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<p class="MsoNormal">Hi,</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">I am new to using R for optimisation and I am trying to set up a simple portfolio minimum variance optimisation with turnover constraints, but am having some difficulty setting up the problem correctly. I would really appreciate any help.
I am trying two approaches one using the Rsolnp library and the other using the the parma library, but am having trouble with both.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Using Rsolnp I am having trouble getting the optimisation to converge, but this may be that the problem is poorly conditioned but please advise if the formulation seems correct.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-family:"Courier New"">ineq.fun.turnover <- function (x, sigma, wInit)
</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">{</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> return(sum(abs(x - wInit)))
</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">}</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> </span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">obj.fun <- function(x, sigma, wInit)</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">{</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> return(as.numeric(x%*%sigma%*%x))</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">}</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> </span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">eq.fun <- function(x,sigma,wInit)</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">{</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> return(sum(x))</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">}</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> </span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">tst <- solnp(initWeights, fun=obj.fun, eqfun=eq.fun, eqB = 1.0, ineqfun = ineq.fun.turnover,</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> ineqLB = 0.0, ineqUB = 0.2, LB = rep(0,numberOfSecurities), UB = rep(0.1,numberOfSecurities),</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> sigma = covarMatx, wInit = initWeights)</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Where <span style="font-family:"Courier New"">initWeights </span>
is a vector of length <span style="font-family:"Courier New"">numberOfSecurities</span>, and the
<span style="font-family:"Courier New"">covarMatx</span> is a covariance Matrix (generated from a factor model) of dimensions
<span style="font-family:"Courier New"">numberOfSecurities</span> by <span style="font-family:"Courier New"">
numberOfSecurities</span>.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Using <span style="font-family:"Courier New"">parma</span>, I cannot seem to get
<span style="font-family:"Courier New"">parmaspec</span> to recognise the turnover constraint inequality functions (using the custom ones in the library), so I am guessing I am using incompatible parameters…. ?</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-family:"Courier New"">servars = list()</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">uservars$turnover <- 0.2</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New"">uservars$wold <- initWeights</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"><span style="font-family:"Courier New"">spec2 <- parmaspec(S = covarMatx, LB = lowerBounds, UB = upperBounds,</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> risk = "EV", riskType = "minrisk",
</span></p>
<p class="MsoNormal"><span style="font-family:"Courier New""> ineqfun = list(ineqfun.turnover.min), ineqgrad = list(ineqjac.turnover.min), uservars = uservars)</span></p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">It simply tries to solve the QP min risk problem ignoring the turnover inequality.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Thank you,</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal">Graham.</p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal"> </p>
<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="color:#00457C">Graham Ewen</span></b><span style="font-size:10.0pt; color:gray"><br>
BlueCrest Capital Management (UK) LLP<br>
40 Grosvenor Place, London, SW1X 7AW, United Kingdom<br>
<b>T</b> +44 20 3180 3530<br>
</span><span style="font-size:10.0pt"><a href="mailto:graham.ewen@bluecrestcapital.com"><span style="color:blue">graham.ewen@bluecrestcapital.com</span></a><span style="color:gray"> </span></span><span style="color:gray">
</span><span style="font-size:10.0pt; color:gray"></span></p>
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<p class="MsoNormal"> </p>
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