[R] Calculating the Sharpe ratio

[Bernd Dittmann]

Hi Mark,

thanks for your email.
I used your formula for cumul. returns and plugged them into sharpe:

 > mysharpe <- function(x){
+ return(sharpe(cret(x), r=0, scale=1))
+ }

whereby "cret" is my cumul. returns function as defined by:

 > cret
function(x){
cumprod(diff(log(x))+1)-1
}

For the index series "Index" I obtain a sharpe ratio (r=0 and scale=1) of:

 > mysharpe(Index)
[1] 0.8836429

Do you reckon this result and the method above are correct?

Many thanks in advance!

Bernd




Leeds, Mark (IED) schrieb:
> If the doc says to use cumulated and you didn't, then I supsect the call
> to shaprp in
> Tseries is not correct.  Also, to get PercetnREturns, I hope you did
> diff(log(series))
> Where series is an object containing prices. It's not so clear
> Form your email.
>
> If you want to send in cumulative returns ( which
> You should do if the doc says to ) you just take the returns ( by doing
> above )
> and then , add 1 to each element, do  a cumprod and then subtract 1 so
> something like :
>
> rtns<-diff(log(priceseries)
> oneplusrtns<-1+rtns
> cumprodrtns<-cumprod(oneplusreturns)
>
> cumrtns<-cumprodrtns-1.
>
> Then, the elements in cumrtns represent the cumulative reeturn upto that
> point.
>
> But, test it out with an easy example to make sure because I didn't.
>
>
>
>
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Bernd Dittmann
> Sent: Monday, February 19, 2007 8:39 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] Calculating the Sharpe ratio
>
> Hi useRs,
>
> I am trying to calculate the Sharpe ratio with "sharpe" of the library
> "tseries".
>
> The documentation requires the univariate time series to be a
> portfolio's cumulated returns. In this case, the example given
>
> data(EuStockMarkets)
> dax <- log(EuStockMarkets[,"FTSE"])
>
> is however not the cumulated returns but rather the daily returns of the
> FTSE stock index.
>
> Is this way of calculating the Sharpe ratio correct?
>
> Here are my own data:
>
> year    Index    PercentReturns
> 1985    117    0.091
> 1986    129.9    0.11
> 1987    149.9    0.154
> 1988    184.8    0.233
> 1989    223.1    0.208
> 1990    223.2    0
> 1991    220.5    -0.012
> 1992    208.1    -0.056
> 1993    202.1    -0.029
> 1994    203.1    0.005
> 1995    199.6    -0.017
> 1996    208.6    0.045
> 1997    221.7    0.063
> 1998    233.7    0.054
> 1999    250.5    0.072
> 2000    275.1    0.098
> 2001    298.6    0.085
> 2002    350.6    0.174
> 2003    429.1    0.224
> 2004    507.6    0.183
> 2005    536.6    0.057
> 2006    581.3    0.083
>
>
> I calculated the Sharpe ratio in two different ways:
> (1) using natural logs as approximation of % returns, using "sharpe" of
> "tseries".
> (2) using the % returns using a variation the "sharpe" function.
>
> In both cases I used the risk free rate r=0 and scale=1 since I am using
> annual data already.
>
> My results:
>
> METHOD 1: "sharpe":
>
>  > index <- log(Index)
>  > sharpe(index, scale=1)
> [1] 0.9614212
>
>
>
> METHOD 2: my own %-based formula:
>
>  > mysharp
> function(x, r=0, scale=sqrt(250))
> {
> if (NCOL(x) > 1)
> stop("x is not a vector or univariate time series") if (any(is.na(x)))
> stop("NAs in x") if (NROW(x) ==1)
> return(NA)
> else{
> return(scale * (mean(x) - r)/sd(x))
> }
> }
>
>
>
>  > mysharp(PercentReturns, scale=1)
> [1] 0.982531
>
>
> Both Sharp ratios differ only slightly since logs approximate percentage
> changes (returns).
>
>
> Are both methods correct, esp. since I am NOT using cumulated returns as
>
> the manual says?
>
> If cumulated returns were supposed to be used, could I cumulate the 
> %-returns with "cumsum(PercentReturns)"?
>
> Many thanks in advance!
>
> Bernd
>
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