I’m working on one of the questions in the mock exam from last year and I realized that there’s no way I can solve the covariance in the exam. The calculation is really easy but it’s so time consuming. Does anyone know of any tricks to calculate it? There must something i’m missing here. Is it doable on the calculator? This goes for variance, std dev and covariance - All time-consuming calculations. According to the CFA website, we’re supposed to answer each question about 90 seconds but these questions are taking me 4-5 minutes to calculate and to make sure I have the numbers right. Thanks
I agree with you on this. A couple of questions requiring such calculations are way too time consuming. You can calculated the std dev if Probability & Returns on 1 Portfolio are given on TA B Plus (the method is there in one of the recent threads) but i doubt if there is any way for co-variance.
Here is the golden trick. For 15% , use 15 instead of 0.15 and so on. Divide the final answer by 100. With this you can solve the question under 90 sec. Cheers
Never thought of that! Brilliant! Thank you and best of luck this weekend.
you can solve covariance on the calculator by inputting X and Y values. and then solving for sigmax, sigma y, and roe (remember to take sample sigmas if they give you a sample) cov = roe * (sigmax * sigmay)
@gartsy: i meant Portfolio Cov with joint probability table…I wish TA would include it on their calculator… 
to calc covariance and std deviation 2nd stat enter each x and y value (if doing st dev just enter x values) hit enter and arrow down after each value. for 15% put in .15 after putting all data points in 2nd data make sure its in LIN mode arrow down till u get to Sx…Sx equals std deviation of all X inputs (if you are solving for only standard deviation u are done…but wait its gets better…Sx is sample std deviation…if you need population std dev hit arrow down one more and it looks like the std dev sign and x. that is population std dev.) to calc covariance when u see Sx hit STO 1 hit down arrow keys until u see Sy- which is std dev of Y values…hit STO 2 hit down arrow keys until u see R- which is correlation coeffcient…hit STO 3 hit CE/C bottom left hit RCL 1 X RCL 2 X RCL 3 = practice with a problem u know…and u will see after practice u can calc this on the BA II + in 30 sec tops HOLLLLAAAAAAAAAAA…EFF DOING CALCS by hand!!!
sorry…reverse that hit 2nd data first…then 2nd STAT
or those who have Schweser Notes - Turn to page 204. This is the example I am using here. PROB 10% EPS 1.80 20% EPS 1.60 40% EPS 1.20 30% EPS 1.00 Now start inputting the data. To do this press 2nd (data)< --is number 7 Then 2nd Clear Work to be safe -clear out data With me so far: Now were ready - -This is sooo easy!! X01: 1.80 Press Enter Y01: 10% (put it in % not decimal for all of them) Press Enter X02: 1.60 Enter Y02: 20% Enter…and so forth press enter for all of them X03: 1.20 Y03: 40% X04: 1.00 Y04: 30% Now first step to do is change the stat to 1V ( I think its in “LIN” by default), which is 1 Variable ----> Button 2nd (stat) (stat is number 8) then 2nd (set) (which is the enter button) Keep pressing 2nd set until you see 1-V…Once you see 1-V, start pressing the arrows (up and down) to get the results. In this case, press arrow down. Pressing down twice will give you the (E)r, which on the calculator is XBAR : Nice $1.28 !!! 4th arrow down is the population std deviation (SIGMA x ) on the calculator : .27129 (Pg 205 Schweser) Square that and you get your VARIANCE!!! I’m not sure how to do the Prob Method for 2 Variables but I do know how to do it using the historical data method (Used in Portfolio Mgmt) Same Concept but now you have to change the 1-V to LIN Enter Data for Stock A as X and Stock B for Y 2nd Stat —> LIN start pressing the arrows It calculates the population and sample mean for , sample std deviation (Sx), Population Std Dev (Sigma x) for stock A&B and the correlation coefficient (which is “r”) on the calculator. For historical data, remember its n-1, so use the sample std deviations for A&B Square the std deviations and you get the Variances and obviously if you have both Std Deviations and the Correlation Coefficient, Guess what? You can get easily get the Covariance…I’ll leave that for you to figure out!! 
Now if someone can figure out a way to get this information for 2 Variables using Probabilities, PLEASE POST IT ASAP!! Thanks and good luck EVERYONE!! Options: Reply To This Message•Quote This Message•Report This Message Re: Variance, Std. Deviation, Weighted Means, E® Posted by: njlevel10610 (IP Logged) [hide posts from this user] Date: May 3, 2010 08:08PM Try using historical data in Portfolio Mgmt Pg 117-118 -Schweser. Enter the returns for both stocks in decimal, in other words, they way they have it listed. Remember switch 2nd stat to LIN for 2 variables You will get the Std Deviations (Calculator Sx for Stock A and Sy for Stock B), and r is the correlation coefficient. Covariance you have to calculate. IT WORKS!! 2nd Data 2nd Clr Work 2004 : X01:+.10 enter Y01: +.20 enter and so forth…once your done entering data 2nd stat 2nd set until you see LIN and press arrow done until you see the info you need! Please post instructions for 2 variable probabilities if anyone can figure it out. Also, does anyone know if this equates to Portfolio std dev and Portfolio Variance? Or do we need to still put in the data in that nasty formula and square it? from a couple days ago…
@KillaBeez – Just a heads up sX and sY are SAMPLE standard deviations, the next one down from sX is σX thats population std deviation for X, and after sY is σY std deviation for Y. I know on the mock exam afternoon Q 119 I did it in 30 sec or less, but it implicitly states SAMPLE variance so i squared sX instead of σX as I normally would. Whats the correct move if your not told sample or population?
old thread: It calculates the population and sample mean for , sample std deviation (Sx), Population Std Dev (Sigma x) for stock A&B and the correlation coefficient (which is “r”) on the calculator. For historical data, remember its n-1, so use the sample std deviations for A&B
If you get a “compute the covariance” or “compute the standard deviation” question where you just have a data set and you have to do all the different calculations, I would honestly suggest skipping the question and coming back to it later. The time saved will likely be better spent elsewhere, even if it means guessing on that one. And I suggest doing that even if you know how to do it. The only exception is if there is some trick you can see to solve the question quickly, or there are only a *very* few data points.
well using 2nd data, and 2nd stat I can calculate std dev of A, std dev ov B, and correlation coefficient within 30 seconds. Given all that, you can compute covariance in another 20 sec with corr = covAB / sigA * sigB
That might work. Just make sure you know whether your calculator gives you sample or population covariance and SD, and that it matches whatever the problem asks for.
I think there’s no built in function for 2 variable probabilities.
ur right theres not, only for 2 variable historical data. But thats good enough. BA II + Can do: 1 variable with prob (std dev of pop, std dev of sample, mean & of course variances) 1 variable historical (std dev of pop, std dev of sample, mean & of course variances) 2 variable historical (std dev(s) of pop, std dev(s) of sample, mean(s), variance(s) and CORR, and thus covarience can be computed in 10 sec)
I don’t think the calcs are too bad. the STO and RCL functions are real time savers.
The calculations aren’t too bad – but there is ALOT of potential for keystroke errors. I will use the DATA and STAT function every single time I see a question like this and laugh knowing I will never make a mistake, and that it will take me about 25 seconds to compute.