portfolio optimization

It might be help,
 
Portfolio Optimisation Models and Properties of Return Distributions, (2005) G Mitra, D Roman, KH Darby-Dowman, Mathematical Programming Journal,
 
Integrating market and credit risk: A simulation and optimisation perspective, (2005) N J Jobst, G Mitra, S Zenios to appear in Journal of Banking and Finance.
 

Quadratic programming for portfolio planning: Insights into algorithmic and computational issues
Part I - Solving a family of QP models


Quadratic programming for portfolio planning: Insights into algorithmic and computational issues Part II - Processing of portfolio planning models with discrete constraints

regards,
MC

________________________________

From: r-sig-finance-bounces at stat.math.ethz.ch on behalf of kriskumar at earthlink.net
Sent: Thu 10/07/2008 01:42
To: markleeds at verizon.net; r-sig-finance at stat.math.ethz.ch
Subject: Re: [R-SIG-Finance] portfolio optimization



There is an interesting paper on optimization with sorts by Almgren and Chriss. This takes ordering information to compute the optimal portfolio. There was an earlier post here on this which you will find in the list archives.

Cheers
Krishna

------Original Message------
From: markleeds at verizon.net
Sender:
To: r-sig-finance at stat.math.ethz.ch
Sent: Jul 9, 2008 18:00
Subject: [R-SIG-Finance] portfolio optimization

does anyone know of academic literature on optimization in finance where
one has the probabilities of the assets being up or down rather than the
expected returns of the assets ? ( and also covariance matrix).  i think
i  saw something in the past somewhere but i could be mistaken. thanks.

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Hi all,

I struggle to understand the output of the CVaR function in the fExtremes package.
The output of VaR (Value at Risk) gives me results I expect to see. However the output of CVaR is less than the output of VaR. From my understanding CVaR gives the mean over a given threshold and should therefore always be bigger than VaR.
The fowling example shows the output of VaR and CVaR:

library(fExtremes)
n <- 1000000
loss.ratio <- rlnorm(n, -0.3479, 0.104)
VaR(loss.ratio, 0.995) # same as quantile(loss.ratio, 0.995)
#    99.5%
# 0.9588572
CVaR(loss.ratio, 0.995)
#    99.5%
#0.7088572

I expected an output more like this:
mean(loss.ratio[loss.ratio > 0.995])
# 1.021089
mean(loss.ratio[loss.ratio > 0.995]) - VaR(loss.ratio, 0.995)
#  99.5%
#0.09783733

Maybe I am just a little bit confused and mix up terminologies.


Markus



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it seems to me there is a sign problem when it comes to upper and lower
tail. try the following (sorry that I change your example, but for the
Gaussian its easier to check)


require(fExtremes)
testData <- rnorm(100000)

# the function
CVaRtest <- function (x, alpha = 0.05, type = "sample", tail = c("lower", 
    "upper")) 
{
    x = as.matrix(x)
    tail = match.arg(tail)
    VaR = VaR(x, alpha, type, tail)
    if (type == "sample") {
        CVaR = NULL
	  if (tail=="lower"){
        for (i in 1:ncol(x)) {
            X = as.vector(x[, i])
		Z <- VaR[i] - X
            CVaR = c(CVaR, VaR[i] - 0.5 * mean((Z + 
                abs(Z)))/alpha)
        }
	  }else{
        for (i in 1:ncol(x)) {
            X = as.vector(x[, i])
		Z <- VaR[i] - X
            CVaR = c(CVaR, VaR[i] - 0.5 * mean((Z - 
                abs(Z)))/alpha)
        }
	  }
    }
    CVaR
}

VaR(testData,.05,tail="lower")
CVaR(testData,.05,tail="lower")
CVaRtest(testData,.05,tail="lower")

VaR(testData,.05,tail="upper")
CVaR(testData,.05,tail="upper")
CVaRtest(testData,.05,tail="upper")


# so, for your data
n <- 1000000
loss.ratio <- rlnorm(n, -0.3479, 0.104)

VaR(loss.ratio,.05,tail="lower")
CVaR(loss.ratio,.05,tail="lower")
CVaRtest(loss.ratio,.05,tail="lower")

VaR(loss.ratio,.05,tail="upper")
CVaR(loss.ratio,.05,tail="upper")
CVaRtest(loss.ratio,.05,tail="upper")

# a quick check
mean(loss.ratio[loss.ratio > quantile(loss.ratio,.95)])
mean(loss.ratio[loss.ratio < quantile(loss.ratio,.05)])

(btw. the documentation states that alpha is `a numeric value, the
confidence interval', but this should rather be `confidence interval =
1-\alpha')


best, enrico

cc: diethelm,yohan


-----Urspr?ngliche Nachricht-----
Von: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von Markus
Gesmann
Gesendet: Donnerstag, 10. Juli 2008 13:05
An: r-sig-finance at stat.math.ethz.ch
Betreff: [R-SIG-Finance] CVaR, fExtremes

Hi all,

I struggle to understand the output of the CVaR function in the fExtremes
package.
The output of VaR (Value at Risk) gives me results I expect to see. However
the output of CVaR is less than the output of VaR. From my understanding
CVaR gives the mean over a given threshold and should therefore always be
bigger than VaR.
The fowling example shows the output of VaR and CVaR:

library(fExtremes)
n <- 1000000
loss.ratio <- rlnorm(n, -0.3479, 0.104)
VaR(loss.ratio, 0.995) # same as quantile(loss.ratio, 0.995)
#    99.5%
# 0.9588572
CVaR(loss.ratio, 0.995)
#    99.5%
#0.7088572

I expected an output more like this:
mean(loss.ratio[loss.ratio > 0.995])
# 1.021089
mean(loss.ratio[loss.ratio > 0.995]) - VaR(loss.ratio, 0.995) #  99.5%
#0.09783733

Maybe I am just a little bit confused and mix up terminologies.


Markus



This message is intended for the personal and confidential use for the
designated recipient(s) named above.  If you are not the intended recipient
of this message you are hereby notified that any review, dissemination,
distribution or copying of this message is strictly prohibited. This
communication is for information purposes only and should not be regarded as
an offer to sell or as a solicitation of an offer to buy any financial
product, an official confirmation of any transaction or as an official
statement of Libero Ventures Ltd.  Email transmissions cannot be guaranteed
to be secure or error-free. Therefore we do not represent that this
information is complete or accurate and it should not be relied upon as
such.  All information is subject to change without notice.

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09.07.2008
18:32