00:01
Today we're looking at two stocks and two investors.
00:02
We have mark and we have jane and we have two stocks.
00:07
We have stock x right here.
00:08
This is stock x.
00:10
Down here this is stock y.
00:12
And currently stock x trades at $80 a share, whereas stock y is $65 a share.
00:26
And we're going to see which stock mark and jane would prefer based on the utility function of each of the stocks.
00:35
So u, which is equal to the expected rate of return, e of r, expected value of r minus 0 .5 times a times sigma squared.
00:46
So a is called the risk aversion coefficient.
00:53
So mark has an a value of two.
00:55
Jane has an a value of five.
00:57
And our question specifically asks us about jane, which of these two stocks jane would prefer? and we're going to compare it to the risk -free rate of return r f of 0 .02.
01:10
And we're going to be doing the same for both for mark as well that are questions about jane.
01:15
So the risk free rate of return is the so there's no variance of sigma square which the variance is as soon to be zero.
01:25
So it's just the expected utility is 0 .02.
01:28
And let's go and do that.
01:33
So the expected value of the return is equal to the sum.
01:40
Of the probability of the return.
01:43
So i'll just put prob for probability, multiplied by the return.
01:46
We're going to sum all of these together.
01:49
Probability, these numbers, multiplied by the return.
01:53
So we have the probabilities already.
01:55
0 .1, 0 .3, 0 .4, 0 .15, 0 .05, and they summed to 1.
01:58
So we've got a distribution, so this is going to work out.
02:01
But we have the year to return in dividends.
02:03
And so we need to figure out the total amount that they'll be worth at the end of the year.
02:08
So we take the year in price plus dividends, and that's going to equal our year -end return.
02:13
But that is not the return.
02:15
That is actually just the year -end.
02:17
I should say, that's my game.
02:18
There's so many returns here.
02:19
This is actually the year -end value.
02:24
Maybe we change that to value.
02:29
Because the return is going to be this less 80, correct? it's $80 per share.
02:33
So the actual return is 172 minus 80.
02:38
So that's what i've got here.
02:40
We're going to take 80 away from each of these values, and we get these.
02:44
And so this is what we would return.
02:46
So if it goes up to 165 and it's 80 bucks, the year end value with the dividends is 172, but we paid 80 bucks for that.
02:53
So that means we've earned 92.
02:55
So this is our return.
03:03
Okay, so that's our return.
03:04
So if it's state of the economy is one, we'd expect our return to be 92.
03:10
If it's two, it's 58.
03:11
If it's $8 .50.
03:13
If it's four, that means we've lost money.
03:15
We've lost $19.
03:16
If it's five, we've lost $43.
03:18
It's gone down.
03:19
So we've lost money.
03:21
So, and we'll call this, but that's not, so that's not the return.
03:31
What we really want is the percent return, the percentage return.
03:35
Since this is percentage right here, that's a percent.
03:38
We need to consider this as a percent.
03:39
So the return is what we're going to do is take this return value and we're going to divide it by 80 because that's the initial value.
03:48
So it's like the percent that it's changed essentially.
03:52
Because if we take 92 divided by 80, it's 1 .15.
03:56
It means we've increased 115%.
04:01
That's how much we've increased.
04:03
We bought $80, bought the share for $80, but the return is 115 % of the 80...