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So another thing I actually wanna show is.
So.

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If we look at returns over time.
So let's, take the ret-, the simple return

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graph here.
And then, create a, a simple line chart.

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And so here is our one month rate of
return.

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And, Now, one of the things you should
sort of look at, this, this graph of

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returns.
And so, you know?

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One thing to, to notice in these monthly
returns.

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That the monthly returns are fluctuating
at about zero, right?

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So on average over this time period, the
rate of return, the monthly rate or return

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was about zero.
Sometimes the monthly rate of return was

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as high as 30%, and sometimes the return
was as low as 40%.

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So in one month you could of lost, you
could of made, you know, a 30 percent

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00:00:57,452 --> 00:01:01,647
increase in your money.
So if you started with $100, then you

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would have $130.
Or in some months, you could of almost

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lost half your money.
So if a rate, you lose 40%, then start

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with $100, then you go down to $60.
Now one of the things that's important to

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recognize about rates of return is that
you know, it's, it's not a symmetric

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relationship.
Right, so if you if say you loose half

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your money, so if the rate returned is
minus 50 percent your $100 goes down to

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$50.
Now what rate of return do you need in

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order to get your investment to get back
up to $100?

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It's not 50%, right?
Cuz if you go, you'd have 50 percent

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positive return, then your $50 goes to
$75.

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You'd need to get 100 percent rate of
return to get your money back whole,

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right?
So this is one of the nasty features of

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returns is that a negative 50 percent
return does not get cancelled out by a

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positive 50 percent return in the next
period.

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You'd need to get 100 percent return to
get you back whole.

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00:02:02,640 --> 00:02:09,130
And so, And then you know by looking at
the data that result is a bit hidden in.

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In this Now one of the things that's often
done.

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So this, this, these are monthly rates of
return, okay?

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Very often you know, we, we Might wanna
plot what is the growth of a dollar

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invested every month.
So the idea is you wanna calculate the,

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the future value of a dollar.
So I start my investment with a dollar and

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00:02:32,572 --> 00:02:37,309
then the next month you know, what does my
dollar grow to, it grows to one plus the

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interest rate, and then after two months
what does my dollar grow to, it's one plus

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the rate of return over the first month
times one plus the rate of return over the

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second month.
So very often in finance you see these

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growth of a dollar graphs.
Right?

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So the idea is.
If you have returns.

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Say R1, R2.
Up to say R capital T.

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00:03:09,206 --> 00:03:19,790
So these are all one month returns.
So what is the growth of a dollar?

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So we start.
With $one.

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00:03:24,080 --> 00:03:28,540
Right?
And so, in month one.

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The future value is, the $one, times one
plus R1, right?

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00:03:44,700 --> 00:03:51,360
Okay, and then in month two.
The future value is my.

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00:03:52,780 --> 00:03:58,819
What I have at one, at month one, and then
that grows by one plus the monthly

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00:03:58,819 --> 00:04:05,335
interest rate between months one and two,
so that's one plus R2, and then similarly,

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00:04:05,335 --> 00:04:12,382
all the way down to month T.
My future value is one plus R one times

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00:04:12,382 --> 00:04:19,280
one plus R two and that gets multiplied
one plus R capital T.

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00:04:19,780 --> 00:04:26,292
So this if you wanted to plot the growth
of a dollar based upon investments giving

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you all of these rates of return, then I
have to plot the cumulative products of

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all of these numbers.
>> Okay.

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00:04:35,551 --> 00:04:42,420
>> So we can do this in Excel.
In a bunch of different ways.

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00:04:46,140 --> 00:04:52,763
But essentially, you know, we need to
compute our, our future value.

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00:04:52,763 --> 00:05:00,920
And so, for example we can make this one
plus the, Rate of return here.

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00:05:01,400 --> 00:05:09,920
And then, what we can do then, is make
this equal to this number times, one plus.

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00:05:10,940 --> 00:05:19,156
The rate of return here.
And so And so that I can just copy this

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formula down all the way.
And so then I can plot the grow of the

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00:05:31,100 --> 00:05:38,440
dollar.
And so we see.

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00:05:38,683 --> 00:05:45,510
Based on the rates return in Starbucks we
started with a dollar in 1992 and we want

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to know at the end of the data sample,
which is I think, I don't know what it is,

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00:05:52,175 --> 00:05:57,132
our $one has now grown into about $30 over
this period of time.

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00:05:57,132 --> 00:06:04,040
So by holding Starbucks since it...
Since it started, you had a huge increase

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in your wealth.
So people investing in Starbucks would

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have done quite well.
So this is called an equity curve, and

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00:06:13,123 --> 00:06:18,465
it's just showing what happens to the
growth of $one based on investing in

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Starbucks, and essentially, you know, what
you're finding is what $one has grown to

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after every month.
And so you saw, Notice that this graph

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here looks, it looks very much like the
price graph of starbucks.

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00:06:34,130 --> 00:06:36,990
Right.
And you'll really think the difference

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between this graph and graphing the price
is that you just normalize the starting

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00:06:42,202 --> 00:06:46,207
price to be equal to one.
Okay, so that's another way of viewing

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00:06:46,207 --> 00:06:49,957
what this graph is.
It, It says if we started with the stock

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00:06:49,957 --> 00:06:55,042
at prices and we made the first price
equal to one we normalize it by the first

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00:06:55,042 --> 00:06:58,539
price and then we just clock the growth of
prices over