Tangency Portfolio (Capital Market Line)

Using the Capital Asset Pricing Model (CAPM) created by William Sharpe, Jack Treynor, John Lintner and Jan Mossin in the 1960’s, a “Tangency Portfolio”, is any portfolio that exists on “Capital market line”. When plotted on a chart, the capital market line is populated by statistically optimal portfolios that provide the best risk-adjusted performance for a given level of risk/return.

Portfolios are evaluated based on the relationship between two parameters:

1) Expected return (mean return during observation period)
2) Risk (standard deviation)

This relationship was codified in William Sharpe’s no universally known “Sharpe Ratio”.

p−f
  σ

p = expected return of investment or portfolio
f = risk free rate
σ = standard deviation of investment or portfolio

Using a mean variance optimisation (MVO) model that computes all possible iterations for allocating a fixed amount of capital across a fixed number of assets, a conclusive list of “efficient” portfolios will be produced. Each of these portfolios will produce the highest possible return for the lowest possible risk at each level. These portfolios, plotted on a chart will form what is referred to as the  “efficient frontier”, and any portfolio on that line is referred to as a “Tangency Portfolio”. Logically, an investor would never choose a portfolio above or below the line as by implication they could have made more money with less risk by choosing a tangency portfolio instead.

Mrs. Client’s investment manager makes investment decisions for her benefit, based on her investment policy statement (IPS). He understands that she is more concerned with capital protection than capital growth, and generally takes a conservative approach with her investments. Based on the risk constraints placed upon him, the investment manager is able to determine a statistically optimal asset mix for her retirement portfolio that lives on the most North Easterly point of the efficient frontier.