00:01
So we have a fund manager who has looking at three mutual funds for investment, stock, bond, and a money market fund.
00:10
And this fund manager is going to invest 43 % in the stock fund and 57 % in the bond fund.
00:21
And we're going to find the expected return and variance for a portfolio that invests in this way.
00:28
So the return, we'll call it capital r, is equal to the, the, the, the, the, the, the, it's the weight of the returns for each fund so 0 .43 which is the stock fund times that return 0 .11 plus 0 .57 times 0 .07 which is the return of the bond fund.
00:48
Add those up and that's our return which is right here 0 .0872 so 8 .7 percent.
00:56
The variance is equal to the it's going to be the weight of one squared, of one of them times the variance of the other.
01:10
So w2 squared 2 plus we have to add in the covariance of them with their respective weights, or correlation, excuse me.
01:34
So let's go and do this.
01:35
We have 0 .43 squared times the variance, which is 0 .31 squared plus 0 .57 squared times 0 .57 squared times 0 .4.
01:50
1 2 squared plus 2 times 0 .43 times 0 .57 times the correlation between the 2, 0 .42.
02:01
And that gives us this variance right there.
02:04
0 .228, so 22 .8%.
02:06
All right.
02:10
Now we want, this is a, i should say.
02:12
And then for b, we want to find the return where they're doing 43 % in the stock fund, and 57 % in the money market.
02:24
So we do the same thing as before for the return.
02:32
It's the weights of 4 .43 times .11 plus 0 .57 times 0 .04, which is the return to the money market.
02:46
That's the return and we get this .0701.
02:52
And the variance is similar to what we have before.
02:58
0 .43 squared times the standard deviation of the stock fund.
03:03
Which is 0 .31 squared plus 0 .57 squared times 0 .04 squared plus the correlation, but the correlation is 0...