Calculating Portfolio Standard deviation

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.psych at gmail.com> wrote:

From: Joshua Wiley <jwiley.psych at gmail.com>
Subject: Re: [R] Calculating Portfolio Standard deviation
To: "Amelia Vettori" <amelia_vettori at yahoo.co.nz>
Cc: "r-help at r-project.org" <r-help at 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_vettori at 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]]