Re: [R] The best solver for non-smooth functions?

2012-07-23 Thread Patrick Burns 

There is a new blog post that is pertinent to this question:

http://www.portfolioprobe.com/2012/07/23/a-comparison-of-some-heuristic-optimization-methods/

Pat

On 18/07/2012 21:00, Cren wrote:

# Hi all,

# consider the following code (please, run it:
# it's fully working and requires just few minutes
# to finish):

require(CreditMetrics)
require(clusterGeneration)
install.packages("Rdonlp2", repos= c("http://R-Forge.R-project.org";,
getOption("repos")))
install.packages("Rsolnp2", repos= c("http://R-Forge.R-project.org";,
getOption("repos")))
require(Rdonlp2)
require(Rsolnp)
require(Rsolnp2)

N <- 3
n <- 10
r <- 0.0025
ead <- rep(1/3,3)
rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
lgd <- 0.99
rating <- c("BB", "BB", "BBB") 
firmnames <- c("firm 1", "firm 2", "firm 3")
alpha <- 0.99

# One year empirical migration matrix from Standard & Poor's website

rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
M <- matrix(c(90.81,  8.33,  0.68,  0.06,  0.08,  0.02,  0.01,   0.01,
   0.70, 90.65,  7.79,  0.64,  0.06,  0.13,  0.02,   0.01,
   0.09,  2.27, 91.05,  5.52,  0.74,  0.26,  0.01,   0.06,
   0.02,  0.33,  5.95, 85.93,  5.30,  1.17,  1.12,   0.18,
   0.03,  0.14,  0.67,  7.73, 80.53,  8.84,  1.00,   1.06,
   0.01,  0.11,  0.24,  0.43,  6.48, 83.46,  4.07,   5.20,
   0.21, 0,  0.22,  1.30,  2.38, 11.24, 64.86,  19.79,
   0, 0, 0, 0, 0, 0, 0, 100
)/100, 8, 8, dimnames = list(rc, rc), byrow = TRUE)

# Correlation matrix

rho <- rcorrmatrix(N) ; dimnames(rho) = list(firmnames, firmnames)

# Credit Value at Risk

cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)

# Risk neutral yield rates

Y <- cm.cs(M, lgd)
y <- c(Y[match(rating[1],rc)], Y[match(rating[2],rc)],
Y[match(rating[3],rc)]) ; y

# The function to be minimized

sharpe <- function(w) {
   - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
}

# The linear constraints

constr <- function(w) {
   sum(w)
}

# Results' matrix (it's empty by now)

Results <- matrix(NA, nrow = 3, ncol = 4)
rownames(Results) <- list('donlp2', 'solnp', 'solnp2')
colnames(Results) <- list('w_1', 'w_2', 'w_3', 'Sharpe')

# See the differences between different solvers

rho
Results[1,1:3] <- round(donlp2(fn = sharpe, par = rep(1/N,N), par.lower =
rep(0,N), par.upper = rep(1,N), A = t(rep(1,N)), lin.lower = 1, lin.upper =
1)$par, 2)
Results[2,1:3] <- round(solnp(pars = rep(1/N,N), fun = sharpe, eqfun =
constr, eqB = 1, LB = rep(0,N), UB = rep(1,N))$pars, 2)
Results[3,1:3] <- round(solnp2(par = rep(1/N,N), fun = sharpe, eqfun =
constr, eqB = 1, LB = rep(0,N), UB = rep(1,N))$pars, 2)
for(i in 1:3) {
   Results[i,4] <- abs(sharpe(Results[i,1:3]))
}
Results

# In fact the "sharpe" function I previously defined
# is not smooth because of the cm.CVaR function.
# If you change correlation matrix, ratings or yields
# you see how different solvers produce different
# parameters estimation.

# Then the main issue is: how may I know which is the
# best solver at all to deal with non-smooth functions
# such as this one?

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--
Patrick Burns
pbu...@pburns.seanet.com
twitter: @portfolioprobe
http://www.portfolioprobe.com/blog
http://www.burns-stat.com
(home of 'Some hints for the R beginner'
and 'The R Inferno')

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Re: [R] The best solver for non-smooth functions?

2012-07-19 Thread Cren 

Roger Koenker-3 wrote
> 
> There are obviously a large variety of non-smooth problems;
> for CVAR problems, if by this you mean conditional value at
> risk portfolio problems, you can use modern interior point 
> linear programming methods.  Further details are here:
> 
>   http://www.econ.uiuc.edu/~roger/research/risk/risk.html
> 
> Roger Koenker
> rkoenker@

# Hi, Roger.

# Unfortunately that "C" does not stand for
# "Conditional" but "Credit"... which means that
# risk measure is obtained via Monte Carlo
# simulated scenarios in order to quantify the
# credit loss according to empirical transition
# matrix. Then I am afraid of every solver finding
# local maxima (or minima) because of some
# "jump" in Credit VaR surface function of
# portfolio weights :(


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Re: [R] The best solver for non-smooth functions?

