[R-SIG-Finance] tseries and efficient frontier
John P. Burkett
burkett at uri.edu
Mon May 5 04:04:36 CEST 2008
Thanks, Charles! You are absolutely correct. Inserting the option
shorts=TRUE produces a symmetrical curve. I'm very grateful to you for
calling this to my attention.
Best regards,
John
Charles Ward wrote:
> I think the reason is that the function "portfolio.optim" has the
> default option, short=FALSE. If you use the option short=TRUE you
> should achieve the symmetrical shape of the efficient frontier.
> When you constain the portfolio only to accept positive weights of
> each asset, there will generally be bumps and asymmetries in the
> efficient frontier.
> The textbook examples usually assume short selling is allowed.
> Charles Ward
>
> 2008/5/4 John P. Burkett <burkett at uri.edu>:
>> Yesterday I reported that my effort to compute and plot an efficient
>> frontier using the fPortfolio package had produced an asymmetric curve
>> rather than the anticipated hyperbola. Using the same data, I have now tried
>> computing and plotting an efficient frontier using the tseries package. The
>> result is again an asymmetric curve.
>>
>> My code is as follows:
>> library(fPortfolio)
>> Data = as.timeSeries(data(smallcap.ts))
>> Data = Data[, c("BKE", "GG", "GYMB", "KRON")]
>> Data
>> x <- as.matrix(Data)
>> vcvd <- cov(Data)
>> pmv <- rep(0,100)
>> psv <- rep(0,100)
>> minr <- min(mean(Data))
>> maxr <- max(mean(Data))
>> vcv <- cov(x)
>> iv <- 0:99
>> mrv <- minr*(1-iv/99) + maxr*(iv/99)
>> pmv[1] <- min(mean(Data))
>> pmv[100] <-max(mean(Data))
>> psv[1] <- 0.2226543
>> psv[100] <- 0.1674082
>> for (i in 2:99) {
>> pmv[i] <- portfolio.optim(x, pm = mrv[i], covmat = vcv)$pm
>> psv[i] <- portfolio.optim(x, pm = mrv[i], covmat = vcv)$ps
>> }
>> plot(psv,pmv)
>>
>> On the resulting curve, risk is minimized at point 62. But the curve is not
>> symmetric around this point. (Moving 37 points in either direction from this
>> point raises risk by the same amount. In contrast moving 37 points back
>> lowers the mean return far less than moving 37 points forward raises the
>> mean return.) I wonder whether this asymmetry is a bug or an accurate
>> portrayal of a type of efficiency frontier different from the hyperbolas
>> that appear in textbooks. I would be most grateful for suggestions about how
>> to resolve this puzzle.
>>
>> Best regards,
>> John
>>
>>
>> --
>> John P. Burkett
>> Department of Environmental and Natural Resource Economics
>> and Department of Economics
>> University of Rhode Island
>> Kingston, RI 02881-0808
>> USA
>>
>> phone (401) 874-9195
>>
>> _______________________________________________
>> R-SIG-Finance at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
>> -- Subscriber-posting only.
>> -- If you want to post, subscribe first.
>>
>
--
John P. Burkett
Department of Environmental and Natural Resource Economics
and Department of Economics
University of Rhode Island
Kingston, RI 02881-0808
USA
phone (401) 874-9195
More information about the R-SIG-Finance
mailing list