this is the S&P Standard & Poor 500
stock price index and it's used as a
benchmark for returns so if so this is
what you did if you just invested in the
whole market monthly from 2002 to 2016
and what it shows is a quite a
rollercoaster ride of value right so
actually I should have maybe plotted it
longer it was rising for a long time
before that and then it had a huge drop
from a hundred it fell about in half and
then starting in 2003 it started a long
increase again and then here's the great
financial crisis 2007 to 2009 and then
since then it's been going up a lot here
you know from here to here this is 2009
from here to here it tripled in value
it's amazingly unstable that this stock
market to think that the risk of any
other company the law of large numbers
is not working here because the the this
is the Standard & Poor 500 index the
it's an it's an average of 500 stocks so
if they were all independent of each
other the law of large numbers would
make the stock market as a whole
almost almost constant but in fact it's
actually gone up hugely so there's
definite dependence across stocks but
I'm not going to be focusing on
forecasting the stock market here we're
going to make the assumption that it's
very hard to forecast so we're gonna
look at risk as something that we can
quantify by looking at the standard
deviation of past risks and and now not
focus on what's new right now now what I
want to do is next is to look at one
firm within the S&P 500 what do you
think it looks like if I were to plot
Apple on the same chart here you know
you ever heard anything about how
they've performed what's that
does anyone know how Apple has performed
in the LAT since 2000 I guess we're not
an eager class of stock market devotees
yes you did yeah he said pretty well
since the release of the iPhone and I
was it 2007 that they did a series of
releases of new different models you're
right they did pretty well so I'll show
you what pretty well me and I'm gonna
superimpose on the same plot Apple okay
that's Apple it looks different because
I had to scale it down to fit Apple onto
it so this is quite a good performance
because I've started both rescale both
of them to start it at 100 and it's now
at what is that 3536 something like that
so that means a 30 let's say a 40 fold
increase in value in 15 years so imagine
that you were taking this class into
thought I was teaching this class and
that would be 15 years ago but imagine
that you were taking this class then and
you came home to your parents and said
you know I think Apple stock is a great
investment I just have a quick request
of you could you take out a second
mortgage on the house borrow $400,000
and put it into Apple stock well if you
did that in 2000 your parents would now
own over 15 million dollars the problem
is what's the problem with that the
problem is nobody knows the future if
you knew that Apple was going to do that
you would have obviously done this but
nobody knew that Apple was going to do
that so you would also face some
problems with your parents if you did
that because starting in 2000 a palapa
quite a bit and you lost it's like three
quarters of your money it's hard to tell
here right it was really limping along
for
for you so you come back four years
later heard your parents said do you
realize what you did you miss about four
hundred thousand and I was just we're
down to one hundred thousand but then
you have to be convincing again no just
hang in there this is the problem with
investing hang in there please and then
it started recovering slowly yeah I
think back to then this was before the
iPhone here back in two thousand one two
and three so it looks like Apple was
washed up and when did they bring in
Steve Jobs back do you anyone know that
anyone read about I'm assuming you know
who Steve Jobs is Steve Jobs was the
founder of Apple Corporation and he was
kind of a difficult guy and kind of
quirky so they fired him it was his own
company but you can get fired from your
own company and they put in some
professional management whereas he was
kind of a little bit strange the
professional management did this they
brought it down to a low value and then
they invited Steve Jobs back they
thought maybe he does have some kind of
genius but they're still doing well
after his death so maybe it's you know a
company develops a sort of culture and
is free that allows them to keep doing
yeah I really think that's true about
organizations they go on for so long
sometimes as a great success so for
example the Economist magazine was
founded in London
in the early 19th century and it was
it's still a great magazine how can they
last so long I went and visited them
once in a I discovered that they don't
even put buy lines they have a different
culture they usually don't put by lines
on articles in other words if you go to
work for The Economist as a writer you
will not become known they will not put
your name print your name on the
articles you write so how can they do
that because young people want to
establish themselves somehow but they do
and it there's a different culture at
the Economist magazine as a result so
every company has its own culture and it