2012-07-19 Thread Cren 

Hans W Borchers wrote
> 
> The most robust solver for non-smooth functions I know of in R is
> Nelder-Mead 
> in the 'dfoptim' package (that also allows for box constraints).
> 
> First throw out the equality constraint by using c(w1, w1, 1-w1-w2) as
> input. 
> This will enlarge the domain a bit, but comes out allright in the end.
> 
> sharpe2 <- function(w) {
>   w <- c(w[1], w[2], 1-w[1]-w[2])
>   - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
> }
> 
> nmkb(c(1/3,1/3), sharpe2, lower=c(0,0), upper=c(1,1))
> ## $par
> ## [1] 0.1425304 0.1425646
> ## $value
> ## [1] -0.03093439
> 
> This is still in the domain of definition, and is about the same optimum
> that 
> solnp() finds.
> 
> There are some more solvers, especially aimed at non-smooth functions, in
> the 
> making. For low-dimensional problems like this Nelder-Mead is a reasonable 
> choice.

# Thank you, I'll try it :)


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Re: [R] The best solver for non-smooth functions?

2012-07-19 Thread Cren 

Roger Koenker-3 wrote
> 
> There are obviously a large variety of non-smooth problems;
> for CVAR problems, if by this you mean conditional value at
> risk portfolio problems, you can use modern interior point 
> linear programming methods.  Further details are here:
> 
>   http://www.econ.uiuc.edu/~roger/research/risk/risk.html
> 
> Roger Koenker
> rkoenker@
> # Hi, Roger.
> 
> # Unfortunately that "C" does not stand for
> # "Conditional" but "Credit"... which means that
> # risk measure is obtained via Monte Carlo
> # simulated scenarios in order to quantify the
> # credit loss according to empirical transition
> # matrix. Then I am afraid of every solver finding
> # local maxima (or minima) because of some
> # "jump" in Credit VaR surface function of
> # portfolio weights :(
> 
> 
> 
> On Jul 18, 2012, at 3:09 PM, Cren wrote:
> 
>> # Whoops! I have just seen there's a little mistake
>> # in the 'sharpe' function, because I had to use
>> # 'w' array instead of 'ead' in the cm.CVaR function!
>> # This does not change the main features of my,
>> # but you should be aware of it
>> 
>> ---
>> 
>> # The function to be minimized
>> 
>> sharpe <- function(w) {
>>  - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
>> } 
>> 
>> # This becomes...
>> 
>> sharpe <- function(w) {
>>  - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
>> } 
>> 
>> # ...substituting 'ead' with 'w'.
>> 
>> --
>> View this message in context:
>> http://r.789695.n4.nabble.com/The-best-solver-for-non-smooth-functions-tp4636934p4636936.html
>> Sent from the R help mailing list archive at Nabble.com.
>> 
>> __
>> R-help@ mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
> 
> __
> R-help@ mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 


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Re: [R] The best solver for non-smooth functions?

2012-07-18 Thread Roger Koenker 
There are obviously a large variety of non-smooth problems;
for CVAR problems, if by this you mean conditional value at
risk portfolio problems, you can use modern interior point 
linear programming methods.  Further details are here:

http://www.econ.uiuc.edu/~roger/research/risk/risk.html

Roger Koenker
rkoen...@illinois.edu




On Jul 18, 2012, at 3:09 PM, Cren wrote:

> # Whoops! I have just seen there's a little mistake
> # in the 'sharpe' function, because I had to use
> # 'w' array instead of 'ead' in the cm.CVaR function!
> # This does not change the main features of my,
> # but you should be aware of it
> 
> ---
> 
> # The function to be minimized
> 
> sharpe <- function(w) {
>  - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
> } 
> 
> # This becomes...
> 
> sharpe <- function(w) {
>  - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
> } 
> 
> # ...substituting 'ead' with 'w'.
> 
> --
> View this message in context: 
> http://r.789695.n4.nabble.com/The-best-solver-for-non-smooth-functions-tp4636934p4636936.html
> Sent from the R help mailing list archive at Nabble.com.
> 
> __
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

__
R-help@r-project.org mailing list
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Re: [R] The best solver for non-smooth functions?

2012-07-18 Thread Hans W Borchers 
Cren  bancaakros.it> writes:
>

The most robust solver for non-smooth functions I know of in R is Nelder-Mead 
in the 'dfoptim' package (that also allows for box constraints).

First throw out the equality constraint by using c(w1, w1, 1-w1-w2) as input. 
This will enlarge the domain a bit, but comes out allright in the end.

sharpe2 <- function(w) {
w <- c(w[1], w[2], 1-w[1]-w[2])
  - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
}

nmkb(c(1/3,1/3), sharpe2, lower=c(0,0), upper=c(1,1))
## $par
## [1] 0.1425304 0.1425646
## $value
## [1] -0.03093439

This is still in the domain of definition, and is about the same optimum that 
solnp() finds.

