ = 0).

The tangent line from the risk-free rate to the efficient frontier dominates every other choice. The portfolio where this line touches the frontier is the market portfolio (M) — the optimal risky portfolio.

The CML equation:

Every investor's optimal portfolio is a combination of the risk-free asset and the market portfolio — varying only the WEIGHT between them based on personal risk tolerance. This is the two-fund separation theorem: portfolio choice reduces to choosing how much risk to take, not which risky assets to hold.

Chart 5: CAPM and the Security Market Line

The Capital Asset Pricing Model (CAPM) describes the expected return on an INDIVIDUAL asset based on its systematic risk (β):

Where β measures the asset's sensitivity to market moves. β = 1: asset moves with the market. β > 1: more volatile than market. β < 1: less volatile.

Plotting this gives the Security Market Line (SML) — a straight line in BETA-return space (not in σ-return like the CML):

Assets PLOTTING ABOVE the SML are undervalued (offering more return than their β justifies). Assets BELOW are overvalued. The SML is the "fair value" line for risky assets.

This is what active managers try to identify — assets that are mispriced relative to the SML.

Chart 6: Systematic vs unsystematic risk

Total risk decomposes into two parts:

• Systematic (market) risk: affects ALL assets. Cannot be diversified away. Compensated by the equity risk premium. Measured by β.
• Unsystematic (specific) risk: firm-specific. Diversifiable through holding many assets. NOT compensated in equilibrium (rational investors diversify it away, so the market doesn't pay a premium for bearing it).

Most of the diversification benefit is captured by the first 20-30 well-chosen assets. Beyond that, marginal benefits are small. Empirically, a portfolio of 30 stocks captures ~95% of the achievable diversification of the broader market.

The three performance ratios (which to use when)

All three reward excess returns; they differ in WHAT risk denominator they divide by. The choice depends on whether you're assessing standalone, portion-of-portfolio, or vs-benchmark performance.

The Efficient Market Hypothesis (EMH)

MPT relies on assets being priced based on available information. EMH formalises three forms of market efficiency:

Most empirical evidence supports weak-form efficiency and largely supports semi-strong. Strong-form is contradicted by data (insider trading does generate excess returns — that's why it's illegal).

Most-tested MPT exam traps

Related guides

• ICWIM Calculation Formulas Cheat Sheet — every formula tested
• Derivatives Payoffs in 8 Diagrams — Chapter 3 visual reference
• Bond Pricing Primer — fixed income deep dive
• ICWIM Chapter 5 Deep Dive: Macro Indicators — the other technical chapter

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