# Treyor or Sharpe

Which one is the better measure for a diversified portfolio - I have got this question wrong twice and it still won’t stick…

Examine the denominator: Treynor = [Rp-Rf]/Beta Beta is a measure of systematic risk Sharpe = [Rp-Rf]/Standard Deviation Standard deviation is a measure of total risk Hm - this question does not seem familiar to me, but here’s my logic: A diversified portfolio eliminates the specific risk component, leaving on market risk. We want to assess risk-adjusted performance based beta then. My final answer = Treynor

That was my thinking too thanks

Conceptually agree, but shouldn’t a well diversified portfolio have very little if any unsystematic risk leaving only systematic risk which is measure by Beta. What I am trying to get at here, Beta and St. Dev. should be very very close. Am I out to lunch on this one?

Agree with passthismofo. My answer is neither…they would both yield the same results and ranking.

they don’t have to have the same results think of two portfolio that have same return and same systematic risk. then Rank A=Rank B considering Treynor. But in these diverisified portfolios ( lets say A= market porfolio + security A and B= market portfolio+ security B) we have some unsystematic risk. the ratio of return/unsystematic risk will determine the ranking in Sharpe mode but won’t change it in Treynor mode. Example. Return A=10% Return B=10% systematic risk A= systematic risk B unsystematic risk A> unsystematic risk B. in this case treynor would be equal but Sharpe would be different

I just did a practice exam question with this type of question. The question was “which portfolio is better diversified?” You had to calculate these types of ratios to get the answer. Portfolio A had a higher Jensen’s Alpha and Treynor ratio. Portfolio B had a higher Sharpe and M-squared ratio. The answer then read: Jensen’s alpha and the Treynor ratio account only for systematic risk as measured by beta. The Sharpe and M-squared measures account for total risk. Thus, since the rankings using alpha and Treynor versus Sharpe and M-squared are reversed, it must be the case that “A” has more unsystematic risk than “B” and that “B” is better diversified.

yeahh~ it is kind of confusing because a lower denominator (risk) will produce a higher risk-adjusted return (sharpe ratio or treynor) so a portfolio with a higher sharpe ratio, better total-risk-adjusted return means that it is better diversified