RAPMs: Treynor, Jensen's, Sharpe (FRM T1-10)
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- Опубликовано: 30 июл 2024
- Risk-adjusted performance measures (RAPMs) include Treynor and Jensen's, both of which are functions of the CAPM/SML, and the Sharpe ratio, which can be understood in the context of the CML. [Here is my the spreadsheet I used for this video, please let me know if you have any questions trtl.bz/rapm-treynor-jensen-sh...]
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The key intention here is to give context to these measures; e.g., how can we interpret a 0.060 Treynor; Is a 0.33 Sharpe strong or weak? The Tryenor's benchmark is the equity risk premium, so something like 6.0% is more is good. The Sharpe's benchmark is an efficient portfolio (ie, slope of the CML) where something like an excess return of 6.0% or more is good, and a volatility of 20.0% or less is good, such that a Sharpe of more than 6%/20% = 0.30 is good. Let us know if you have any questions!
Bionic Turtle You say Treynor is more suited to a well diversified portfolio. I've heard that before, but don't understand where that comes from. Do you cover that in another video?
Hi Francois, Right! I didn't elaborate on why Treynor is suited for diversified portfolios. This notion follows from Treynor's reliance on the CAPM in the first place and its implication that well-diversified portfolio should effectively eliminate non-systematic (aka, idiosyncratic risk). If the portfolio is diversified, then the non-beta risks don't matter because they should "cancel out" in the portfolio. To put maybe another way, to include other risks in the denominator would overstate actual risks in the diversified portfolio where such additional risks are supposedly, effectively eliminated. For this same reason, if the portfolio is not well diversified, then the Treynor is arguably NOT justified. I hope that explains, thanks!
Bionic Turtle Great, thanks. Makes sense now.
One more question about this, please. Some sources also claim that Sharpe is more appropriate when the portfolio represents the total wealth of the investor. I'm struggling to grasp this. Is this also related to systematic vs idiosyncratic risk? e.g. here is a paragraph that I found online:
"When the portfolio is not well diversified or when it represents the total wealth of the investor, the appropriate measure of risk is the standard deviation of returns of the portfolio, and hence the Sharpe ratio is the most suitable. "
Yes, that's also in my source (Noel Amenc) where he writes, "It is also for that reason [i.e., the Treynor only takes the systematic risk of the portfolio into account] that the Treynor ratio is the most appropriate indicator for evaluating the performance of a portfolio that only constitutes a part of the investor’s assets. Since the investor has diversified his investments, the systematic risk of his portfolio is all that matters." ... He seems to argue that if the portfolio is only a fraction of wealth, the non-systematic risk will be diversified away in the rest of the (un-measured) portfolio, so the Treynor is sufficient. And, further, if the portfolio is the investor's total investment (or total wealth) then presumably the investor is not well diversified and Sharpe is required. It seems to me the presumption here is: if it's a fraction of wealth, the investor is diversified (use Treynor), but if it is the entire wealth, the investor is presumably not diversified. That's the best I can make of this follow-on argument, but I admit that it's not quite logical to me (or I may not understand the exact arguments, sorry). Thanks!
Nice video.You are an intelligent person.You Teaches very Easily
Thanks. I'm writing exams on this next week, so your timing is perfect.
You're welcome! We are happy to hear that our video was helpful! :)
Brilliant. Lectures of this quality should not be free 😂. Thank you!!
Hello, thanks for the great videos. I have 3 questions about calculating Jensen's alpha. 1. The period considered on the returns and market returns has to be the same as it was for the beta calculation? 2. The calculation of the market return is log(newest_market_return / oldest_market_return), correct? 3. What risk-free rate should I consider, the rate at the newest return date, the oldest return date or do the same calculation as the return, like rf = log(newest_rf / oldest_rf) and if so, what value should I consider if the oldest_rf is 0? Thanks.
Capm... It is ex ante measure... If portfilio return is only a function of only sys risk commonmkt factor and idiosyncratic risk is zero then capm% is 7%....shown on sml anchored at rf.... Slope of sml is rm - rf/ beta m= treynor ratio
Better if more steep in line
Sml cuts x axis at rf... And rises up... On sml is rm marked 8% and at that pt is slope made rise over run.. Rise is numr... Run is denominator
Treynor ratio is used for well Diversified portfolio
Jensen alpha is a type of alpga... It I simpler single factor alpha... It is the outperformance of the portfolio
It is vertical distance from the sml
3% = 3% outperformance.. Till 9.30