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To me, the most fundamental subject to learn
at the intermediate level at the wolf level
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is the subject of volatility. An options trader
cannot be a complete options trader without
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understanding what volatility is. The implications
of volatility. This is a very complex subject
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is a subject that is well suited for more
advanced classes but I think right now it
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is a good opportunity to start scratching
the surface in terms of volatility.
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Why do I think it is a good opportunity? because
the most common mistake that every beginner
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options trader makes is to ignore, and if
you ignore volatility you can lose money.
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In one the examples for instance, and this
might have happened to all of you, I think
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it is a rite of passage to everyone that is
new to options. Imagine that is earnings day.
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Earnings will be announced after the close
and you think the company is going to report
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really well and you want to play it with a
call option. And you go out and buy a call
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option. So imagine the company trades at $100
and you buy the $105 call expiring next week
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and you pay 4.60, that is what the slide is
showing. So you pay $4.60 for this particular
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option and you are very happy, you really
think this thing is going to move really well.
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But it doesn't. Because even though the company
reports amazing numbers and even though there
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is a tremendous move after earnings. Let's
say $108 I want to do something even higher,
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let's say $110 the stock goes really really
high and you are so happy about to count the
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money, and you just suddenly notice that the
option is actually priced at $3.35, this actually
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a real modeling that I did in terms of realistic
values of volatility. So, you actually lost
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money in this particular trade. You should
have made more money but you actually lost
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money. And that is a question that everyone
wonder, every rookie, every beginner options
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trader wonders why did I lose money? And at
this point, most people just go back to trading
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shares, or futures. They abandon options forever.
And, the question is what happened? What happened
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is that after earnings volatility tends to
collapse and the price of the option collapses
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with it and that is why you lost money even
though the direction was correct. So you bet
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on the correct direction but you failed to
account for volatility risk in your options.
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That is why it is important and volatility
is present at every moment that we trade.
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So, ok, we know that volatility is important,
we know that for options trader we are concern
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about volatility but then, what is volatility?
How is it measured? What is the concept? In
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order to explain that, and I have to tell
you right now, in your face, that volatility
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is a statistical concept. That's it. The funny
thing is, you will not find it in a single
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statistics book, you go to the library, you
get a statistics book, even for high school,
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something really basic, and you will not find
it there. You will not find it anywhere because
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it's a statistical concept but with a name
that is very peculiar. The finance industry
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gave it that name, no, why?, Because I don't
know, I guess the finance industry loves to
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give names to things, but you will notice
that volatility is actually a very well known
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statistical property, it' s just with a different
name. Let's see what it is. In order to explain
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Volatility, like this slide is telling you,
we have two worlds. The real world where the
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action happens in the market is a price world.
You see prices, you see a chart with prices
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changing up and down, that is the real world,
that is where the trades are happening but
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there is a different world, and I'm going
to show right here. I'm showing you two graphs,
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one graph on the left and one graph on the
right. And I'm going to ask you, do you recognize
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them? So, if you really have a great eye you
might recognize that the chart on the left
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is actually the stock market, the S&P 500
since 2010. And is very easy, it is just "the
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market goes up", that is what price is telling
you, the price is telling you the market always
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tends to go up with a couple of exceptions
you can see a few moments where the market
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pause but it continues going up. But what
is the graph on the right? Well, the graph
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on the right is exactly the same things. Both
graphs are actually the same thing, it is
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just the market from 2010 until now but represented
in two different ways and if you notice, something
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interesting about the representation on the
right, the red chart, you notice that it actually
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looks interesting because even in the price
chart we see that price always goes up but
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in the red chart we see that that thing stays
within a range, it just goes up and then it
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comes back and it tends to trade around a
range and that is why volatility is so useful,
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so I'm going to reveal right now what the
charts are. The charts are actually, the second
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chart is actually a chart of what we call
the log returns. So the red thing that you
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see on the screen is actually a display of
the log returns of the market. That is very
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simple. So, now, what is a log return? Or
in general, what is a return? We need to understand
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this concept in order to understand volatility.
So we saw that the market has a price and
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it moves up but the price is really not useful
if you tell me that the market is at 2860
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right now, I'll say fine, that seems useful,
but, is not that useful. But if you tell me
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that the is 1% up from yesterday, that is
even more useful, you see? the fact that you
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told me that market has moved a certain amount
over a previous value, conveys way more information
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than the absolute price. And that is what
the return is. The return is the difference
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between the price today from the price in
a previous period. The return could be a daily
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return so in that case, it will be the difference
between the current price and the price from
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yesterday. It could be weekly or monthly,
you can define the range for the returns.
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So, in this case, the returns are computed
the way they taught you back in High School,
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you take final price, you subtract the initial
price, divide by the initial price, multiply
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by 100 and it gives you a percentage return.
