sharpe A > Sharpe B could happen bcos
=============================
1. (RpA > RpB and StdDevA <= StdDevB ) -- A is more diversified.
OR
2. (RpA=RpB) and StdDevA < StdDevB ) -- A is more diversified
OR
3. If RpA < RpB then StdDev A must be << StdDev B -- again A is more diversified.
treynor A < Treynor B
================
1. RpA > RpB and BetaA > BetaB (more systematic risk for A)
or
2. RpA = RpB and Beta A > Beta B (more systematic risk for A)
or
3. RpA < RpB then beta A >> beta B ...
so higher systematic risk for A.
more diversified
there is a particular scenario where A could achieve lower return than B.
(Not sure about the 3rd part of the question).
CP作者: Colum 时间: 2011-7-11 19:30
Albeit the assumption Rp and Rf are the same for both.作者: pennyless 时间: 2011-7-11 19:30
I made a new example, the old one seemed too sloppy:
RF Rate = 3
Portfolio A return = 25
Portfolio B return = 20
Portfolio A SD = 30
Portfolio B SD = 25
Portfolio A Sharpe = (25-3)/30 = .73
Portfolio B Sharpe = (20-3)/25 = .68
Portfolio A Beta = 1.7
Portfolio B Beta = 1.2
Portfolio A Treynor = (25-3)/1.7 = 12.94
Portfolio B Treynor = (20-3)/1.2 = 14.17
So, 1 is true (unless I'm assuming something in all these calcs that I shouldn't be). If I lower Portfolio A's beta to 1.2, the Treynor measure will actually be higher. The only way to force it down is to increase beta.
If my logic is way off please correct me 12:10am >6 hours of sleep every day in the past 10
1) Portfolio A has a higher systematic risk: true or false
True
2) Portfolio A is more diversified: true or false
True
3) Portfolio A has achieved a positive return for taking more risk: true or false
False
I'm thinking the positive return is being generated by increasing Beta, if the Sharp is lower then they must have a lower std dev, going back to L2 on Treynor Black,
Var a= Beta^2 X Var of Mkt + Var ea
Port A and B both produce returns of 15, RFR= 10 (15-10= 5)
Portfolio A Sharpe: 5/10 = .5
Portfolio B Sharpe: 5/15 = .33333
Portfolio A Treynor: 5/1.5 =3.3333
Portfolio B Treynor: 5/1 = 5
Edited 1 time(s). Last edit at Friday, May 20, 2011 at 12:28AM by cpepin.作者: cityboy 时间: 2011-7-11 19:30
Actual answers?作者: thommo77 时间: 2011-7-11 19:30
1. false (it may be so, we do not know if higher systematic risk)
2. true (always need one ratio with beta and one with stdev, cannot be judged using just one ratio)
3. false (this sentence is unclear, more risk than what?)作者: infinitybenzo 时间: 2011-7-11 19:30
V6, page 174
However, it is pos- sible for the Sharpe ratio and M2 to identify a manager as not skillful, although the ex post alpha and the Treynor measure come to the opposite conclusion. This outcome is most likely to occur in instances where the manager takes on a large amount of nonsystematic risk in the account relative to the account’s systematic risk.
this is B portfolio, high non-systematic, worse diversification, therefore 2. is True.作者: Unforseen 时间: 2011-7-11 19:30
true
true
cannot possibly be determined from the info given, thus false作者: zwjy 时间: 2011-7-11 19:30
1) True: Systematic risk = market risk ONLY which is the measure of Treynor.
2) True: High sharpe means that it therefore diversified away most of the non-systematic risk
3) False: Cannot confirm that with the data provided. They could both have negative sharpe ratios作者: Zestt 时间: 2011-7-11 19:30
to all who say 1. True:
beta of those portfolios can be same, only the return of B could be higher to have better Treynor....作者: IAmNeil 时间: 2011-7-11 19:30
pfcfaataf Wrote:
-------------------------------------------------------
> to all who say 1. True:
>
> beta of those portfolios can be same, only the
> return of B could be higher to have better
> Treynor....
Beta measures systematic risk. Therefore if A has a lower Treynor measure, it has higher systematic risk, holding all else constant.作者: justin88 时间: 2011-7-11 19:30
soddy1979 Wrote:
-------------------------------------------------------
> pfcfaataf Wrote:
> --------------------------------------------------
> -----
> > to all who say 1. True:
> >
> > beta of those portfolios can be same, only the
> > return of B could be higher to have better
> > Treynor....
>
>
> Beta measures systematic risk. Therefore if A has
> a lower Treynor measure, it has higher systematic
> risk, holding all else constant.
where does question say this "holding all else constant."?作者: Windjammer 时间: 2011-7-11 19:30
Thank you all. This question is more complicated than I thought -- I should have added a line that assumes the returns of the two portfolios are then same. In this case,
1) True
2) True
3) False or undefined.
This is similar to essay(morning) question 11, 2009.
I agree with pfcfaataf, the answers will be different if the two betas are the same. The problem is complicated because there are many variables which could affect the results: beta, total risk(sigma), and returns.
*** One conclusion from this discussion: Portfolio A is more diversified.
The question like this could show up in the exam, and probably is more specific. Great discussion, thanks.
