Treynor Ratio and Sharpe Ratio higher, return, achieved, positive, 2011

krause2

If portfolio A has a higher Sharpe Ratio but a lower Treynor ratio than portfolio B, then

1) Portfolio A has a higher systematic risk: true or false

2) Portfolio A is more diversified: true or false

3) Portfolio A has achieved a positive return for taking more risk: true or false



Edited 1 time(s). Last edit at Thursday, May 19, 2011 at 11:22PM by deriv108.

strikethree

1. false
2. false
3. true

Analti_Calte

False
True
True

mp3bu

treynor = rp-rf/beta
sharpe = rp-rf / stddev

A has higher sharpe
A has lower treynor

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

Colum

Albeit the assumption Rp and Rf are the same for both.

pennyless

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.

NO EXCUSES

Valores

1 true
2 true
3 false

jmh530

Great Question keep them coming:

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.

cityboy

Actual answers?

thommo77

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?)