# FIN500 Mod07 P1 How to find the Expected Return and Risk

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Hi guys, welcome to I hate math group. In this video we're going to learn
the relationship between risk and return.
So let's say that you have a $100 dollars
and you want to invest all this money. Well
you decide to go to the bank and ask the guy
that is working at the bank where you should put your money.
He tells you look I have a Stock A and I have a Stock B.
Basically you can put your $100 dollars either here or here.
However, you need to understand that the economy can be good,
can be average, or it can be bad.
The probability that this can happen is going to be 45% that it is good,
40% that is average, and there's a 15% probability that
there's going be a bad economy (which that's actually pretty good).
So you have different scenarios. For example
just concentrate on these areas here. This is the Stock A
and this is a probability. There is a 45% probability you're going to have
a 15% return. A 40%probability you're going to have only an 8% return.
And if the economy is really bad you will actually lose money because you have a -11%.
Now, with Stock B if you have a good economy is 16% return;
40% probability on an average economy that you're going to get a 9% return,
and if you have a bad economy you can actually lose money because look
it's a -13%. It is very important you understand here
that the probability can never be negative, however,
the return can be negative because you can lose money.
So when you have problems like this your probability always
has to add up, up to one. However,
the return can be positive or negative.
Awesome. So you ask yourself 'well
which one is better? Is it Stock A or Stock B?' This is when you're going to go ahead and
calculate expected return. We're going to calculate expected return
of each stock A and B. The one that has the highest expected return
is the one that's going to give you the most money.
How do I do that? Okay, so
it is very easy. Obviously the bigger the problem
the more calculations but I just want to do this like a simple problem,
and then, I'm going to create another video with a little bit more complicated numbers and
we're going to do this in Excel© because by hand it's very tedious.
But look how easy, we're going to go ahead and multiply
the probability by the return
and then I'm going to add all that up.
So look what I'm doing .45 times .15
plus .40 times .08 and then plus .15
times, yes -.11.
So as you can see here even though I have a negative here I still have to put it,
because, remember, you have a probability of losing money.
So basically you just multiply the probability times the return
and add all that up. And look what you're going to get:
you're going to get this, and then multiply it by 100 and it tells me that
that with all these probabilities most likely I'm going to get an 8.3%. Awesome.
Let's do the same with Return B. Look what I'm doing.
.45 times .16 - basically I just make everything into decimals -
plus .40 times .09 plus .15 times -.13
and viola! I get a .885 (translates to 8.85)%. Awesome.
I can figure it out that Return B is actually the best investment.
However, I'm very excited with my $100 dollars
and the guy tells me 'O-ho hold on. You need to figure out how much risk you're going to have.
Because remember anytime you have a return you're going to have a risk'.
So how do I measure risk? Well in order to determine the risk
we're going to figure out the standard deviation.
This will tell me the percentage of risk
that I'm going to have. So the formula is
a pain in the neck, not to say the other word,
but not impossible. So look what we're going to do
we're going to go ahead and do this whole formula
which is going to be the probability times, and then you put a parenthesis,
.15 (which is the Return A) - the expected return (which we just calculated).
Look I'm putting everything in decimals because that way's easier.
You're going to go ahead and do, the first thing you're going to do is .15 - .083
Then you're going to square that and then you're going to do times .45.
You're going to do it with every single one, look at this:
.40(.08-.083) squared
plus .15(-.11-.083) squared.
All of this is gong to go ahead and give me this number.
Finally, I'm going to do the square root because before I just had the variants.
But when you do the square root of the variants you find the standard deviation.
Yes. And we get that my risk is 8.7% (.087 decimal format).
We're going to do the same with Return B.
I never said this was going to be an easy calculation, it's a pain in the freaking neck, but we're going to do an Excel©
video next tome so we can do all this in Excel© and make it easier.
Again, I'm going to do .45(.16-0.0885)squared and I'm going to do all this math.
And finally I get this number SD=square root of 0.0946. I do the square root
and viola, I get 9.7% (0.097).
Finally, I can conclude
the higher the risk the higher the return. It makes sense.
If you're making something that has a lot of risk, most likely you're going to have return.
But, you know, if you want something with a lower risk
you're going to have probably a lower return.
So these are the important points: the expected return will calculate the return of one single stock.
And the standard deviation is going to calculate the risk.
Let me tell you, once you do these problems in Excel© they're very, very easy.
Thank you so much for doing such an amazing job. ♪ Music playing in background ♪
Please don't forget to watch our other videos and also thanks so much for learning.