The Slope
Take nine stocks. Change only the weights and you get thousands of different portfolios, each with its own return and risk. Plotted together they form a cloud, and the Sharpe ratio becomes geometry: a ray from the cash rate, steepened until it barely touches the cloud. The dot it touches is the best mix. Steer it yourself below.
What the
slope means
The Sharpe ratio is return per unit of risk: what a portfolio earns above cash, divided by the volatility you sat through to earn it. SHARPE = (return − cash) / volatility. On a risk-return chart that is literally a slope: cash sits on the left axis, a portfolio sits somewhere in the plane, and the line between them is the deal you are accepting.
Every dot below is a real candidate portfolio: the same nine US names, only the weights differ, five thousand times, simulated from three years of daily returns. The steepest ray that still touches the cloud points at the tangency portfolio, the mix with the highest Sharpe. That geometry is the heart of portfolio optimization: allocators are not hunting the highest return, they are hunting the steepest slope.
Five thousand portfolios
Hover the cloud to inspect a mix. Then flip the toggle: gold returned far less than the best names in this window, yet the best mix improves the moment it joins. Low correlation cancels noise; that is the whole trick of diversification.
Your mix
Drag the faders; weights are renormalized to 100% and your dot moves through the cloud live.
Sharpe is not
a constant
The same asset can look brilliant and broken within one year. This strip computes a 90-day rolling Sharpe over five years of daily closes, against today's bill rate. Type any ticker.
It assumes normal markets
Sharpe treats volatility as the whole story. Fat tails, crashes and illiquidity do not fit in one standard deviation; a strategy can carry a beautiful Sharpe straight into a drawdown it never priced.
It is backward-looking
Means and covariances drift. The tangency portfolio of the last three years is not a promise about the next three; that is why the cloud above names its window.
Annualization flatters
Daily Sharpe times the square root of 252 assumes independent days. Trending or mean-reverting returns break that; treat headline numbers above 2 with suspicion.
Under the
hood
SIMULATION: SEEDED, WEIGHTS DRAWN UNIFORMLY ON THE SIMPLEX. MARKET DATA: DAILY ADJUSTED CLOSES, REFRESHED WITH THE DATA BUILD. BILL RATE: FRED DTB3. RESEARCH NOTES, NOT INVESTMENT ADVICE.