Efficient frontier playground
Mean-variance portfolio theory is one chart, and this is it, live. Set three assets' returns, risks and correlations, then watch the frontier, the minimum-variance portfolio, the tangency portfolio and the capital market line move as you drag.
Risk against return (σ horizontal, E[R] vertical)
tangency Sharpe 0.46Assets
Correlations and cash
The purple curve is the analytic frontier, which permits short positions; negative weights in the tables are shorts. The faint cloud is 700 random long-only portfolios, which is why it sits inside the curve. The dashed gold line is the capital market line: cash at the risk-free rate blended with the tangency portfolio beats every purely risky portfolio below it. Drag a correlation towards −0.9 and watch the frontier bulge left: that is diversification, priced.
What the exam wants from this picture
Every efficient portfolio is a trade-off between expected return and variance, and the frontier is the set of portfolios you cannot improve on in both at once. Without a risk-free asset the story ends at the curve. Add one and it collapses to a single straight line: every investor holds the same tangency portfolio of risky assets and adjusts risk by blending it with cash, which is the separation theorem, and the line itself is the capital market line with slope equal to the tangency Sharpe ratio. The classic exam manipulations, two-asset portfolio variance and the effect of correlation on diversification, are all visible here: pull a correlation negative and the frontier pushes towards the axis.
Make it stick. Portfolio theory shares CM2 with option pricing and stochastic models; the option payoff tool and Brownian motion simulator cover those. Memori is a flashcard app built by actuarial students, with a ready-made CM2 set in the shop. Join the beta.
For education only: illustrative parameters, single-period mean-variance world, and not investment advice.