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]]
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]] > > ______________________________________________ > R-help at 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.
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)> VdatABC 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@gmail.com> wrote: From: Joshua Wiley <jwiley.psych@gmail.com> Subject: Re: [R] Calculating Portfolio Standard deviation To: "Amelia Vettori" <amelia_vettori@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_vettori@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.[[alternative HTML version deleted]]