# Quant

-------------------- Personal Advisers, Inc., has determined four possible economic scenarios and has projected the portfolio returns for two portfolios for their client under each scenario. Personal’s economist has estimated the probability of each scenario as shown in the table below. Given this information, what is the covariance of the returns on Portfolio A and Portfolio B? Scenario Probability Return on Portfolio A Return on Portfolio B A 15% 18% 19% B 20% 17% 18% C 25% 11% 10% D 40% 7% 9% A) 0.001898. B) 0.890223. C) 0.002019

Is there a way to enter problems like this on the TI-BAII Plus? Thanks!

I wrote up something long that was not how to do it, be curious about the math. Eyeballing it, they look pretty close to 1 so B.

Did you calculate it this way? (scenario weight 1) * (Return A1 - Mean A) * (Return B1 - Mean B) + … the same for all the four scenarios Somehow I couldn’t get any of the 3 possible solutions that Damil mentioned. I recalculated it several times, but maybe I just made a simple error that I am not realizing…

Trust me, the answer is one of the options. Do you skip this type of question on the exam? Just too much calculations?

C

A

E[A] = .1165 E[B] = .1255 E[AB] = .0165 Cov = E[AB] - E[A]E[B] = .001899

can we not do this prob with the help of ta 11 plus calculator…please can someone guide on this ?

^ Will like to get an answer to that question as well. Correct Answer is A.

So why does mihau’s way not work? that is how I was taught it?

Sorry, it does work - yesterday I was just too tired and calculated the mean return as if the scenarios had an equal weighting (Return1+…+Return4 / 4). The correct way is to calculate the mean as Return1 x Prob(Scenario1)…+ Return2 x Prob(Scenario4). I appologise for the confusion!

A guess ! Is it not possible to calculate r and sd of portfolio A and Portfolio B using the stat (8) key in Texas BA II Plus …once we have r ,sd of A and B we know that COV a,b = r *sd A * sd B . However I am getting negative correlation ®

But how would you incorporate the scenario probabilities then?

^ Excellent Question!

I like this method… for easy grasp jic my memory does not serve right… wyantjs… do you know the intuition behind this? wyantjs Wrote: ------------------------------------------------------- > E = .1165 > E = .1255 > E = .0165 > Cov = E - EE = .001899

ov25 Wrote: ------------------------------------------------------- > I like this method… for easy grasp jic my memory > does not serve right… > > wyantjs… do you know the intuition behind this? > > > > wyantjs Wrote: > -------------------------------------------------- > ----- > > E = .1165 > > E = .1255 > > E = .0165 > > Cov = E - EE = .001899 It is just an alternate way to express covariance. If instead of using the sum(x - mean(x))… you recognize that, after some algebra, the relationship can be expressed as Cov(a,b) = (expected value of product) - (product of expected values). Hence, E[A] = probability weighted average. Same for B. Expected value of product is .15*.18*.19 + … +.40*.07*.09. Then, Cov(A,B) = E[A*B] - E[A]*E[B]. I am not sure that there is much intuition behind it, but rather it is a result of applying facts about the expectation operator and a little algebra.