 # Quant

Given the following probability distribution, find the covariance of the expected returns for stocks A and B. Event P(Ri) RA RB Recession P(Ri) 0.10 RA-5% RB 4 Below Average P(Ri)0.30 RA-2% RB8 Normal P(Ri)0.50 RA10% RB10 Boom P(Ri)0.10 RA31% RB12 A) 0.00109. B) 0.00174. C) 0.00032. D) 0.00213. "can any body slove this one with a shortcut on the BAII " !!!

i have no idea how to parse that data

alright, i finally figured it out no, there is no shortcut on the BA-II to solve this problem you need to do it manually BA-II can only solve for covariances where all the results have equal probability of occurring

Not that I am aware of. Now, if you were given the returns, without the probabilities, you could plug it into the STAT/DATA function and obtain the sigmaX, sigmaY, and CORR, and solve for covariance.

its a lengthy process, I’ think its the product of each deviation multiplied by the respective probability first compute the E(a) and E(b) then do Sum (P(i) E(observeda - E(a))(observed b - E(b))) man if this comes on exam… itll tkae me atleast 4 mins to do this.

Is it B, .00174? I calculated .00164 really fast…

I get .00166 The calculation is E[(A - Abar)(B - Bbar)] which simplifies to E[AB] - E[A]E[B] E[AB]=(.1*.05*.04)+(.3*.02*.08)+(.5*.1*.1)+(.1*.31*.12)= .0094 E[A] = .092 E[B] = .09 So, .0094 - (.092*.09) = .00166

wyantjs Wrote: ------------------------------------------------------- > I get .00166 > > The calculation is E[(A - Abar)(B - Bbar)] which > simplifies to E - EE > E=(.1*.05*.04)+(.3*.02*.08)+(.5*.1*.1)+(.1*.31*.12 > )= .0094 > E = .092 E = .09 > So, .0094 - (.092*.09) = .00166 Are you supposed to ignore the (-) in the returns???

Ok. I tried, might help. Using DATA and STAT. 2ND DATA Step 1: input probabilitites into X, input Ra into Y Step 2: 2ND STAT arrow up, you get the expected Ra, note it down Step 3: 2ND DATA input Rb into Y, don’t change X Step 4: 2ND STAT arrow up, you get the expected Rb, note it down Step 5: 2ND DATA don’t change X (probability), input (Ra-E(Ra))*(Rb-(E(Rb)) into Y, is not as difficult as it seems Step 5: 2ND STAT arrow up, there you have it. Now, accounting for appropriate %, must be B.

The easiest way is to find the returns per stock: A =(-.05 x .1) + (-.02 x .3) + (.1 x .5) + (.31 x .1) = .07 B =(.04 x .1) + (.08 x .3) + (.1 x .5) + (.12 x .1) = .09 (.1 x .05 x .04)+(.3 x .02 x .08)+(.5 x .1 x .1)+(.1 x .31 x .12)= .0094 .0094 - (.07 x .09) = .00174

thanks guys, it is very clear right now,

soxboys21 Wrote: ------------------------------------------------------- > wyantjs Wrote: > -------------------------------------------------- > ----- > > I get .00166 > > > > The calculation is E[(A - Abar)(B - Bbar)] > which > > simplifies to E - EE > > > E=(.1*.05*.04)+(.3*.02*.08)+(.5*.1*.1)+(.1*.31*.12 > > > )= .0094 > > E = .092 E = .09 > > So, .0094 - (.092*.09) = .00166 > > > Are you supposed to ignore the (-) in the > returns??? No, and that is why my numbers were off. Thanks for seeing that. I couldn’t figure out why they were wrong, and didn’t even notice a negative number there at all.