Dear Amelia,
I find it hard to believe I'm not reinventing the wheel here, but
here's a little function. If no weights are specified it uses all 1s.
## Define function
lvar <- function(x, weights, na.rm = TRUE) {
if (missing(weights)) {
weights <- rep(1, ncol(x))
}
covmat <- var(x = x, na.rm = na.rm)
utc <- upper.tri(covmat)
wt.var <- sum(diag(covmat) * weights^2)
wt.cov <- sum(weights[row(covmat)[utc]] *
weights[col(covmat)[utc]] *
covmat[utc])
variance <- wt.var + 2 * wt.cov
return(variance)
}
## example with weights
lvar(x = prices_df, weights = c(0.10, 0.25, 0.20, 0.45))
HTH,
Josh
On Mon, Jan 10, 2011 at 3:14 AM, Amelia Vettori
<amelia_vett...@yahoo.co.nz> wrote:
>
> Dear Patric and Joshua sirs,
>
> Thanks a lot for the great solution. This code works perfectly when we are
> assigning equal weights, however problem is I do need to use the weights
> assigned.
>
> And yes I will be calculating the co-variance for the price returns only.
> Here for an example sake I had taken the prices. I am working on equity, bond
> and currency portfolio and since the valuations methods differ in each case,
> I am for the time being dealing separately with these instruments. Once, the
> portfolio value series is ready, I will be taking the returns and then
> calculate the covariance matrix etc and proceed on. Just for the sake of
> simplicity, I am as an example taking prices rather than the return on
> prices. But sir, thanks a lot for bringing this to notice as others may
> follow this thread in future.
>
> As regards the R code provided by Joshua sir, there is no problem in
> assigning the weights to the diagonal elements as I had done below
>
> diag_elements = sum(diag(Vdat)*weights^2). However, the problem does exist
> for the elemnts appearing in the upper covariance matrix (i.e.
> Vdat[upper.tri(Vdat)] ). Perhaps one may have to use the loop.
>
> # For Non diagonal elements
>
> weights = c(0.10, 0.25, 0.20, 0.45)
>
> > Vdat
> ABC DEF GHI JKL
> ABC 11.2111111 -0.7111111 -1.833333 -11.011111
> DEF -0.7111111 15.6000000 6.222222 4.511111
> GHI -1.8333333 6.2222222 24.722222 -21.055556
> JKL -11.0111111 4.5111111 -21.055556 87.211111
>
>
> B = NULL
>
> for(i in 1:4)
> {
> for (j in 1:4)
> {
> if(i!=j)
> {
>
> B[i] = weights[i]*weights[j]*Vdat[i,j]
> }
> }
> }
>
> B # The idea is the sum(B) would give me the weighted non-diagonal
> elements. This gives me
>
> > B
> [1] -0.4955 0.5075 -1.8950 -1.8950
>
> However, actually I should be getting
>
> -0.017778, -0.036667, -0.4955, 0.31111, 0.5075, -1.8950
>
> That's because when I consider (1,2), (1,3) or(1,4) it stores the value for
> B[1] only once and likewise.
>
> Kindly guide.
>
>
> regards
>
> Amelia
>
> --- On Mon, 10/1/11, Joshua Wiley <jwiley.ps...@gmail.com> wrote:
>
> From: Joshua Wiley <jwiley.ps...@gmail.com>
> Subject: Re: [R] Calculating Portfolio Standard deviation
> To: "Amelia Vettori" <amelia_vett...@yahoo.co.nz>
> Cc: "r-help@r-project.org" <r-help@r-project.org>
> Received: Monday, 10 January, 2011, 9:05 AM
>
> Dear Amelia,
>
> If you have the actual data you should be able to use the variance covariance
> matrix to simplify this
>
> Vdat <- cov(prices_df)
>
> sum(diag(Vdat)) + 2*Vdat[upper.tri(Vdat)]
>
> By using covariances instead of correlations you do not need to multiply by
> he standard deviations and by using variances there's no need to square. The
> only trick would be adding your weights back in. See ?diag and ?upper.tri
> and ?vcov for relevant documentation.
>
> Cheers,
>
> Josh
>
> On Jan 10, 2011, at 0:26, Amelia Vettori <amelia_vett...@yahoo.co.nz> wrote:
>
> > Dear R helpers
> >
> > I have following data
> >
> > stocks <- c("ABC", "DEF", "GHI", "JKL")
> >
> > prices_df <- data.frame(ABC = c(17,24,15,22,16,22,17,22,15,19),
> > DEF =
> >c(22,28,20,20,28,26,29,18,24,21),
> > GHI =
> >c(32,27,32,36,37,37,34,23,25,32),
> >
> > JKL =
> >c(47,60,60,43,62,38,44,53,61,41))
> >
> > sd_prices <- c(3.3483,3.9497,4.9721,9.3387) # standard deviations
> > say(sd1, sd2, sd3, sd4)
> >
> > weights <- c(0.10, 0.25, 0.20, 0.45) # say (w1, w2, w3, w4)
> >
> > I need to calculate the standard deviation of the portfolio. The formula is
> >
> > stdev_portfolio = sqrt((w1*sd1)^2+(w2*sd2)^2+(w3*sd3)^2+(w4*sd4)^2 +
> > 2*w1*w2*sd1*sd2*correlation(ABC, DEF)+
> >
> > 2*w1*w3*sd1*sd3*correlation(ABC, GHI)+
> > 2*w1*w4*sd1*sd4*correlation(ABC, JKL)+
> > 2*w2*w3*sd2*sd3*correlation(DEF, GHI)+
> > 2*w2*w4*sd2*sd4*correlation(DEF, JKL)+
> > 2*w3*w4*sd3*sd4*correlation(GHI, JKL))
> >
> >
> >
> > OR if we define
> >
> > P = sd_prices*weights
> >
> > I need to calculate
> >
> > stdev_portfolio = sqrt((P1)^2+(P2)^2+(P3)^2+(P4)^2 +
> > 2*P1*P2*correlation(ABC, DEF)+
> > 2*P1*P3*correlation(ABC, GHI)+
> > 2*P1*P4*correlation(ABC, JKL)+
> > 2*P2*P3*correlation(DEF,
> > GHI)+
> > 2*P2*P4*correlation(DEF, JKL)+
> > 2*P3*P4*correlation(GHI, JKL))
> >
> > In reality I will be dealing with not 4, but many stocks and hence I can't
> > generalize this as
> >
> > stdev_portfolio = sqrt((P[1])^2+(P[2])^2+(P[3])^2+(P[4)^2 +
> > 2*P[1]*P[2]*correlation(ABC, DEF)+
> > 2*P1*P3*correlation(ABC,
> > GHI)+
> > 2*P1*P4*correlation(ABC, JKL)+
> > 2*P2*P3*correlation(DEF, GHI)+
> > 2*P2*P4*correlation(DEF, JKL)+
> > 2*P3*P4*correlation(GHI, JKL))
> >
> > Kindly advise as to how do I
> > calculate the portfolio standard deviation?
> >
> > Thanking in advance
> >
> > Amelia Vettori
> >
> >
> >
> > [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
>
--
Joshua Wiley
Ph.D. Student, Health Psychology
University of California, Los Angeles
http://www.joshuawiley.com/
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