Value of liquidity

Thanks for everyone's thoughtful responses.  Mark, I checked out the
paper you referred me to it's a pretty good read and is available on
ssrn title "portfolio rebalancing: a test of the markwiz-van dijk
heuristic".  I am still struggling with the Monte-Carlo simulation so
I'm taking your advice Brian and posting some code.  Maybe someone on
this list can give me some guidance as to where I'm going wrong.  The
reason I think that I'm making a mistake is that the code below
simulates an equally weighted portfolio with three assets.  The problem
is that the average simulated portfolio return is not the same as the
equally weighted return of the underlying assets.  I'm not sure if this
is because I'm misinterpreting the drift term or because there is an
error in my code.  Any guidance would be greatly appreciated.

Thanks,

Ben  

monteCarlo=function(spot,drift,T,nSteps,covmat,nSims=10000){
	##this is an alteration of work done by Kris Kumar
	##spot = Vector of asset prices at t=0
	##drift = Foreign risk - domestic risk for each asset
	##T = total time for monte carlo simulation
	##nSteps = number of steps (This should be more important for
path dependent options
	##covmat= the variance covariance matrix (should be number of
assets squared)
	##nSims = number of monte carlo simulations should use 10,000
according to haug

	nAssets=nrow(covmat)
	path=array(0,c(nSteps,nSims,nAssets))
	deltaT=T/nSteps
	shocks=array(0,c(nSteps+1,nSims,nAssets))
	for(i in 1:nAssets){
		shocks[1,,i]=spot[i]
	}
	muDt=drift*deltaT
	covmat=covmat*deltaT

randmat=matrix(rnorm.sobol(nSims,nAssets*nSteps),ncol=nAssets*nSteps)
	cholmat=chol(covmat)
	for(k in 1:nSims){
		randmatt=matrix(randmat[k,],nrow=nSteps,ncol=nAssets)
%*% cholmat
		for(l in 1:nSteps){
			for(m in 1:nAssets){
shocks[l+1,k,m]=shocks[l,k,m]*exp(muDt[m]+randmatt[l,m])
			path[l,k,m]=shocks[l+1,k,m]
			}
		}
	}	
	return(path)
}

###Make up some data for ret std correl
expret=c(.09,.1,.01)
stdev=c(.17,.195,.055)
correlation=matrix(c(1,.8,.5,.8,1,.5,.5,.5,1),nrow=3,ncol=3)
###Calculate covariance matrix	
covmat=matrix(ncol=3,nrow=3)
for(i in 1:nrow(correlation)){
	for(j in 1:ncol(correlation)){
		covmat[i,j]=correlation[i,j]*stdev[i]*stdev[j]
	}
}

price=c(100,100,100)
T=1
nsteps=1
nsims=10000
path=monteCarlo(price,expret,T,nsteps,covmat,nsims)
weights=c(1/3,1/3,1/3)
portPath=path[1,,] %*% weights

averagePortReturn=mean(portPath)
expectedPortReturn=mean(expret)

-----Original Message-----
From: markleeds at verizon.net [mailto:markleeds at verizon.net] 
Sent: Thursday, October 16, 2008 2:57 PM
To: Chiquoine, Ben
Cc: r-sig-finance at stat.math.ethz.ch
Subject: RE: [R-SIG-Finance] Value of liquidity

  hi: i can't answer your questions below but Markovwtz-Van Dijk  ( 
spelling on Van Djil may be incorrect ) came up with some heuristic a 
few years back for balancing the cost of rebalancing versus the expected

gain in return  from rebalancing. mark kritzman ( state street ) has a 
powerpoint presentation that gives an overview of the idea ( that's on 
the net. i can find it , if you can't ) but I don't know the title of 
the original paper nor the journal it's in, assuming it was published 
somewhere. if you find it, can you let me know where it is. thanks.

Value of liquidity

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