robRiskBudget: Simple and Robust Risk Budgeting with Expected Shortfall

Description Usage Arguments Details Value Author(s) References Examples

View source: R/robRiskBudget.R

Description

This function implements the Philips and Liu method to compute an optimal set of risk budgets. It takes into account both the volatility and the tail risk of strategies to create a portfolio with a targeted level of volatility but with a lower level of tail risk than achieved by a mean-variance risk budget. One of the option it provides is the option to average all off diagonal entries in the correlation matrix, and with this option in use, it works particularly well with weakly correlated strategies, as one often finds in multi-strategy hedge funds and absolute return portfolios.

Usage

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robRiskBudget(returns = NULL, rf = 0, ER = NULL, IR = NULL, TE = NULL,
  corMat = NULL, ES = NULL, ESMethod = c("modified", "gaussian",
  "historical"), corMatMethod = c("auto", "mcd", "pairwiseQC", "pairwiseGK"),
  targetVol = 0.02, shrink = FALSE, avgCor = FALSE, p = 0.95,
  lower = 0, upper = 1, K = 100, maxit = 50, tol = 1e-05)

Arguments

returns

A matrix with a time series of returns for each asset / strategy

rf

A vector with the risk free rate in each time period; could also be the returns of a common benchmark

ER

A vector of exogeneously derived prospective expected returns. Either IR or ER must be specified.

IR

A vector of exogeneously derived prospective information ratios. Either IR or ER must be specified.

TE

A vector of exogneously derived prospective volatilites (tracking errors). If it is not specified, it will be estimated from the time series of asset / strategy returns.

corMat

Exogneously derived correlation matrix. If it is not specified, it will be estimated from the time series of asset / strategy returns.

ES

The user's speculated expected shortfall. If it is not specified, it will be estimated from the time series of asset / strategy returns using one of 3 user-selectable methods.

ESMethod

The method used to compute ES (the methods are available in PerformanceAnalytics)

corMatMethod

the method used to estimate the robust correlation matrix, (the methods are available in library robust, and the default is "auto")

targetVol

The target volatility

shrink

Logical value that determines whether or not we want to shrink the IRs toward their grand mean. using James-Stein shrinkage.

avgCor

Logical value that determines if we want to set each off-diagonal element in the correlation matrix to the average of all its off-diagonal elements

p

User-specified confidence level for computing ES

lower

A numeric or vector of lower bounds \vec{σ}^L of risk budgets. Default is 0.

upper

A numeric or vector of upper bounds \vec{σ}^U of risk budgets. Default is 1.

K

A tuning factor for the iterative algorithm. Default is 100

maxit

A number of maximum iterations. Default is 50.

tol

An accuracy of the estimation with respect to the targeted volatility. Default is 10^-5

Details

In the absence of any constraints, mean-variance risk budgets are given in closed form in terms of the Information Ratio IR and the correlation matrix C. In general, it is not obvious to allocate Expected Shortfall between strategies (or securities) in a way that achieves a target level of Expected Shortfall for the portfolio. This algorithm finds a pragmatic middle way to include tail risk in optimization - it starts by allocating risk using volatility as the measure of risk, but then uses Expected Shortfall to modify its allocations in such a way that the Expected Shortfall of the overall portfolio is reduced.

This simple closed form solution, with the inclusion of tail risk and with a stabilized correlation matrix, works surprisingly well in practice - it does not often result in negative solutions, and obviates the need for a long-only constraint - we just round up to 0 on the few occasions when a small negative risk budget appears. However, in the general case, if we want to bound the risk budgets between upper bound and lower bound, we either have to solve a full mean-variance optimization (and ignore tail risk) or create a simulation based historical optimization that includes it. Instead, we approximate the solution using an iterative scheme that clamps each risk budget between its applicable bounds, and uses a simple heuristic to increment or decrement all risk budgets in a way that allows the process to convergence in a few (usually two) iterations

Value

robRiskBudget returns a list containing the following objects:

initialRiskBudget

The vector of unconstrained risk budgets

finalRiskBudget

The vector of final risk budgets for each asset

iterativeRiskBudget

The matrix of risk budgets in each iteration columnwise

targetVol

The target volatility for the portfolio

avgCor

The average of all off-diagonal correlations

ER

The average returns (shrunk if called for) or the user supplied expected returns

TE

The estimated tracking errors or the user supplied tracking errors

ES

The vector of estimated ESs or the user supplied ESs

IR

The shrunk average IRs or the user supplied IRs

modIR

The vector of modified IRs

Author(s)

Thomas Philips, Chindhanai Uthaisaad

References

Thomas Philips and Michael Liu. "Simple and Robust Risk Budgeting with Expected Shortfall", The Journal of Portfolio Management, Fall 2011, pp. 1-13.

Examples

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data("RussellData")
rf = RussellData[, 16]
robRiskData = RussellData[, 1:15]

riskBudget = robRiskBudget(robRiskData, rf = rf, shrink = TRUE, avgCor = TRUE,
ESMethod = "historical", corMatMethod = "mcd")
robRiskBudget(robRiskData, shrink = TRUE, corMatMethod = "pairwiseQC", avgCor = TRUE)
robRiskBudget(robRiskData, shrink = TRUE, corMatMethod = "mcd", avgCor = TRUE, upper = 0.0123)

chindhanai/factorAnalytics documentation built on Aug. 30, 2017, 10:22 p.m.