There is a 20 percent probability the economy will boom 70...

There is a 20 percent probability the economy will boom, 70 percent probability it will be normal, and a 10 percent probability of a recession. Stock A will return 18 percent in a boom, 11 percent in a normal economy, and lose 10 percent in a recession. Stock B will return 9 percent in boom, 7 percent in a normal economy, and 4 percent in a recession. What is the expected return and variance of a portfolio which is invested 40 percent in Stock A and 60 percent in Stock B?

Transcript

00:02 We have to calculate the expected return and variance of a portfolio.

00:06 So we can use the following formula first expected return of a portfolio e that is expected rb is equal to wa multiplied by e ra added to wb multiplied by e rb.

00:41 Then second formula is variance of portfolio is variance rb is equal to wa squared multiplied by variance ra added to wb square multiplied by variance rb added to 2 multiplied by wa multiplied by wb added to uv ra comma rb where erp is expected return of the portfolio wa is the weight of stock a in the portfolio wb is the weight of stock b in the portfolio e ra is equal to expected return of stock a e rb is equal to expected return of stock b then variance ra is equal to variance of stock a variance rb is equal to variance of stock b and we are a comma rb is covariance between stock a and stock b.

03:45 Now now given the information wa is equal to 0 .40.

03:56 That is 40 % wb is equal to 0 .60.

04:02 That is 60 % e ra is equal to 0 .20 multiplied by 0 .1 a added to 0 .70 multiplied by 0 .11 added to 0 .10 multiplied by 0 my sorry minus 0 .10 which is equal to we get 0 .106 or 10 .6 % e rb is equal to 0 .20 multiplied by 0 .09 added to 0 .70 multiplied by 0 .07 added to 0 .10 multiplied by 0 .04 which is equal to 0 .066 that is 6 .6 % variance ra is equal to 0 .18 subtracted from 0 .106 whole square multiplied by 0 .20 added to 0 .11 subtracted from 0 .106 whole square multiplied by 0 .70 added to minus 0 .10 subtracted from 0 .106 whole square multiplied by 0 .10 which is equal to we get 0 .01162 then variance b the variance rb is equal to 0 .09 subtracted from 0 .066 whole square multiplied by 0 .20 added to 0 .07 subtracted from 0 .066 whole square multiplied by 0 .70 added to 0 .04 subtracted from 0 .066 whole square multiplied by 0 .10 which is equal to we get 0 .000244 then covariance ra comma rb is equal to 0 .18 subtracted from 0 .106 multiplied by 0 .09 subtracted from 0 .066 multiplied by 0 .20 added to 0 .11 subtracted from 0 .106 multiplied by 0 .07 subtracted from 0 .066 multiplied by 0 .70 added to minus 0 .10 subtracted from 0 .106 multiplied by 0 .04 subtracted from 0 .066 multiplied by 0 .10 which is equal to we get 0 .000235 now, we can plug these values into the formulas...

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