produces these strange outlier effects
this is the return
on Apple stock in red the red dashed
line and the return on the SNP Standard
& Poor 500 stock price index so you can
see that the returns on Apple have been
very variable much more variable than
the return on the on the S&P 500 in fact
when you look at this it's hard to judge
from this picture which one did better
right it looks like Apple is going up
and down all the time it's this noise it
really nice and this aggregate stock
market
it looks pained by comparison it's hard
for you to judge which one did better
but you see it maybe if you look you can
sort of tell it there more ups and downs
but it's so noisy from month-to-month
these are monthly returns so here it
lost them Apple lost almost 60% in one
month so it was horrible the other thing
is I know if you can tell that it's
correlated with the S&P 500 that when
the S&P 500 moves up it moves up and
when the S&P 500 is down for example but
say this is the experience of investing
is puzzling because the Nori's dominates
it's just so scary you're watching these
things go up and if you take an
interesting investment like Apple it can
it just goes up and down so much for a
month-to-month and it can look and it
can be under four years and you can
really lose faith in your acumen after
it's gone badly for years so this is
just the variance of Apple versus the
variance of S&P 500 so the standard
deviation of Apple capital gain was
twelve point eight cents a month that's
not an EULA annualizing it means
multiplying it by twelve this is a
scatter diagram showing the returns on
the S&P 500 on the horizontal axis and
the returns on Apple on the vertical
axis and you can see that the scatter
has an upward slope to it which
means they're correlated but there's a
lot it's not that strong an upward slope
so but when S&P is high Apple tends to
be high in return and when the S&P is
low Apple tends to be low but it's more
variable well this goes from plus 62
minus 80 and on this axis I have minus
52 plus 50 so it's it's Apple is more
variable than S&P 500 but you can see
that there's a correlation actually it's
better if I put a regression line in
this is a line fitted through the
scatter of points and it shows it has a
slope of one point four five which is
greater than one which means that Apple
over reacts to what happens in the
aggregate stock market and then it has
noise on top of that Apple noise like
Steve Jobs death noise it doesn't affect
the overall stock market so Apple
actually had so this is going to be a
fundamental concept in this course the
beta of a stock is a measure of how it
relates to the stockmen if the beta is 1
then the asset tends to go up and down 1
for 1 in terms of returns with the
aggregate market if the beta is 2 that
they're kind of rare to see beta 2
stocks beta 1.45 is getting high
so Apple reacts more than directly to
the stock market
so when times are good people who think
they're really good for Apple and when
times are bad they think it's really bad
for Apple well the concept here is
market risk versus idiosyncratic risk so
market risk is the risk of the whole
stock market and for an Apple investment
the market risk of that investment is
the risk that Apple will do something in
reaction 2 they argued stock market but
idiosyncratic risk is Apple only risk so
that would be the death of Steve Jobs or
the eye flop the iPhone that nobody
liked that occurred about so they make
mistakes and they take risk the people
at Apple have a heavy
history of taking risks they'll try
something that might not work out that's
how they they don't always work out but
on average they do so the variance of
the return on a stock is equal to its
beta squared times the variance of the
market return and that's called
systematic risk
plus the variance of the residual in the
regression the residual in this
regression I think some of this might be
you are graduate students can clarify
some of these concepts for you a
regression line is a single line that
best fits the data in your scatter plot
so how is this calculated imagine you
have a scatter plot with 50 dots and you
start by drawing a line through them the
vertical distance between a given dot
and the regression line is that dots
residual also known as the error of your
proposed line with regards to that
single dot so to get a better fits
I can try changing the slope or constant
parameter to force the line to go
perfectly through dots 1 & 2 but that'll
make the residual associated with dot
three really big so what do we do we
want to minimize some combination of all
50 residuals so statistics proposes the
least squares method what are the
different slopes mean remember the
equation for a line in algebra class y
is equal to MX plus B the slope M is how
much Y changes for a one unit increase
in X in finance we call Y as the return
on Apple stock X as the return on the
market slope M as beta and the constant
B as alpha slope beta tells how much a
particular stock Co moves with the
market and thus is a measure of the
stock systematic risk
so the idiosyncratic risk is the risk
that the point will lie above or below
that line you can see there's a lot of
idiosyncratic risk for Apple