The Return and Risk of a Financial PortfolioLocked: included in All Access

The return and risk of a portfolio: expected return, variance and covariance of a portfolio, the benefit of diversification, the minimum-variance portfolio and efficient frontier, and choosing an optimal portfolio with the CAL and CML.

1. 1. Portfolio expected return and varianceA portfolio's expected return is a plain weighted average of its holdings, but its risk is not, because risk also depends on how the holdings move together.Video · 6 minLocked: included in All Access13 min
2. 2. Portfolio returns over time: drift and rebalancingOver several periods a portfolio's return depends on how its weights evolve: left alone, winners grow into bigger weights (portfolio drift), so the realised return differs from the fixed-weight one.Locked: included in All Access13 min
3. 3. The covariance matrix and many-asset portfoliosWith more than two assets, portfolio variance is the weighted sum of every entry in the covariance matrix, and the covariance entries quickly outnumber the variances.Locked: included in All Access13 min
4. 4. Correlation and diversificationLower covariance between holdings lowers portfolio risk without lowering expected return; that free risk reduction is the diversification benefit.Locked: included in All Access12 min
5. 5. Scenario-based portfolio risk and the many-asset limitPortfolio risk can be forecast directly from economic scenarios, and in a large portfolio it shrinks toward the average covariance, the part diversification cannot remove.Locked: included in All Access13 min
6. 6. Minimum-variance and efficient frontiersOf all the portfolios risky assets can form, only those on the upper half of the minimum-variance frontier, the efficient frontier, are worth holding.Video · 7 minLocked: included in All Access12 min
7. 7. Finding the minimum-variance portfolio and optimising weightsPortfolio optimisation picks weights that minimise variance for a target return (or maximise return or the Sharpe ratio); for two assets the minimum-variance weights have a closed-form answer.Locked: included in All Access14 min
8. 8. Risk aversion and utilityA utility function turns each investor's attitude to risk into one number per investment, so investments can be ranked: $U = E(r) - \tfrac{1}{2}A\sigma^2$.Video · 7 minLocked: included in All Access13 min
9. 9. Indifference curves and the capital allocation lineIndifference curves show what an investor wants, the capital allocation line shows what is available, and the optimal portfolio is where the two just touch.Video · 7 minLocked: included in All Access14 min
10. 10. Theory assumptions, risk-aversion measures and the Sharpe ratio of the CALPortfolio theory rests on a few simplifying assumptions; within it, the slope of the capital allocation line is the Sharpe ratio, the same for every mix on the line, and a steeper line is always better.Locked: included in All Access12 min
11. 11. Optimal risky portfolio and the optimal investor portfolioAdding a risk-free asset turns portfolio choice into two steps: everyone picks the same optimal risky portfolio, then each investor chooses how much to lend or borrow.Video · 7 minLocked: included in All Access14 min
12. 12. The risk-free asset, the market portfolio and the CMLMixing a risk-free asset with the best risky portfolio gives a straight line of choices; when everyone agrees on expectations, that portfolio is the market and the line is the capital market line.Video · 7 minLocked: included in All Access14 min
13. 13. Beta, the security market line and the CAPMIn equilibrium only systematic risk is rewarded: an asset's expected return is the risk-free rate plus its beta times the market risk premium, $E(r_i) = r_f + \beta_i[E(r_m) - r_f]$.Locked: included in All Access15 min