lossfunc | R Documentation |
This functions allows for the calculation of loss functions for the selection of models.
lossfunc(obj = list(Loss = NULL, ES = NULL), beta = 1e-04)
obj |
a list that contains the following elements:
Please note that a list returned by the |
beta |
a single numeric value; a measure for the opportunity cost of
capital; default is |
Given a negative return series obj$Loss
, the corresponding Expected
Shortfall (ES) estimates obj$ES
and a parameter beta
that
defines the opportunity cost of capital, four different definitions of loss
functions are considered.
Let K
be the number of observations and r_t
the observed return series.
Following Sarma et al. (2003)
l_{t,1} = \{\widehat{ES}_t (\alpha) + r_t \}^2,
if -r_t > \widehat{ES}_t(\alpha)
l_{t,1} = \beta * \widehat{ES}_t (\alpha),
otherwise,
is a suitable loss function (firm's loss function), where \beta
is the
opportunity cost of capital. The regulatory loss function
is identical to the firm's loss function with the exception of
l_{t,1} = 0
for -r_t \leq \widehat{ES}_t (\alpha)
.
Abad et al. (2015) proposed another loss function
l_{t,a} = \{\widehat{ES}_t(\alpha) + r_t\}^2,
if -r_t > \widehat{ES}_t(\alpha)
l_{t,a} = \beta * (\widehat{ES}_t (\alpha) + r_t),
otherwise,
that, however, also considers opportunity costs for r_t > 0
. An adjustment has
been proposed by Feng. Following his idea,
l_{t,2} = \{\widehat{ES}_t(\alpha) + r_t\}^2,
if -r_t > \widehat{ES}_t (\alpha)
l_{t,2} = \beta * \min\{\widehat{ES}_t(\alpha) + r_t, \widehat{ES}_t(\alpha)\},
otherwise,
should be considered as a compromise of the regulatory and the firm's loss
functions. Note that instead of the ES, also a series of Value-at-Risk values
can be inserted for the argument obj$ES
. However this is not possible if
a list returned by the varcast
function is directly passed to
lossfunc
.
an S3 class object, which is a list of
Regulatory loss function.
Firm's loss function following Sarma et al. (2003).
Loss function following Abad et al. (2015).
Feng's loss function. A compromise of regulatory and firm's loss function.
Sebastian Letmathe (Scientific Employee) (Department of Economics,
Paderborn University)
Dominik Schulz (Scientific Employee) (Department of Economics,
Paderborn University),
Abad, P., Muela, S. B., & MartÃn, C. L. (2015). The role of the loss function in value-at-risk comparisons. The Journal of Risk Model Validation, 9(1), 1-19.
Sarma, M., Thomas, S., & Shah, A. (2003). Selection of Value-at-Risk models. Journal of Forecasting, 22(4), 337-358.
# Example for Walmart Inc. (WMT)
prices <- WMT$price.close
output <- varcast(prices)
Loss <- -output$ret.out
ES <- output$ES
loss.data <- list(Loss = Loss, ES = ES)
lossfunc(loss.data)
# directly passing an output object of 'varcast()' to 'lossfunc()'
x <- WMT$price.close
output <- varcast(prices)
lossfunc(output)
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