What is Treynor measure & Jensen's alpha？

Treynor measure is a ratio that measures the excess return earned by a portfolio over the risk-free rate, relative to the portfolio's systematic risk or beta. It is calculated as follows:

Treynor measure = (portfolio return - risk-free rate) / beta

Jensen's alpha, on the other hand, is a measure of the excess return of a portfolio over its expected return, given its level of systematic risk or beta. It is calculated as follows:

Jensen's alpha = portfolio return - (risk-free rate + beta * (market return - risk-free rate))

Both Treynor measure and Jensen's alpha are used to evaluate the performance of investment portfolios and managers.