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15.5 Jupyter Notebook Sharpe Ratio Calculations - YouTube
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[Music]
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so
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we will start by the sharp ratio and
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figure out what it is by calculating
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inside jupyter notebook so let's get
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started so we are here inside jupiter
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notebook and we have something about the
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sharp ratio we remember it represent
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both the risk and return simultaneously
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if you want to read more about it you
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can actually follow the link here to
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investopedia and i actually think also
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to have a video this
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telling a bit more about it if you're
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interested otherwise we're just going to
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use it as it is and so on and the
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formula here and this is the formula
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we're going to use to calculate it and
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again here in this tutorial here not
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tutorial this is a lecture here we're
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going to use zero free
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zero as the risk-free return because the
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risk-free return is so low and many
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people when you look
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currently are actually using that value
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and for instance for me in denmark the
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risk return is zero and sometimes it's
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even negative
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interest rate in denmark it's crazy so
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you actually pay money to
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it doesn't make sense to me either but
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actually that's how it is okay and then
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we're gonna use the standard deviation
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of the portfolio
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and again here the goal is to get a high
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sr ratio as sharp ratio here right
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so
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i did what we usually did here i
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imported pandas i imported numpy i
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imported matplotlib that means i didn't
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do that yet
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now i did here we are and you did it too
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right yes good
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and then we do the same thing here we
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read the data here
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for the tiggers facebook nvidia amazon
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hp and apple and we do the magic here
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i've gone through this so many times now
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so i think you feel comfortable about
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that so let's just take a look at the
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data here
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head it is as we are used to
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so
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what is the first thing we need to do
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well let's look at the formula again
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right we need to find
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the return of the portfolio right the
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return of the portfolio well i actually
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already said that we actually did that
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already in the previous lecture so let's
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do that so let's make it a portfolio
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portfolio
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later we're going to call these
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portfolio weights but that's when we
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calculate a lot of them right now we
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just keep the name portfolio
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and we use an array numpy array nd array
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and
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let's try to make a different allocation
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than last time because i found that
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there were too many 20
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huh don't you think i think so
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okay so let's try to do 20
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15
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oops i was not 15 15
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35
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[Music]
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what 10 and
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25 right we do this one is that one even
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actually i don't know i'm so good at
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math when i'm sitting in front of a
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computer so let's just verify this
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no this is not one so what what did i
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mess up so let's
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say this one is 30 right
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here we have it one
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good and for some reason inside when you
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use jupiter notebook it represent the
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numbers quite annoying but this is the
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same as one 0.9999 infinitely is the
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same as one
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luckily when you do the calculations
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within
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numpy's and the
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pandas it never does represent the
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numbers in this awkward way
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but
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the numbers are identical
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good now we have the portfolio so we
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also wanted to normalize the data right
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so data
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equals to data
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divided by data
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i log
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zero right that was how we
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normalized it maybe just do it in a
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different cell actually
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not that it matters that much but i
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actually just
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want to keep it separated here data hit
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and here we have it normalized right
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so what we're looking for in the first
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place was actually
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figuring out what is the return of our
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investment right so that's what we are
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aiming to figure out so how do you get
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that
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do you have a guess
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yeah
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good
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so what we're actually going to do in
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this one here is actually put data and
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we put
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log returns because that's we need to
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calculate uh the
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we need to calculate the standard
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deviation right so how do you do that
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the log return of the
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data
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um
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we need actually to take the sum of the
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data and then we take the data here
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and uh
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yeah we need to take the log
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log of data
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divided by data shift
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correct me if i am wrong so what we're
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doing here in this one here this is
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maybe a many step at the time right we
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do the
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log returns so the log returns of the
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normalized data is the same as log
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returns on non-normalized data because
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it's percentages right so that's a log
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return and then we actually sum all
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these up to find the log return of the
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full investment but we also
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need to actually calculate the
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port
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folio
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how it's weighted portfolio here
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and then finally we need to sum it along
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axis one here right this is it data head
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here we have it right so what we have
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out here is a log return of the
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portfolio and not the individual
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stocks here right so here we have it
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right so this is how you can see it so
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these are the daily log returns as we
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know them
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awesome so far so good are you
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comfortable i am so let's continue so
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let's actually try to visualize this
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this could be funny fig axis
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plc sub
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plots
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perfect and what is it we want to
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visualize is actually this data log
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returns
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log return
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and then we want to
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we want to plot it
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we want to plot it as
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kind hist
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histograms and how many bins do we want
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50
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i don't know
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and then axis axis let's try to do this
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it was not entirely happy here i can see
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so what am i missing here
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so what i'm missing here is actually
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it's not called bin it's called bins
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right here we have it okay good uh so
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here we have it
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that's actually nice right so what you
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can see here is actually let's just
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do this
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what we can see here is actually that we
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have most of them around zero here
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obviously and the outliers are often
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down in the negative side here that's
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how it is because when people panic they
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panic right but actually not that bad we
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actually have some really positives here
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as well
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so it's quite nice
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so let's calculate this magic sharp
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ratio after we've seen this picture well
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how do we do that
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well let's look at the formula right so
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now we actually should be able to
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calculate the risk-free return
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the risk-free return here or the return
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of the portfolio apologies not risk
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return and the standard deviation of the
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portfolio so let's do that
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so the sharp ratio
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is equal to
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two
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so we take the data
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and then we have the
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log return
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and then we actually take the mean value
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of that
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and
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let's do the daily first and then we
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take data
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and
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then we do log return
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and then we do the standard deviation
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here so this is also the daily standard
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deviation and so we don't do the
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normalized first so sr so then we have a
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value like this so this is a daily so
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get the annualized sharp ratio
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then you actually take the sharp ratio
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and
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multiply
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25
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2
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and the square root of that
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so here we have a annualized sharpe
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ratio which is 0.87 or 7.8 almost right
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so
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a bit note on the calculations here
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because this might confuse you a bit but
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actually what we are looking let's try
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to do the same calculation here again
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because if you take the mean here what
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you do is actually calculate a yearly
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return mean here
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i just add parenthesis
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here this is a yearly return and then we
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actually take the square root of this
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one down here
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or 252
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square root of that
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i put two
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commas here and then we actually get the
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same value here so
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the key thing is that actually
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multiplying by this and
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multiplying by this below is actually
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the same as doing this one here this is
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just mathematics
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but it can be a bit confusing why i'm
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multiplying by this value here but this
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is exactly what we do here in
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we do here we calculate the mean return
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we take the mean return so this is the
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average return and multiply that by 252
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trading days and then we take the daily
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standard deviation and multiply that out
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by the square root of 252. that was a
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formula remember okay so here we
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actually have the sharp the annualized
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sharp ratio and this calculation we're
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going to use later
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to find the best portfolio because right
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now it's just one and is this value good
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well we are trying to get at least above
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one of this but in theory we just need
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to compare each of the sharp ratio with
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each other and to see what is best and
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the higher the better so this was one
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portfolio we could see
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if you needed to do this manually trying
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each one of them to find the best one
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that will take a long time so this is
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where monte carlo simulation comes into
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the picture so this is exciting right
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okay
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so what did we do here well we
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calculated the sharp ratio with a
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risk-free return of zero you can add any
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value but you see it really doesn't make
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a diff big difference it just
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changes the value of the sharper ratio
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obviously so
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we did that and we did
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do that by making some random portfolio
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here and then
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we just plotted it for fun and then we
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calculate the sharpe ratio and the
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annualized shop ratio so that's
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basically it straightforward so let's
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continue to the next one see you
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