# Getting Stuck on A simpe q

I’m getting really stuck on this simlpe questions. Maybe i’ve just been looking at it for too long but could someone please just explain it: screnerio 1 scenario 2 scenario 3 Probabiliy 0.5 0.3 0.2 rates of return Stock A 25% 10% -25% Stock B 1% -5% 35% 50/50 weighting in portfolio find expected return and variance. Can someone just explain the following: “Calculate portfolio returns for the three scenarios using equal weights and get 13%, 2.5%, and 5%.” From then on i get it. I know i’m probably being really retarded here but hey, better now than in the exam! Thanks

E(Rportafolio)= SUM of PixRi Scenario1: E(Rporfolio)= (0.5)(0.25)+(1-0.5)(0.01)=13% Scenario2: E(Rportfolio)= (0.3)(0.1)+(1-0.3)(-0.05)=-0.5% Scenario3: e(Rportfolio)= (0.2)(-0.25)+(1-0.2)(0.35)=23% This is the results I get and I think they are the correct one

25% * 1/2 + 1% * 1/2 = 13% scenario 1 10% * 1/2 + (-5% * 1/2) = 2.5% scenario 2 -25% * 1/2 + 35% * 1/2 = 5% scenario 3

Strangedays: What you wrote is wrong i think. The question doesn’t ask to use the probability of each scenario happening. If that was the case, we would : Prob scenario * Return scenario (13, 2.5, 5) No?

akukuu Wrote: ------------------------------------------------------- > Strangedays: > What you wrote is wrong i think. > The question doesn’t ask to use the probability of > each scenario happening. > If that was the case, we would : > Prob scenario * Return scenario (13, 2.5, 5) > > No? Akukuu, Yes sorry, I was reading the question better: “Calculate portfolio returns for the three scenarios using equal weights and get 13%, 2.5%, and 5%” And you are right, they want to know the Return just for the single scenario requested. My mistake…anyway I completely agree with you

screnerio 1 scenario 2 scenario 3 Probabiliy 0.5 0.3 0.2 rates of return Stock A 25% 10% -25% Stock B 1% -5% 35% E(A) = 0.5 * .25 + 0.3 * .1 + .2 (-.25) = 0.105 E(B) = .5 * .01 + .1 (-0.05) + .2 *.35 = 0.07 Now portfolio is a 1:1 mix of the above 2 E§ = .5 * 10.5 + .5 * 7 = 5.25 + 3.5 = 8.75% Now use the variance formula to get the variance of the portfolio. .5 * (10.5 - 8.75)^2 + 0.5 * (3.5 - 8.75)^2 = 15.3125 P.s. Not sure if 0.5^2 needs to be done with this version… CP