PerformanceAnalytics - Style Analysis

Guys,

Not sure about any package updates but based on Eric's description, I think the constrained regression looks something like this:


conReg = function(R.fund,R.style)
{
   # make LHS and RHS matrices
   y = as.matrix(R.fund)
   x = as.matrix(R.style)

   # subtract x1 from both sides for constrained regression
   x1 = x[,1]
   y.new = y - x1
   x.new = x[,-1] - x1

   # perform constrained regression
   lm.con = lm(y.new ~ x.new - 1)

   # solve for b1.hat
   b1.hat = tail(cumsum(c(1,-1*coef(lm.con))),1)
   con.coef = c(b1.hat,coef(lm.con))
   names(con.coef) = colnames(x)

   # calc fitted values
   y.hat = x %*% con.coef

   # compute R2
   resid = y - y.hat
   tss<- sum(y^2)
   rss<- sum(resid^2)
   R2 = 1-rss/tss

   # return results
   con.mod = list(coefficients = con.coef,fitted.values=y.hat,residuals=resid,r.squared=R2)
   return(con.mod)
}

# compare constrained regression with quadratic programming
data(edhec)
data(managers)
sf = style.fit(managers[97:132,2,drop=FALSE],edhec[85:120,], method="constrained", leverage=FALSE)
cr = conReg(R.fund=managers[97:132,2,drop=FALSE],R.style=edhec[85:120,])
par(mfrow=c(2,1))
barplot(sf$weights[,1],names.arg=rownames(sf$weights),las=2,cex.names=0.5)
barplot(cr$coefficients,las=2,cex.names=0.5)


Perhaps this will help you out in the near term.

Best,

-- G



-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch [mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Thomas Etheber
Sent: Tuesday, June 29, 2010 3:06 AM
To: Eric Zivot
Cc: r-sig-finance at stat.math.ethz.ch; brian at braverock.com
Subject: Re: [R-SIG-Finance] PerformanceAnalytics - Style Analysis

Dear Eric,
dear Brian,

thank you for your helpful comments and your regression example below. I
just updated my R distribution and I am now running:

R:  version 2.11.1 (2010-05-31)
PerformanceAnalytics: version 1.0.2.1

It seems that your bugfix for the constrained StyleAnalyiss is not yet
included in the new PerformanceAnalytics. Maybe the timespan between
your fix and the release of PerformanceAnalytics 1.0.2.1 in mid April
was too short to include it.

Eric, if you have fixed the code already, could you please send it to
me? Maybe I can include the code in my actual project, so that I don't
have to wait for the next release of the package.

Regards,
Thomas



Am 23.03.2010 18:59, schrieb Eric Zivot:
   

You are right. The correct way to enforce that the regression coefficients
sum to unity is to impose this in the regression instead of just normalizing
the coefficients to sum to unity. It is not difficult to do this because it
is a linear restriction and the restriction can be substituted into the
linear regression to create another linear regression. I was supposed to add
this fix to the style.fit() function last year. I'll do it now and send the
fix off to Brian so he can put it in the PerformanceAnalytics package.
Briefly, consider the simple linear regression

Y = x1*b1 + x2*b2 + e

The restriction to impose is b1 + b2 = 1. Equivalently, b1 = 1 - b2.
Substituting into the regression gives

Y = x1*(1 - b2) + x2*b2 + e = x1 + b2*(x2 - x1) + e =>   Y - x1 = b2*(x2 - x1)
+ e

Therefore, the linear regression to run to impose the restriction b1+b2 = 1
is

(Y - x1) = b2*(x2 - x1) + e

Once you have b2.hat, then just solve for b1 using the constraint: b1.hat =
1 - b2.hat. (Note that it doesn't matter if you define the restriction in
terms of b1 = 1 - b2 or b2 = 1 - b1.)  Of course, to get the right R2 you
have to base it on Y as the dependent variable and not Y - x1. That is,
compute the R2 from the fitted values

Y.hat = b1.hat*x1 + b2.hat*x2

Where b1.hat and b2.hat are the restricted least squares coefficients.

Eric Zivot                  			
Professor and Gary Waterman Distinguished Scholar
Department of Economics
Adjunct Professor of Finance
Adjunct Professor of Statistics
Box 353330                  email:  ezivot at u.washington.edu
University of Washington    phone:  206-543-6715
Seattle, WA 98195-3330
www:  http://faculty.washington.edu/ezivot




-----Original Message-----
From: r-sig-finance-bounces at stat.math.ethz.ch
[mailto:r-sig-finance-bounces at stat.math.ethz.ch] On Behalf Of Thomas Etheber
Sent: Tuesday, March 23, 2010 4:03 AM
To: r-sig-finance at stat.math.ethz.ch
Subject: [R-SIG-Finance] PerformanceAnalytics - Style Analysis

Dear List,

I had a look at the code of the PerformanceAnalytics package and I use
this package on a regular basis.

The style.fit function for Style Analysis provides thrree supported
methods, which can be chosen via a parameter. I am talking of the
normalized method here. This method requires the regression coefficients
to sum to 1.
Indeed the code in Version 1.0.0 says something like this:

[... Default implementation ...]
column.weights = as.data.frame(coef(column.lm))
[...]
   if (method == "normalized") {
                  column.weights = column.weights/sum(column.weights)
   }

I suppose here we are just scaling the coefficients to sum to 1, in my
view the regression should a priori deal with this restriction (some
sort of constrained regression or the like).
At least if you look at Tabel 2 of Sharpe (1992) the coefficients do not
support the actual implementation and I think somebody might want to
have a look at this code fragment.
Unfortunately I do not know how to implement this kind of restricted
regression in R, but I believe there are already ways of doing this.
Perhaps somebody from the list can guide us to the right direction.

Anyway great thx to the authors of this packkage!
Thomas

PS: In Stata the right command seems to be cnsreg.