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Year 2 · Core Finance · Portfolio & Risk

Portfolio Theory & CAPM

Build the quantitative foundations of portfolio construction: expected return, variance, covariance, correlation, diversification, the efficient frontier, Sharpe ratio, systematic risk, beta, CAPM and the Security Market Line.

Estimated time120–145 min
Saved progressGuest
Completion rule70% quiz
LEARNING OBJECTIVES

What you should be able to explain after this lesson

01

Calculate portfolio expected return from asset weights and expected returns.

02

Distinguish variance, volatility, covariance and correlation.

03

Calculate two-asset portfolio variance and explain mathematically why diversification works.

04

Interpret the efficient frontier, minimum-variance portfolio and tangency portfolio.

05

Use the Sharpe ratio to compare excess return per unit of total volatility.

06

Explain systematic versus idiosyncratic risk, beta, CAPM and the Security Market Line.

CONCEPT MAPFrom one asset to a market-pricing model
01MeasureReturn · variance · volatility
02CombineCovariance · correlation · diversification
03OptimizeEfficient frontier · Sharpe
04Price riskBeta · CAPM · SML
01 · EXPECTED RETURN

Portfolio expected return is the weighted average of asset expected returns

CORE FACTS · SAME IN EVERY MODE

Expected return is a probability-weighted or model-based estimate of future return, not a guaranteed outcome.

Portfolio expected return is linear in portfolio weights.

Portfolio weights sum to one for a fully invested unlevered long-only portfolio, though leverage or shorting can change this convention.

Expected return alone is insufficient for portfolio choice because it ignores uncertainty and co-movement.

BeginnerTeaching style changes, knowledge does not.

Suppose 60% of a portfolio is in Asset A with expected return 8% and 40% is in Asset B with expected return 12%. Expected portfolio return is 0.60×8% + 0.40×12% = 9.6%.

FORMULAPortfolio expected return
E[Rₚ] = Σ wᵢ × E[Rᵢ]

wᵢ is the portfolio weight and E[Rᵢ] the expected return of asset i.

Worked example

60%×8% + 40%×12% = 9.6%.

PROFESSIONAL VOCABULARY
Portfolio weight / poids de portefeuille / portfolio weight

Fraction of portfolio capital allocated to an asset or exposure.

Expected return / rendement attendu / expected return

Model-based expectation of future investment return.