[R-SIG-Finance] tseries and efficient frontier

[John P. Burkett]

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
>>
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> 


-- 
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