There are some more solvers, especially aimed at non-smooth functions, in the 
making. For low-dimensional problems like this Nelder-Mead is a reasonable 
choice.


> # Whoops! I have just seen there's a little mistake
> # in the 'sharpe' function, because I had to use
> # 'w' array instead of 'ead' in the cm.CVaR function!
> # This does not change the main features of my,
> # but you should be aware of it
> 
> ---
> 
> # The function to be minimized
> 
> sharpe <- function(w) {
>   - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
> } 
> 
> # This becomes...
> 
> sharpe <- function(w) {
>   - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
> } 
> 
> # ...substituting 'ead' with 'w'.
>

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Re: [R] The best solver for non-smooth functions?

2012-07-18 Thread Cren 
# Whoops! I have just seen there's a little mistake
# in the 'sharpe' function, because I had to use
# 'w' array instead of 'ead' in the cm.CVaR function!
# This does not change the main features of my,
# but you should be aware of it

---

# The function to be minimized

sharpe <- function(w) {
  - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
} 

# This becomes...

sharpe <- function(w) {
  - (t(w) %*% y) / cm.CVaR(M, lgd, w, N, n, r, rho, alpha, rating)
} 

# ...substituting 'ead' with 'w'.

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[R] The best solver for non-smooth functions?

2012-07-18 Thread Cren 
# Hi all,

# consider the following code (please, run it:
# it's fully working and requires just few minutes
# to finish):

require(CreditMetrics)
require(clusterGeneration)
install.packages("Rdonlp2", repos= c("http://R-Forge.R-project.org";,
getOption("repos")))
install.packages("Rsolnp2", repos= c("http://R-Forge.R-project.org";,
getOption("repos")))
require(Rdonlp2)
require(Rsolnp)
require(Rsolnp2)

N <- 3
n <- 10
r <- 0.0025
ead <- rep(1/3,3)  
rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
lgd <- 0.99
rating <- c("BB", "BB", "BBB")  
firmnames <- c("firm 1", "firm 2", "firm 3")
alpha <- 0.99

# One year empirical migration matrix from Standard & Poor's website

rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
M <- matrix(c(90.81,  8.33,  0.68,  0.06,  0.08,  0.02,  0.01,   0.01,
  0.70, 90.65,  7.79,  0.64,  0.06,  0.13,  0.02,   0.01,
  0.09,  2.27, 91.05,  5.52,  0.74,  0.26,  0.01,   0.06,
  0.02,  0.33,  5.95, 85.93,  5.30,  1.17,  1.12,   0.18,
  0.03,  0.14,  0.67,  7.73, 80.53,  8.84,  1.00,   1.06,
  0.01,  0.11,  0.24,  0.43,  6.48, 83.46,  4.07,   5.20,
  0.21, 0,  0.22,  1.30,  2.38, 11.24, 64.86,  19.79,
  0, 0, 0, 0, 0, 0, 0, 100
)/100, 8, 8, dimnames = list(rc, rc), byrow = TRUE)

# Correlation matrix

rho <- rcorrmatrix(N) ; dimnames(rho) = list(firmnames, firmnames)

# Credit Value at Risk

cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)

# Risk neutral yield rates

Y <- cm.cs(M, lgd)
y <- c(Y[match(rating[1],rc)], Y[match(rating[2],rc)],
Y[match(rating[3],rc)]) ; y

# The function to be minimized

sharpe <- function(w) {
  - (t(w) %*% y) / cm.CVaR(M, lgd, ead, N, n, r, rho, alpha, rating)
}

# The linear constraints

constr <- function(w) {
  sum(w)
}

# Results' matrix (it's empty by now)

Results <- matrix(NA, nrow = 3, ncol = 4)
rownames(Results) <- list('donlp2', 'solnp', 'solnp2')
colnames(Results) <- list('w_1', 'w_2', 'w_3', 'Sharpe')

# See the differences between different solvers

rho
Results[1,1:3] <- round(donlp2(fn = sharpe, par = rep(1/N,N), par.lower =
rep(0,N), par.upper = rep(1,N), A = t(rep(1,N)), lin.lower = 1, lin.upper =
1)$par, 2)
Results[2,1:3] <- round(solnp(pars = rep(1/N,N), fun = sharpe, eqfun =
constr, eqB = 1, LB = rep(0,N), UB = rep(1,N))$pars, 2)
Results[3,1:3] <- round(solnp2(par = rep(1/N,N), fun = sharpe, eqfun =
constr, eqB = 1, LB = rep(0,N), UB = rep(1,N))$pars, 2)
for(i in 1:3) {
  Results[i,4] <- abs(sharpe(Results[i,1:3]))  
}
Results

# In fact the "sharpe" function I previously defined
# is not smooth because of the cm.CVaR function.
# If you change correlation matrix, ratings or yields
# you see how different solvers produce different
# parameters estimation.

# Then the main issue is: how may I know which is the
# best solver at all to deal with non-smooth functions
# such as this one?

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