It's a very simple formula. Scratch that,
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no one uses that formula in finance, that
formula is not used. There are many reasons
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why the formula is not used, it is not because
it is complex, that is not the reason. It
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is because of the way the market works if
you use that formula you could arrive at negative
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prices and that is why they don't want to
have negative prices, so in finance, to avoid
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the problem of negative pricing they use what
is called the log-return. The log return is
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just a logarithm, it's a mathematical function
and the only thing you take is the logarithm
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of the final price divided by the initial
price and that's it. And if you did that and
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compare, it's basically the same number within
a range. Let's say within the first 10% they
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are basically the same if the normal definition
of returns gives you like 1%, the log return
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will also give you 1%, very close. They start
to differ if the move is really big and also,
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in particular, they start to diverge if the
move is really big down. If the current price
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is substantially below the previous price
the log return gives you a smaller value.
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But anyway, beyond that, that's what a log
return is.
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Now we know what a log-return is, so don't
let the fancy name throw you off, is just
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we are computing a return based on the relative
price of something today, something from yesterday,
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or different periods, but we are using a logarithm,
for many reasons, but it isn't very important
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why we are using logarithms. Now, with that
information, we can take a look at the charts
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again you can see price and you can see log-returns,
now officially I can tell you that log returns
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are on the right. But notice something, price
doesn't tell me anything useful. Let's try
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to measure from the collection of information
that I have, let's try to get the mean. I
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would say what is the mean price in the last
9 years since this graph started? And you
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will notice that the mean price is not that
useful because it doesn't tell you anything,
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the mean price of the market? who cares? it
was 1000 points down and now is up, it will
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be up later on so the mean price doesn't mean
anything. The mean price will keep moving
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up but in the log returns, notice that the
mean is very close to zero. And that is an
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interesting property, log-returns having a
mean of zero it gives you a hint of an interesting
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property that we can exploit. It is one of
those things, it is what we call mean reverting.
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The mean tends to be zero, and if you notice,
the graph of the log-returns tends to be around
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that zero, they don't deviate very far. Just
in a few years, you can see there are lots
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of deviations but then it kind of comes back.
And that is starting to give some hints that
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log-returns are useful.
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In a more formal way, we can say that the
price itself is what is called non-stationary.
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Non-stationary quantity is something that
doesn't stay in a single point so, if we measure
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what the SPX, the S&P 500 was back in 1950
it would be probably 20, that was what it
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was in 1950, 20 or 40, an outrageously low
value that you will love if I tell you that
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the S&P is 50 points today. What is today?
Today is exactly 2860 so, wow, price went
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from like 40 or some low value to 2860. Clearly,
the market is getting richer and richer and
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that is what I would call when price is non-stationary,
price keeps moving up and 10 years from now
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who knows where the market will be. And that
is a problem. if we want to do a statistical
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analysis of price is worthless. When you have
a non-stationary quantity you cannot really
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do any statistical analysis on it, it is completely
worthless, the mean will be worthless the
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standard deviation will be worthless, variance
will be worthless because the quantity is
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completely non-stationary. So statistics won't
help if we look at price and that is one of
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my, let's say pet peeves in general with most
of the methods that people teach on the Internet.
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So you go on the internet and read about market
and technical analysis, you will notice that
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most of those methods are based on price which
is non-stationary so those methods are in
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essence completely worthless because price
just moves out of whatever they are teaching
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you and that's it. So that is not a good way
to come up with statistical analysis. Log-returns,
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on the other hand, are very good. Log-returns
are stationary as you saw in the previous
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graph, they tend to remain very near the mean,
so because log-returns are stationary they
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are a good way to use statistical techniques
on the market itself. So we cannot use statistics
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on the price, fine, we'll use statistics on
the log returns and that is the key insight
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of the whole lecture, that log-returns allow
us to use statistics. And by statistics I
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mean I can compute mean, I can compute standard
deviation, I can compute skew, kurtosis and
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so forth and so on. For those of you that
are versed on statistics, I can compute the
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full thing and it's very useful. Now, with
this, we arrive to the core: What is volatility
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then? And finally, I can tell you that volatility
is just the standard deviation of those log-returns.
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That is what it is. Volatility is nothing
else and nothing more than a standard deviation
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and standard deviation is a word that you
will find on any statistics book, open the
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book, and the only thing you'll see about
is standard deviation this, standard deviation
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that. It's all over the place, so that is
what volatility is, it is the standard deviation
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but not of the price, notice this, volatility
is not the deviation of the price of the market,
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it is the deviation, the standard deviation,
of the log-returns of the market and that
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is why it is so useful. So, it is a fancy
word yet is a very simple concept, just as
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an anecdote: why it is called volatility in
finance circles? I don't know, really I don't
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know, I have always, this is not the only
case, I'm sure as I start recording more videos
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about this more examples will come to my brain
but this is not the only example where a particular
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area like finance comes up with a term for
something that is being used more formally
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in mathematics, so in mathematics, statistics
is standard deviation, finance and economics
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they call it volatility.