Difference between Sharpe's ratio, Treynor's ratio and Jensen's alpha

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Ace_28

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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) <– this is a measure of total risk adjusted performance
Treynor = (return - riskfree return) / beta <– this is a measure of systematic risk-adjusted performance where the systematic risk is the market risk (non-systematic risk is event risk that can not be diversified away, e.g. the CEO stepping down or a law suit being filed)
Jensen’s Alpha = (Return of security - riskfree return) - {beta * (return on market - riskfree return)} <– notice that if CAPM is correct the first term on the right hand side equals the second term on the right hand side and Jensen’s Alpha = 0. A positive value for Jensen’s alpha implies the portfolio has value in excess of the expected return for a given risk level whereas negative alpha implies the opposite.
 
DJS05101985 wrote:
Treynor = (return - riskfree return) / beta <– this is a measure of systematic risk-adjusted performance where the systematic risk is the market risk (non-systematic risk is event risk that can not be diversified away, e.g. the CEO stepping down or a law suit being filed)
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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?
 
“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.
 
S2000magician wrote:
Galli wrote:Beta is the porfolio’s COV(a,b)/market standard deviation variance
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Fixed that for you.
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opps!! Always there correcting me s2000, one of these days I will return the favor! ;)
 
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