So another thing I actually wanna show is.
So.
If we look at returns over time.
So let's, take the ret-, the simple return
graph here.
And then, create a, a simple line chart.
And so here is our one month rate of
return.
And, Now, one of the things you should
sort of look at, this, this graph of
returns.
And so, you know?
One thing to, to notice in these monthly
returns.
That the monthly returns are fluctuating
at about zero, right?
So on average over this time period, the
rate of return, the monthly rate or return
was about zero.
Sometimes the monthly rate of return was
as high as 30%, and sometimes the return
was as low as 40%.
So in one month you could of lost, you
could of made, you know, a 30 percent
increase in your money.
So if you started with $100, then you
would have $130.
Or in some months, you could of almost
lost half your money.
So if a rate, you lose 40%, then start
with $100, then you go down to $60.
Now one of the things that's important to
recognize about rates of return is that
you know, it's, it's not a symmetric
relationship.
Right, so if you if say you loose half
your money, so if the rate returned is
minus 50 percent your $100 goes down to
$50.
Now what rate of return do you need in
order to get your investment to get back
up to $100?
It's not 50%, right?
Cuz if you go, you'd have 50 percent
positive return, then your $50 goes to
$75.
You'd need to get 100 percent rate of
return to get your money back whole,
right?
So this is one of the nasty features of
returns is that a negative 50 percent
return does not get cancelled out by a
positive 50 percent return in the next
period.
You'd need to get 100 percent return to
get you back whole.
And so, And then you know by looking at
the data that result is a bit hidden in.
In this Now one of the things that's often
done.
So this, this, these are monthly rates of
return, okay?
Very often you know, we, we Might wanna
plot what is the growth of a dollar
invested every month.
So the idea is you wanna calculate the,
the future value of a dollar.
So I start my investment with a dollar and
then the next month you know, what does my
dollar grow to, it grows to one plus the
interest rate, and then after two months
what does my dollar grow to, it's one plus
the rate of return over the first month
times one plus the rate of return over the
second month.
So very often in finance you see these
growth of a dollar graphs.
Right?
So the idea is.
If you have returns.
Say R1, R2.
Up to say R capital T.
So these are all one month returns.
So what is the growth of a dollar?
So we start.
With $one.
Right?
And so, in month one.
The future value is, the $one, times one
plus R1, right?
Okay, and then in month two.
The future value is my.
What I have at one, at month one, and then
that grows by one plus the monthly
interest rate between months one and two,
so that's one plus R2, and then similarly,
all the way down to month T.
My future value is one plus R one times
one plus R two and that gets multiplied
one plus R capital T.
So this if you wanted to plot the growth
of a dollar based upon investments giving
you all of these rates of return, then I
have to plot the cumulative products of
all of these numbers.
>> Okay.
>> So we can do this in Excel.
In a bunch of different ways.
But essentially, you know, we need to
compute our, our future value.
And so, for example we can make this one
plus the, Rate of return here.
And then, what we can do then, is make
this equal to this number times, one plus.
The rate of return here.
And so And so that I can just copy this
formula down all the way.
And so then I can plot the grow of the
dollar.
And so we see.
Based on the rates return in Starbucks we
started with a dollar in 1992 and we want
to know at the end of the data sample,
which is I think, I don't know what it is,
our $one has now grown into about $30 over
this period of time.
So by holding Starbucks since it...
Since it started, you had a huge increase
in your wealth.
So people investing in Starbucks would
have done quite well.
So this is called an equity curve, and
it's just showing what happens to the
growth of $one based on investing in
Starbucks, and essentially, you know, what
you're finding is what $one has grown to
after every month.
And so you saw, Notice that this graph
here looks, it looks very much like the
price graph of starbucks.
Right.
And you'll really think the difference
between this graph and graphing the price
is that you just normalize the starting
price to be equal to one.
Okay, so that's another way of viewing
what this graph is.
It, It says if we started with the stock
at prices and we made the first price
equal to one we normalize it by the first
price and then we just clock the growth of
prices over