Investment Science: Portfolio Optimization

Tucker Balch, Ph.D., Lucena's CTO describes the science and algorithms behind portfolio optimization.

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Closed Caption:

Hall hot
of of
home
of
I am after soccer ball
with him soon research and in this video
minute tell you about
portfolio optimization now this video is
about the
science a portfolio optimization there's
another video that
tells you how to use the portfolio
optimizer thats article that said it's
quite this
I know where polio optimization as the
really important to our a cornerstone of
quantitative analysis
um and our what is it
well what it does is a given a set of
equities that you want to invest in
and a target return that you want to
achieve a portfolio optimizer
we'll figure out the best allocation
for cash to equities to give you the
lowest
Rhys for that portfolio I know before I
get too deep into this
you need to go through all disclaimers I
was in a research
is not a registered investment advisor
I'm not
you there you should definitely your
speak with the
license financial advisor a do not
assume that the
techniques were gonna show you your will
be profitable
and the the the the supplement show you
is a
hypothetical it's based on historical a
data and there's there's no guarantee
that
the this and it's tough work in the
future on real trading
okay back to portfolio optimizer
portfolio optimizer czar or to fall
serious investment techniques on
are used by you know largest hedge funds
and investment banks
and again what it what it does is that
the
to figure out among a set of equities
how much you should allocate
each one so that you can or
given return have the lowest risk
now what do we mean by
risk was loose what's answer that by
taking a look at the
to hypothetical stocks the stock XYZ
a pretty good historical performance
what about 10 percent a note though that
it's a
are also what goes up and down a lot
let's compare that now to this other
stock
ABC they also gain 10 percent over the
same time period
but it wasn't quite as volatile it's
this volatility
that is a measure risk and
this what's traditionally used in the in
the finance and
industry to measure risk this other
measures Rhys
that are also valid a this one
a is convenient in the sense that it's
easy to measure
I'm volatility how much stock goes up
and down
is standard deviation a returns
and it's a it's a calculation that so
easy to do
to do work you now
we can consider equities stocks yes
whatever in two dimensions one dimension
is this risk
we're talking about or volatility and
the other is
Richard now ideally of course we want is
a
little risk high return stocks but
a as is usually the case you don't see
return without
without risk so the highest return
stocks also and
have I asked both or the or Chris
but you can you can view each other the
equities you might want to invest in in
this
in this sorta two dimensional view and
when you build portfolio
by allocating a waited about 20
for for of cash to
each one of these equities you know
portfolio that's sort of a weighted
combination
exactly's a now the portfolio itself is
somewhere on this graph it has a
a certain amount of Chris in a certain
amount
for return or expected return and you
would think
that 'em it will be sore somewhere in
the middle
a whole pizza world equities or what
turns out that
a portfolio optimization
allows us to do better weekend weekend
for
portfolios or given target return
actually have a lower risk and any of
the
individual equities and I'm gonna show
you how this the
I'm actually doing better
well in the in the sixties and
seventies a 0
but the real finance evolve call them
modern portfolio theory
this guy hurting markowitz was one of
the leaders
a and he discovered a way to combine
equities
portfolios that actually have lower
risk than any of the individual equities
you got the Nobel Prize for their
and 1990 are we use the
so that's a no for the most part were
quite best to or not whether
give you example that little bit unblock
me a
introduce you now to the a
to the science behind with what mark
with well
it's a well Bill Maher but it's a it's
not too bad thank you
I think it you you have an interest in
this you'll find it
okay so what goes into area portfolio
optimizer
the inputs what we had talked about
or for each equity
a measure return what we expected to see
I'm as return for each equity
also measure up risk for each equity we
have you see there the
your burger king that's their represents
a an equity on this on this matter
I'm a target return so you can ask the
optimizer
were gonna get only this target return
own and no fun for me the the los tres
portfolio that's the thing together this
is so
this is another piece of data that it's
called a coup variance matrix and that's
probably the most
how quickly it all this an argument that
the moment
a but to the you think these inputs on
to the to the optimizer it
does a lot a number crunching it's a
really serious algorithm in it finds the
weights for each
equity give you this portfolio and as
you can
as you can see as you can see here
its lower risk then the in your the
other constituent equities next canada
magical
for portfolio optimization okay
what is covariance and why does it
matter
what said let's take a look at that and
60 three examples thought so
UTC is the Blue Star year as they bring
Ghiz the or star with a creative name
pair
now notice how other Bluestar
and the green star tend to move together
than
closely together a where is this other
star I G H i
it shows the same return but it it moves
so
for opposite those other two stocks
another thing to notice is
each of these equities has about the
same volatility
and they have about the same a the same
return
and the magic have portfolio
optimization there's a way that you can
combine them
getting much lower fault with the
portfolio
for the same lecture okay now there's a
there's important concept here
about the relationship between two
stocks and how they've moved from day to
day
and it's called covariance
there's a another measure that's very
closely related a
on I'm not going to the mathematical
distinction but
correlation we also use
and the correlation between stock
a abc&d yes in this case
is this point nine a high number think
the highest correlation you can happen
1.0
and the lowest you can is negative 1
okay
so it a high positive number
means a move together very similarly
on a negative number say Moo oppositely
