Compute and Plot Alpha Proxy

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Description

Computes (and possibly generates a contour plot of) the alpha proxy – a measure of the effect that volatility and correlation have on the utility of the investor. As the name might suggest, it is in the same units as alpha (that is, expected returns).

Usage

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alpha.proxy(weight = 0.2, vol.man = 0.2, vol.bench = 0.2, 
	vol.other = 0.2, cor.man = 0.2, cor.bench = 0.2, 
	plot.it = TRUE, transpose = FALSE, ...)

Arguments

weight

a number or vector of the fraction of the value of the investor's entire portfolio that is given to the manager.

vol.man

a number or vector giving the volatility of the manager's portfolio.

vol.bench

a number or vector giving the volatility of the benchmark.

vol.other

a number or vector giving the volatility of the rest of the portfolio.

cor.man

a number or vector giving the correlation between the manager's portfolio and the rest of the investor's portfolio.

cor.bench

a number or vector giving the correlation between the benchmark and the rest of the investor's portfolio.

plot.it

logical value. If TRUE and two of the arguments above have length greater than 1, then a contour plot is created.

transpose

logical value. If TRUE, then the variables on the axes of the contour plot are switched.

...

additional arguments to filled.contour may be given.

Value

a vector of the alpha proxies (in basis points) if less than 2 of the first 6 arguments have length more than 1.

Otherwise it is a list (returned invisibly if plot.it is TRUE) with the following components:

x

one of the vectors of inputs.

y

the other vector of inputs.

z

a matrix of the computed alpha proxies where rows correspond to the values in x and the columns correspond to y. The values are given in basis points.

call

a character string of the image of the command that created the object.

Side Effects

if plot.it is TRUE, then a contour plot is created.

An error occurs if more than 2 of the first 6 arguments have length greater than 1.

Details

The first 6 arguments are the variables that determine the alpha proxy. The investor is faced with the decision of hiring the manager for some portion (the weight) of the portfolio rather than using a replication of the benchmark. If the alpha proxy is positive, then the volatility and correlation of the manager's portfolio is improving whatever outperformance the manager may have (or is offsetting the losses).

Revision

This help was last revised 2010 January 05.

References

Burns, Patrick (2003). "Portfolio Sharpening". Working Paper, Burns Statistics http://www.burns-stat.com/.

See Also

partial.rainbow.

Examples

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# return vector of alpha proxies
alpha.proxy(weigh=.05, vol.man=.17, cor.man=seq(0, .2, len=21))

# create a contour plot
alpha.proxy(weigh=.05, vol.man=seq(.15, .25, len=20), 
	cor.man=seq(0, .2, len=21))

# commands used to create figures in the paper
alpha.proxy(vol.man=seq(.15, .25, len=50), weight=seq(.01, .7, leng=60), 
        color.palette=partial.rainbow(start=0, end=.32))

alpha.proxy(cor.man=seq(0, .3, len=50), weight=seq(.01, .7, leng=60), 
        color.palette=partial.rainbow(start=.07))

alpha.proxy(cor.man=seq(0, .3, len=50), vol.man=seq(.15, .25, leng=60), 
        color.palette=partial.rainbow(start=0))