returns: Computing Returns and Inverse Transformation

In qrmtools: Tools for Quantitative Risk Management

Computing Returns and Inverse Transformation

Description

Compute log-returns, simple returns and basic differences (or the inverse operations) from given data.

Usage

returns(x, method = c("logarithmic", "simple", "diff"), inverse = FALSE,
        start, start.date)
returns_qrmtools(x, method = c("logarithmic", "simple", "diff"),
                 inverse = FALSE, start, start.date)

Arguments

x	matrix or vector (possibly a xts object) to be turned into returns (if inverse = FALSE) or returns to be turned into the original data (if inverse = TRUE).
method	character string indicating the method to be used (log-returns (logarithmic changes), simple returns (relative changes), or basic differences). Note that this can also be a vector of such methods of length equal to the number of columns of x.
inverse	logical indicating whether the inverse transformation (data from given returns) shall be computed (if TRUE, this requires start to be specified).
start	if inverse = TRUE, the last available value of the time series to be constructed from the given returns x.
start.date	character or Date object to be used as the date corresponding to the value start; currently only used for xts objects.

Details

If inverse = FALSE and x is an xts object, the returned object is an xts, too.

Note that the R package timeSeries also contains a function returns() (and hence the order in which timeSeries and qrmtools are loaded matters to get the right returns()). For this reason, returns_qrmtools() is an alias for returns() from qrmtools.

Value

vector or matrix with the same number of columns as x just one row less if inverse = FALSE or one row more if inverse = TRUE.

Author(s)

Marius Hofert

Examples

## Generate two paths of a geometric Brownian motion
S0 <- 10 # current stock price S_0
r <- 0.01 # risk-free annual interest rate
sig <- 0.2 # (constant) annual volatility
T <- 2 # maturity in years
N <- 250 # business days per year
t <- 1:(N*T) # time points to be sampled
npath <- 2 # number of paths
set.seed(271) # for reproducibility
S <- replicate(npath, S0 * exp(cumsum(rnorm(N*T, # sample paths of S_t
                                            mean = (r-sig^2/2)/N,
                                            sd = sqrt((sig^2)/N))))) # (N*T, npath)

## Turn into xts objects
library(xts)
sdate <- as.Date("2000-05-02") # start date
S.  <- as.xts(S, order.by = seq(sdate, length.out = N*T, by = "1 week"))
plot(S.[,1], main = "Stock 1")
plot(S.[,2], main = "Stock 2")


### Log-returns ################################################################

## Based on S[,1]
X <- returns(S[,1]) # build log-returns (one element less than S)
Y <- returns(X, inverse = TRUE, start = S[1,1]) # transform back
stopifnot(all.equal(Y, S[,1]))

## Based on S
X <- returns(S) # build log-returns (one element less than S)
Y <- returns(X, inverse = TRUE, start = S[1,]) # transform back
stopifnot(all.equal(Y, S))

## Based on S.[,1]
X <- returns(S.[,1])
Y <- returns(X, inverse = TRUE, start = S.[1,1], start.date = sdate)
stopifnot(all.equal(Y, S.[,1], check.attributes = FALSE))

## Based on S.
X <- returns(S.)
Y <- returns(X, inverse = TRUE, start = S.[1], start.date = sdate)
stopifnot(all.equal(Y, S., check.attributes = FALSE))

## Sign-adjusted (negative) log-returns
X <- -returns(S) # build -log-returns
Y <- returns(-X, inverse = TRUE, start = S[1,]) # transform back
stopifnot(all.equal(Y, S))


### Simple returns #############################################################

## Simple returns based on S
X <- returns(S, method = "simple")
Y <- returns(X, method = "simple", inverse = TRUE, start = S[1,])
stopifnot(all.equal(Y, S))

## Simple returns based on S.
X <- returns(S., method = "simple")
Y <- returns(X, method = "simple", inverse = TRUE, start = S.[1,],
             start.date = sdate)
stopifnot(all.equal(Y, S., check.attributes = FALSE))

## Sign-adjusted (negative) simple returns
X <- -returns(S, method = "simple")
Y <- returns(-X, method = "simple", inverse = TRUE, start = S[1,])
stopifnot(all.equal(Y, S))


### Basic differences ##########################################################

## Basic differences based on S
X <- returns(S, method = "diff")
Y <- returns(X, method = "diff", inverse = TRUE, start = S[1,])
stopifnot(all.equal(Y, S))

## Basic differences based on S.
X <- returns(S., method = "diff")
Y <- returns(X, method = "diff", inverse = TRUE, start = S.[1,],
             start.date = sdate)
stopifnot(all.equal(Y, S., check.attributes = FALSE))

## Sign-adjusted (negative) basic differences
X <- -returns(S, method = "diff")
Y <- returns(-X, method = "diff", inverse = TRUE, start = S[1,])
stopifnot(all.equal(Y, S))


### Vector-case of 'method' ####################################################

X <- returns(S., method = c("logarithmic", "diff"))
Y <- returns(X, method = c("logarithmic", "diff"), inverse = TRUE, start = S.[1,],
             start.date = sdate)
stopifnot(all.equal(Y, S., check.attributes = FALSE))

qrmtools documentation built on March 19, 2024, 3:08 a.m.