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
>
>
>
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>
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