Re: [R] Calculating Portfolio Standard deviation

[Patrick Burns]

That should be the variance matrix
of returns, not prices.  (I have a
blog post on this already written
that will be published later this week.)

On 10/01/2011 09:05, Joshua Wiley wrote:

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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--
Patrick Burns
pbu...@pburns.seanet.com
twitter: @portfolioprobe
http://www.portfolioprobe.com/blog
http://www.burns-stat.com
(home of 'Some hints for the R beginner'
and 'The R Inferno')

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PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.