### CFA Practice Question

A portfolio earned the following rates of return over a period of twelve months.

What is the portfolio's Sharpe ratio?
A. 0.28
B. 0.15
C. 0.13
Explanation: Calculate the average portfolio return and risk-free return:

Average portfolio return = 0.24%
Average risk-free return = 0.13%

Calculate the standard deviation of the portfolio return = 0.85% (add the sum of squared deviations from the average return and divide by 11 [i.e., 12 - 1]).

Sharpe ratio = [0.24 - 0.13]/0.85 = 0.13. It does not have any units.

User Comment
mtcfa Since this is the actual data and not a sample, shouldn't the denominator for standard deviation be n and not n-1?
nike it is sample data. The population is all returns of this portfolio.
DAS11 Is there a shortcut for this problem? Possibly using the calculator?
cpt28 poooh, although not difficult, it takes me ages... (even in excel ;-)
anricus Yes there is a shortcut on the calculator for calculating mean and variance for population and sample. This is the Data and Stat keys on the BAII Plus.
anricus I would agree with mtcfa that this is a population since we are not told that it is a sample and it is not evident that there any more returns available for any other months! What if the portfolio was only in existance for 12 months then this is the population.
stevenzliu to calculate the average (mean?) return of the portfolio, we shall use arithmetic mean or geometric mean? advice is wellcome.
osebeyo anricus could u pls help me with the steps to follow if one is to use BA 11 CALCULATOR for this question
mullrich I don't see how you could possibly solve this in 1.5 minutes, even if you're able to figure out what needs to be done right away. Would probably take 3-5 minutes to run the numbers.
anricus Within the BA11 Calculator

2nd then Data

Then 2nd and Clear to clear the memory

X1 is 1.25
Y1 is the number of times this occurs which is once, therefore 1
X2 is the second observation and this occurs once therefore Y1 is also 1
X1

Complete this for the 12 months and then press 2nd followed by Stat. 1-V should appear, then use the downkey arrows to scroll through n, x bar, sample standard deviation (Sx), population standard deviation etc. Hope this helps.
julamo Totally agree with mullrich, 1.5 minutes for this question is ridiculous. Unless you have a trick with your calculator I think it's a waste of time
hanny I did that calculation of (.24-.13)/.85 and it gives me .14===.1412 which is not closer to .13..if this is real exam i would have picked the wrong answer or thought that all I did was just rubbish
dipuo with the hp?
dimanyc (0.24-0.13)/0.85 =0.1294. Something is wrong with your calculator.

To calculate mean and st dev fast using HP, enter all returns using the Sum+ (Epsilon +) button. Then go "g" -> "0" for mean. Go "g" -> "." for st dev.

My question is, i don't divide by 11 (i believe in HP you do that by adding mean as another unit) and still get 0.85 standard deviation as this was a population, not mean. Why is that?
thekapila its a waste of time question...i hope not getting long calculations in exam..
cahiz84 I didnt answered this quesitons, too time wasting.
umair read anricus post above, gives a great shortcut to use on calc
rgat i just solved this prob with my HP and it took ~1 min. read dimanyc's HP stdev trick above
Mavizo Thank you anricus!!!
vadklim Anricus, I beleive Y1, Y2 and so on are the second variables for 2 variables statistics ...
Kuki Anricus - your note saves me 5 minutes! Thanks buddy
AkashKB For HP
1. Input First Value e.g. 1.25
2. Press Enter
3. Input 2nd Value e.g 0.13
4. Press Epsilon +
5. Repeat for the remainder of the values
6. Press g s

If you wanted the mean
Repeat 1 to 5
g x-bar - mean for the first values
x >< y - mean for the 2nd values

Note, you can find the Standard Deviation by using the first section above( i.e. you do not need to calculate the mean, HP calculator will do it for you)
grezavi Anricus- Thanks for the TI Steps !
deeb Anricus, you are amazing thank you so very much. This has been one of the biggest 'light bulbs' since I started preparing.
BigDogof1983 dimanyc, thank you! this makes calculating averages and standard deviations so much easier now.

this problem can be solved in 1 minute if you use the HP shortcuts.
morek hp12c, sample stDev is "g""." for population, use "g"" 0 "" Epsilon "" G ""."

EL122784 my hp 12 c displays the mean and the standard deviation in the reverse order.. why is that..
SuperKnight took me like 5 minutes to enter all this stuff into the calculator, hope we don't get any like this!
Sunderi thanks.. anricus... does help a lot :)
AUAU not worth to waste time !!!!
just guess it & save time to answer the remaining Qs.
just keep the bsaic concepts.

Remember never loss 20 marks & just get 2 marks.
mattg dimanyc I love you!
mekc oooohhhh...that is so cool! thanx anricus
mpapwa22 Amen to Anricus....WAY TO GO MAN, Thanks
boddunah how in the haven we can do this in 1.5 min. it takes more than 2.5 to find out averages and standard deviation even with using epsilon short cut in hp
pstebelp Wow, anricus, thanks!
Mutsa anricus, you the dude man
kutch ancirus - thumbs up
frants54 dimanyc - when calculating standard deviation on hp, this will return the result for the sample (ie. use n-1). If you want the population standard deviation you have to add another observation (zero value)
harpalani ancirus,thx a ton dude!!
chandsingh Hi - for BAII if we want the population ST dev what extra step should we take? tnx
ColonelCFA wow even with the data and stat functions of BA II i can't get my time less than 3 min... total time waister this question is
Oksanata where on earth would they use n-1 for standard deviation of portfolio returns even it's a sample? someone could pls refer to textbook chapter for that formula?
moneyguy Thanks, ancirus!!
stevo takes too long arrh
CalebMast Yeah, it's doable in the 1.5 minutes allotted per question (180 minutes for 120 questions), but it may be something worth saving - slightly my test approach is to complete easy ones first and mark tougher ones (more computational steps or complicated verbal scenario) until end. Though doable, I foresee this one as easiest. Recalling Sharpe Ratio will be biggest factor - being able to reverse engineer and type into calculator efficiently will be big, as well.
ewaniek Arnicus, super helpful calcuating on the BAII calcualtor but wouldnt that mean that the standard deviation is based off of a sample of 12 and not 11?
sinmani need to check
jeeychung How did you get 0.85???