CVaR Portfolio Optimization

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Create and optimize Conditional Value at Risk portfolios. For more videos, visit http://www.mathworks.com/products/fin...

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in this video we will show conditional
value at risk portfolio optimization
in the financial tool box using the
portfolio see bar
object using these tools you can perform
your entire portfolio optimization
workflow
from defining the portfolio problem to
evaluating the efficient frontier
to setting up a record of purchase and
sales conditional value-at-risk
or CPR takes a look at the losses
and the tail and at the distribution of
scenarios for example
Cech's my part folio and calculate the
losses for several different scenarios
the losses might look something like
this: pot
where the scenarios with the highest
loss are on the right
redefine a probability level
here it's 95 percent and consider the
scenarios
whose losses exceed this level the
ninety-five percent mean
conditional value-at-risk is defined as
the average
up the losses in these scenarios now
let's see how the tools can be used
first will load in daily close prices
for some large-cap stocks small-cap
stocks
and body T acts the data is coming from
my yahoo connection
you can also connect to Bloomberg fax at
Thompson Reuters and others using the
debt a fee to a box
will convert the close prices to returns
data for our analysis
and then do a quick sanity check on the
returns to make sure everything looks
right
as expected the small-cap stocks have a
higher variance at the returns
well the bond ETF Sperry lasts will
combine all about
turns data into a single matrix to be
used in the analysis
everything I need for setting up the CVR
portfolio problem is right here
I start by creating a portfolio C var
object
and then use the methods that object to
specify the assets in my portfolio
the returns data the basic portfolio
weight constraints
and the probability level but defining
the probability level to be 0.95
rich using to minimize the average loss
in the five percent of portfolios with
the highest law sis
now we have everything to find
that we need for the CPR portfolio
optimization problem
so let's plot 10 portfolios along the
efficient frontier
here we have the CVR efficient frontier
which is the mean portfolio return
plotted against the mean conditional
value at risk
it's a good idea to compare the results
are different portfolio optimization
models
to see if they agree another common
portfolio optimization
formulation is mean variance if we look
at an example product portfolio returns
the mean variance risk is the variance
out one segment standard deviations
it's important to note that this method
assumes that the returns are well
approximated by a normal distribution
so let's calculate the mean variance
efficient frontier
and compare it to our CPR fronteer the
workflow is very similar to the CFR Part
fully a workflow
except that we use the estimate asset
moments method now
estimate the mean and covariance are
returned data
will calculate the efficient frontier
for this portfolio
but if I would like to compare this
result to my seat I result I need a way
to convert from one risk measure to the
other
well one way to do this is to calculate
the mean variance risk
up the CFR Part folios and then at the
converted frontier
to the mean variance pot as you can see
the frontiers are similar with some
differences in these areas
a different way to compare the results
is to look at the weights at the
efficient portfolios will visualize the
weights side by side using an area
lot this allows us to see where the
allocation differences are
in our efficient portfolios
while the
tears were somewhere for these two risk
measures the allocation of certain
assets
for example a GG various quite a bit
at this point we might want to do some
further investigation
to see whether results at the portfolio
optimization step for
let's look at a histogram at the returns
for our body T aP's
if we try to fit a normal distribution
to this data
it becomes evident that a normal
distribution may not be a good
assumption to make
this helps explain the difference
between army invariance portfolio
which assumes that returns are normally
distributed and RC car port folio
which uses simulations that don't
necessarily need to be normal
this demonstration showed some other
more commonly used features perceive our
portfolios
with the CVR portfolio object you can
also specify buy and sell costs per
individual assets
and sect group and turnover constraints
which allow you to place an upper bound
other purchases and sales for more
information
please select the link from this page or
return to the financial tool box page