Covariance calculation tricks, question, something, calculator

Jupiter

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

amqata

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

johnnyBuz

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)

jim8z3

@gartsy: i meant Portfolio Cov with joint probability table...I wish TA would include it on their calculator.... :|

disiz64

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...

rgonzalez

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!!!!!!

mnieman

sorry...reverse that hit 2nd data first.....then 2nd STAT

Beatnik

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!!

Matori

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.

kamara5

@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?