18th letter to friends of Brunei [Portfolio Management (Part 4)]

Another commonly used risk-adjusted portfolio return measurement is the Treynor Ratio.

Treynor ratio calculates the excess returns per unit of systematic risk.

(whilst Sharpe ratio calculates the excess returns per unit of total portfolio risk; i.e. unsystematic AND systematic risk of a portfolio)

Consider a portfolio A,

Treynor A = [Rp - R f] / β p

Rp = Portfolio return
Rf = Risk free asset return
βp = Portfolio beta, which represents the systematic risk.

Let's do an example:

Portfolio A: [Return 12%] ; [Beta 1.2]
Portfolio B: [Return 14%] ; [Beta 1.1]
Portfolio C: [Return 16%] ; [Beta 1.4]

Assuming T-bill rate is 7%.

Calculate and rank the portfolios using Treynor ratio.

Treynor A = R A - R T-bill / Beta A = 12% - 7% / 1.2 = 4.17


Treynor B = 14% - 7% / 1.1 = 6.36


Treynor C = 16% - 7% / 1.4 = 6.43


Ranking = Portfolio C (rank = 1) , Portfolio B (rank = 2), Portfolio A (rank = 3)

i.e. Portfolio C produces the most return per unit of systematic risk.