# Sharpe Ratio & Treynor Measure

Portfolio return = 42%, Standard deviation = 1.2%, Beta = 1.8, Risk-free rate = 6% Sharpe Ratio = (0.42-0.06) / 1.2 = 0.3 or (42%-6%) / 1.2% = 30 ? Treynor Measure = (0.42-0.06) / 1.8 = 0.2 or (42-6) / 1.8 = 2 ?

Sharpe ratio should be 0.42-0.06/ 0.012 or 42-6/1.2 = 30 Treynor measure should be 0.42.0.06/1.8 = 0.2

sharpe ratio = 42-6 / 1.2 = 30 treynor = 42-6 / 1.8 = 2

Then the Sharpe Ratios in the solution to 2009 Schweser Practice Exam V2 Exam 1 Q11A are wrong ! Funny !

not surprised, those exams are filled with errata… pretty useless

still not sure … which is the right combination of calculations? till now i was pretty sure i knew this material … not any more …

Isn’t that in Volume 1 exam 1? (I just finished taking it about 4 minutes ago, but haven’t graded.)

AMC Wrote: ------------------------------------------------------- > Portfolio return = 42%, Standard deviation = 1.2%, > Beta = 1.8, Risk-free rate = 6% > > Sharpe Ratio = (0.42-0.06) / 1.2 = 0.3 or > (42%-6%) / 1.2% = 30 ? > Treynor Measure = (0.42-0.06) / 1.8 = 0.2 or > (42-6) / 1.8 = 2 ? AMC, I think the Schweser answer is correct. Not ehte Standard deviation is 1.2 instead of 1.2% in the original question. You changed the Standard deviation to 1.2% when posting to this forum. so the correct answer is Sharpe ratio =0.3, Treynor measure =0.2

AMC Wrote: ------------------------------------------------------- > Portfolio return = 42%, Standard deviation = 1.2%, > Beta = 1.8, Risk-free rate = 6% > > Sharpe Ratio = (0.42-0.06) / 1.2 = 0.3 or > (42%-6%) / 1.2% = 30 ? > Treynor Measure = (0.42-0.06) / 1.8 = 0.2 or > (42-6) / 1.8 = 2 ? AMC, I think the Schweser answer is correct. Note in the original question, the Standard deviation is 1.2 instead of 1.2%. You changed the Standard deviation to 1.2% when posting to this forum. so the correct answer is Sharpe ratio =0.3, Treynor measure =0.2

happyking02, If the Standard deviation is 1.2 (w/o unit indicated), does it mean the Standard deviation is 120% ? It seems 120% is beyond my imagination. On the other hand, if it means 1.2% , then it is so small ! The point shall be that no unit is indicated.

AMC Wrote: ------------------------------------------------------- > happyking02, > > If the Standard deviation is 1.2 (w/o unit > indicated), does it mean the Standard deviation is > 120% ? It seems 120% is beyond my imagination. On > the other hand, if it means 1.2% , then it is so > small ! > > The point shall be that no unit is indicated. Not knowing the nature of the investment, I agree that SD=1.2 seems high. But mathmatically, Schweser is correct.

happyking02, Usually the unit of standard deviation is %, right ? That’s why I took it as 1.2%.

Standard deviation is NOT a percentage. It is derived by taking the square root of the variance, and has no units. I’m not a mathematician, and could be wrong on that, but I don’t think I am.

just curious, if SD is in fact quoted in %, wouldn’t the result be same if (1) divide a % over by a % or (2) %changed to decimals divided by a %changed to decimals…

My impression is that all standard deviations are indicated in the unit of %, at least for the measurement of risk (volatility) of investments. If no unit is indicated, then the unit is %. If anyone find that standard deviation not in the unit of % when measuring risk (volatility), please kindly advise.

if the original stuff for which you were measuring was in % - then the std deviation would be in % and variance in % squared. if stuff was being measured in Dollars - then std dev will be in Dollars, variance in Dollars^2.

I think what is confusing everyone is that standard deviation measures the variance in a distribution, and has no unit attached to it in and of itself. Rather, Standard Deviation assumes the units of the sample it is measuring. If you are measuring returns than standard deviation is a percentage, as is the case here. If you were measuring the beta of stocks in the S&P 500, the units of standard deviation would not be a percentage. If the sample measures the miles driven daily by NYC taxicabs than standard deviation would be in miles. The confidence interval IS always a percentage with +/- 1 standard deviation = 68%, and 95% probability falling within +/- 2 standard deviations, in a normal distribution. But it is incorrect to state that “Standard Deviation is always a %.”

I was just doing a CFA exam where they had sharpe and treynor calculations. In this case, sharpe will be 30 and Treynor will be 20. Use the same units ! Sharpe = (42-6)/1.2 =30. Looks high or unrealistic, but thats what it is. (42% return with 1.2% SD, I’ll have this in my portfolio anyday) Treynor = (42-6)/1.8 = 20. Seems unrealistic here again, but that’s what it is. Follow schewser as your own risk sparty419, Which CFA exam where they had sharpe and treynor calculations ?

One of the older ones…2000 or 2001…i’ll check and get back…