one almost critics which way the other
one is going to go
so in same way that the the relationship
when the first two stocks is positive
number close to one
relationship between the Louis or star
is that negative number because they
move office at one
okay let's look at a couple hypothetical
a portfolio is built using
equities let's suppose we bill portfolio
that's half ABC and half yes
now because the stocks move similarly
we expect the resulting portfolio moves
like they do
and as you can see this this no red 1
represents
work for you combine those two stocks so
it's got about the same reliability
the same return are as as
as those to equities so we don't gain
too much
by combine those two work with ease into
work for you
now about another portfolio what about a
44 year we put term
a 25 percent in the blue forty-five
percent in
green and fifty percent and the other
one GH I
so what that means now as we go about
half in the to equities at work together
and the other half inequity moves
opposite
now because some we've the Versa fight
now
and and in a stock that's anti
correlated
that's the that's a fancy term for the
that they move opposite one another
we're gonna get a much smoother
performance and as you can see
your or so this ruthless
up but as you can see when you combine
these a
stocks that are into corley you get a
much smaller performance
and these relationships are
relationships that are discovered
automatically by a
by optimization cool like that one that
we can use this
are Qantas after center
okay salute so let's go back to the
summer this so
map we've got a risk and return
and the any jeopardy is little green dot
there that represents a
its particular risk and its particular
return
are and as you recall there that there
are that was a or
all we were able to discover well it
turns out that for
each well target return
are there is a unique portfolio
that that is the minimum risk for folio
or that Amanda return and that it
defines a
you know curve a whopping here
so this wine represents essentially a
incident number different portfolios and
each one
is a different target return that so
wonderfully we discovered is just one of
them
but there's a continuum along that line
now there's a
three very important portfolios are
along that line that the Wii provide
access to an
on yes one is the maximum return
portfolio
let's let me give you the highest return
on and and unfortunately it's it's
usually
hope all thats often also the the
highest
risk work for you I and that's in the
that's an upper right corner so are
a you can also ask for the lowest risk
portfolio
that's in the lower left there up and
and thats love listen to the portfolio
that has the lowest volatility
from and you end up with a particular
return
is usually lower where that up this is
other interesting point along that line
which is we call balance which is in
between the two
and that's the one that maximizes the
race you know I'll
will ward or return to volatility
that what maximizes sure ratio
on okay so let's look at a couple
examples from
with work want this again there's
another video that goes into much
deeper specific examples on how to work
with
our portfolio of my for me to show you
couple simple ones
okay we're we have this portfolio was
gonna the
it's good for equities a there's a GG
a bond fund GLD
you'll be which is of course a year yeah
that represents
goal St y is an e.t.a
the represents the S&P 500 and USO which
is oil
now built an example portfolio it's just
the
a quarter of the portfolio isn't each
equity
and you can you can see it so you can
see it so you're the
performance your water bottle we've got
a few were
a few data points over here the
volatility is a
173 percent that means that on average
it changes some recorders percent for
the
it's so short ratios point 15 which
which is not the not all that great
I'm okay seles go to the optimize have
and we'll take a look at how we can
optimizes portfolio
I'm remember now is for equities
to start with right now we're comparing
to is a your portfolio that Scott
one-quarter up the one-quarter
the holdings in each of those four
equities
okay we'll have a look back over six
months
they were optimization let's start with
I'm
with the maximum return optimization
so what we should discover here is that
cool little slut
the single equity has the as I stryker
re okay so
a turns out that over this period geo
the
goal has never the highest return
and it's it's actually puts a hundred
percent to the whole things into
GOP and you can see this chart along the
bottom
the blue the blue line is what so
what we started with our original work
for you and the orange line
is what we can would have made if we had
if we have been dollar eggs into a bowl
and as you can see going forward there's
the
forecast volatility in the forecast
return
on and as you can see the
by the volatility going forward is is is
forecast to be
I'm more volatile than what we did
already are
okay with Silas what's so we'll save
that
I'm sore new work for you now that we're
working with
essentially has a everything and GOP
or let's try another optimization what's
instead go
or minimum risk and before
before you have to start doing that take
a look at the volatility of its
portfolio
where so for leave all the portfolio
and going forward the forecast cone
there
no divergence significantly because I've
the because the forecast for
or right now will try to optimize for
minimum risk
across these for equities
okay now we've got character back
take a look at that I'm a
very smooth return if you
compare that the the two returns I'm
we you know we don't get nearly as much
as
high-return with the with the river
earlier we
I'm with the with all the
all the eggs into govt we're going
forward
I'm we have a much lower much lower bowl
no okay no strike a balance
optimization were were asking it to
to find the a balance between maximum
return
and maximum volatility
I'm sorry memorable
okay so this is the the balanced
portfolio
and now look it's a it isn't the much
less
fall/winter ritual portfolio on
not quite as I return looking back
but looking forward also much lower
both will be stepping forward I'm
again a not are so that's who
a that's the science behind portfolio
optimization
check out our other videos in particular
the
video about the your details love you
know all the
or who think you can do portfolio
optimization all the car
for to see you again and the thanks
world thanks for checking out with some
research holes
so you can surf
call home
all