targetbeta_twofunds: Implement a Two-Fund Strategy that Targets a Particular Beta

In stocks: Stock Market Analysis

Description

Implements a two-fund strategy where allocations to each fund are adjusted to maintain some user-specified portfolio beta. For example, you could back-test a zero-beta (i.e. market neutral) VFINX/VBLTX strategy using this function.

Usage

targetbeta.twofunds(tickers = NULL,
                    intercepts = NULL, slopes = NULL, ...,
                    benchmark.ticker = NULL,
                    reference.tickers = NULL,
                    tickers.gains = NULL,
                    benchmark.gains = NULL,
                    reference.gains = NULL,
                    target.beta = 0,
                    tol = 0.15,
                    window.units = 50,
                    failure.method = c("cash", "closer"),
                    maxall.tol = tol - 0.05,
                    initial = 10000)

Arguments

tickers	Character vector specifying 2 ticker symbols.
intercepts	Numeric vector of values to add to daily gains for each ticker. For example, if you want to simulate a 1% annual expense ratio for only the second fund, you would set intercepts = c(0, convert.rate(-0.01, units.in = 252, units.out = 1)).
slopes	Numeric vector of values to multiply daily gains for each ticker by. For example, if you want to simulate a 2x leveraged version of the first fund, you would set slopes = c(2, 1). The slopes are multiplied prior to adding the intercepts.
...	Arguments to pass along with tickers, intercepts, and slopes to load.gains function, if you wish to load data on the fly rather than specify tickers.gains.
benchmark.ticker	Character vector indicating ticker symbol for benchmark index that beta should be calculated from. If unspecified, the first fund is used as the benchmark.
reference.tickers	Character string or vector of ticker symbols to include for comparative purposes.
tickers.gains	Numeric matrix of gains (daily or otherwise) for the two funds.
benchmark.gains	Numeric vector or matrix of gains for the benchmark index that beta should be calculated from. If unspecified, the first fund is used as the benchmark.
reference.gains	Numeric vector or matrix of gains for reference funds.
target.beta	Numeric value indicating what portfolio beta you want to achieve.
tol	Numeric value indicating how far the effective portfolio beta has to deviate from target.beta to trigger a rebalancing trade.
window.units	Numeric value indicating the width of the trailing moving window used to estimate each fund's beta.
failure.method	Character string or vector specifying method(s) to use when fund betas are such that the target portfolio beta cannot be achieved. Possible values are "cash", "fund1", "fund2", "fund1.maxall", "fund2.maxall", "inverse1", "inverse2", and "closer". See Details.
maxall.tol	Numeric value indicating tolerance to use when implementing the "fund1.maxall" or "fund2.maxall" failure method. To illustrate, if target.beta = 0, fund 1 has a current beta of 1, fund 2 has a current beta of 0.25, failure.method = "fund2.maxall", and maxall.tol = 0.1, a trade will be triggered that results in 40% fund 2 and 60% cash. The portfolio beta is 0.4 * 0.25 = 0.1. The reason you might want maxall.tol to be less than tol is to avoid frequently triggering another trade on the very next day, as fund 2's beta changes a little and moves the portfolio beta outside of [target.beta - tol, target.beta + tol].
initial	Numeric value giving the initial value of the portfolio.

Details

If tickers is specified, it gets passed to load.gains to load historical prices from Yahoo! Finance using the quantmod package [1]. If tickers.gains is specified, gains from that matrix are used.

The general implementation is as follows. Beta for each of the two funds is estimated based on the first window.units gains. Initial allocations are selected to achieve portfolio beta of target.beta. If that is not possible - for example, if target.beta = 0 and both funds have positive beta - then the action taken depends on what method is selected through the failure.method input (details below).

Assuming the target beta is attainable, the function moves over 1 day, and applies each fund's gains for that day. It then re-calculates each fund's beta based on the window.units-width interval, and determines the effective portfolio beta based on fund allocations and betas. If the effective beta is outside of [target.beta - tol, target.beta + tol], a rebalancing trade is triggered. As before, if the target beta cannot be achieved, certain actions are taken depending on the selected method.

When outside of a trade because the target beta could not be achieved, the function attempts to rebalance each time it shifts over to a new day, regardless of the effective portfolio beta.

When failure.method = "cash", the entire portfolio balance is allocated to cash when the target beta cannot be achieved.

When failure.method = "fund1" (or "fund2"), the entire portfolio balance is allocated to the first (or second) fund when the target beta cannot be achieved.

When failure.method = "fund1.maxall" (or "fund2.maxall"), when the target beta cannot be achieved, fund 1 (or fund 2) is combined with cash, with the fund 1 (fund 2) allocation as high as possible while staying within maxall.tol of target.beta.

When failure.method = "inverse1" (or "inverse2"), an inverse version of the first (or second) fund is used when the target beta cannot be achieved. In many cases where the target beta cannot be achieved with the two funds, it can be achieved with an inverse version of one and the other. If the target beta still cannot be achieved, the entire portfolio balance is allocated to cash.

When failure.method = "closer", the entire portfolio balance is allocated to whichever fund has a beta closer to target.beta.

Value

For each method, a 4-element list of the following: (1) Numeric matrix named fund.balances giving fund balances over time; (2) Numeric matrix named fund.betas giving fund betas over time; (3) Numeric vector named effective.betas giving effective portfolio beta over time; and (4) Numeric value named trades giving the total number of trades that were executed. If multiple methods are requested, a list of lists is returned.

Note

NA

Author(s)

Dane R. Van Domelen

References

1. Jeffrey A. Ryan (2016). quantmod: Quantitative Financial Modelling Framework. R package version 0.4-6, https://cran.r-project.org/package=quantmod.

Acknowledgment: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-0940903.

Examples

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Example output

Loading required package: rbenchmark
[1] NA

stocks documentation built on May 2, 2019, 5:22 p.m.