I’m kinda getting confused between the three. From what I gather, Sharpe’s measures excess return on risky portfolios. Treynor’s measures excess return compared to riskless portfolios. And Jensen’s measures excess returns over CAPM and portfolio beta. Is this correct? If not can someone please simplify these three for me.
From what i gather…
Sharpe measures excess return over total risk (std dev of portfolio)
Treynor mesaures excess return over market (beta)
Jensens Alpha measures excess over CAPM expected return
Formula wise it should be rather straightforward:
Sharpe = (return - riskfree return) / (std. dev. of portfolio)
Treynor = (return - riskfree return) / beta
Jensen’s Alpha = (Return of security - riskfree return) - {beta * (return on market - riskfree return)}
Correct me if I am wrong but I believe you have this backwards. I was under the impression that systematic risk (beta) cannot be diversified away but non-systematic risk can be diversified away?
Remember: Treynor’s only appropriate for well-diversified portfolios.
Sharpe & M2 = Total Risk
Treynor & Jensens = Systematic Risk
“Correct me if I am wrong but I believe you have this backwards. I was under the impression that systematic risk (beta) cannot be diversified away but non-systematic risk can be diversified away?”
You are correct.
Beta is the porfolio’s COV(a,b)/market standard deviation
Doesn’t that mean B is non-systematic risk? If the market falls by 100, and you have a B of 1, your portfolio will fall by 100.
Fixed that for you.
opps!! Always there correcting me s2000, one of these days I will return the favor! 