00:01
So let's see here.
00:02
We want to optimize our portfolio using a sharp ratio.
00:07
That means that the weight we're going to use for portfolio a is the expected return for a minus the risk -free return divided by sigma -squared for a minus risk -free rate divided by sigma -squared for a minus risk -free rate divided by sigma -b squared.
00:30
Times row a, b, all divided by r .a.
00:41
Minus r .f divided by sigma a squared, plus rb minus rf over sigma b squared, minus two times row or return for a minus risk free rate divided by sigma squared a times r b minus r f divided by sigma r f divided by sigma b squared times a row ab and this is going to be then let's see here 0 .08 minus 0 .05, divided by 0 .2, minus 0 .13 minus 0 .05, divided by 0 .05, divided by 0 .05, times negative 0 .625, all divided by 0 .08 over 0 .05, divided by 0 .08 over 0 .05, divided by 0 .2 .2.
01:58
Plus 0 .13 minus 0 .05 divided by 0 .4, minus 2 times 0 .08, minus 0 .05 over 0 .2 times 0 .13, minus 0 .05, divided by 0 .4 times negative 0 .625, 5 over 0 .25 .5.
02:28
And that is equal to, let's see here, 0 .08 minus 0 .05, divided by 0 .2.
02:41
This is 0 .15 minus 0 .2 times negative 0 .625, divided by 0 .15 plus 0 .25, minus 2 times negative 0 .625, divided by 0 .15 plus 0 .2 minus 2 times 0 .15 .5.
03:03
Times 0 .2 times negative 0 .625.
03:12
So this then is, let's see here, 0 .275 divided by 0 .3875, which is equal to 0 .70968.
03:51
And then the weight for b, is going to be one minus the weight for a, so that is going to be 0 .2903.
04:06
So that means then the expected return for my portfolio is going to be w .a...