Value at Risk - based Portfolio Optimization

Dr. Emanuele Canegrati explains the future of Portfolio Optimization Techniques which respects Basle II Protocol to manage the market risks of banks and financial institutions

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Closed Caption:

hello everybody and
I want to discuss today
the value at risk the spur for the
optimization
which he is and may appear in very
useful to
which in the future
as whose will be a sort of benchmarks
for four you up to ease Asian als why is
it important
to his new approach financial analysis
as you probably know
that basil comity
in 1998 decided to implement
to strengthen dallas is served at risk
him banks and financial institutions
so
it becomes really important to
deal with tears system an hour's
the risk is becoming more and more
important and
DD activity
health banks and financial institutions
well
let me briefly tell you about the
assumptions
of modal supposed to have to perform
your which an
assets index it by II suppose
far the more to have an expat to return
of portfolio
equal to some
call wades seater J times expected
return called the single past
J and two variants
far the more introducer
typical feasibility constraint
coat into which some way
should be 21 now
I start to show today Medina
minimization problem hola Marco V its
kilobits
showed debt said
minimization problem is minimization
called their ins for full you Sigma
T squared subject to to
expect to return portfolio you and this
is a bill to constrict
so what we have to calculate is
talked about the actor seater which
represents
people tomorrow weights portfolio
the fair HD Lagrangian
sanction a obtain basically fears so
I wrote the first order set a
first-order conditions
and I EF and plus
to first-order conditions tried am plus
two derivatives
and derivatives with respect to the
Oakton always
and shoe derivatives I'll Lagrangian
multipliers
perhaps
his much more useful to use a simple
metrics
notation I can
ride the system into following
fashion capital Tsai times
capital who make your equal to be where
capital sigh he is too variances
hands could move there is plus expected
returns
metrics can capital Omega he is
to opt back to compact Singh ok to wait
and to Lagrangian multipliers and
a capital be he is distract would expect
a return of perform you
if I sold the system
are you changing 02 Mar capital
Omega star which is my solution which is
obtained by in 13 to capture sigh
metrics and multiplying its
by be secondly
I introduce valued at risk
be East portfolio optimization
it is important to to sign
to value at risk for a given quantile
cue to the a are
convict car tyre cue is equal to minus
T initial portfolio value the
0 times his expression
which income passes
is expected to return poor fool you my
news
D's parameter see which
arise cauldron tutor distribution
our rent unbearable times to standard
deviation
called Delta prices and
using variation
to the Sikh Marco V Spurs told analysis
by sharp
I obtain his expression which use
to return call
hasset hi his equal
to alpha I which is Coast component
plus be to hi times hair
are I which is too poor for your return
is that deterministic component
classist sarcastic component which is
given
by silent II father more
I also right not a constraint
with cheers people to do some of Peter's
times fetus which must be equal to a
given
capital G a gain
as before I right like version
tension Shinde is K's s3
their corrosion multipliers and a
also right sake of simplicity
his expression with the standard
deviation to
derivative 02 standard deviation with
respect to
away it hi and
derivative hav the standard deviation
we respected Chi which is dis
chamber some
expression gain
a ride to say it of first-order
conditions deuce case I will have
and plus 3 state of Chu
number
call for to religious am
hope to Wade's 3
migration multipliers so
exploits given
substitution
I can obtain can rewrites the first
order conditions
in the following fashion now
the problem is how to seoul D's
system equations since
it is impossible soul practically
dis system
can be solved quadrant very interesting
technique page scored which is called
to T cars I to rage actually I'm not
really an expert in
only our programming and because
in this case we have to school no leader
equations
so iPhone to
T Karzai to rations very useful and is
sort of heater to process procedure
according to which
Moscone searched words solution
as you can see you
some loops and which
start I to racin procedure
Iran across corner for for the
construction
for four standard deviation calculation
and of course we're
care to point where the convergence is
acceptable
and if
each is acceptable to software which
used saudis Teresa procedure
stops find to optimal so
just to give you a brief very brief
recap
he showed at Dr some
differences between two classy macoutes
per fully optimize Asian
and value tourist the spur for the
optimization
of course the second one is much more
complex because
to complexity he's due to defect to T
it is almost impossible to find or
impossible to find
a solution
and you have to run across geez
procedure she is of course
require some
program you programming skills so if
you're interested in
I suggest you check on Google and
to fines useful materials to
to work on so the seats
if you have had a question so we'll be
glad
to answer and of course
you to write my email address thank you
by