alg_UP: Universal Portfolio Algorithm (UP)
In ngloe/olpsR: Algorithms and functions for On-line Portfolio Selection

Description Usage Arguments Details Value Note References Examples

approximates the Universal Portfolio Algorithm by Cover, 1991

1	alg_UP(returns, method = "rand", ...)

`returns`	Matrix of price relatives, i.e. the ratio of the closing (opening) price today and the day before (use function `get_price_relatives` to calculate from asset prices).
`method`	The method used to calculate UP. "`rand`" generates random CRPs to find UP. By default the number of random portfolios is "`samplings=1000`". "`approx`" limits the set of CRPs to the portfolios of the form b=(b_1, 1-b_1), where b_1 runs from 0 to 1 in steps of length "`step=0.05`".
`...`	further arguments (`samplings`, `step`) dependend on the "`method`" argument.

For the "approx" method the calculation may require very much memory dependend on the number of assets and the "step" argument. If an error occurs due to memory problems the "rand" method may work.

Object of class OLP containing

`Alg`	Name of the Algorithm
`Names`	vector of asset names in the portfolio
`Weights`	calculated portfolio weights as a vector
`Wealth`	wealth achieved by the portfolio as a vector
`mu`	exponential growth rate
`APY`	annual percantage yield (252 trading days)
`sigma`	standard deviation of exponential growth rate
`ASTDV`	annualized standard deviation (252 trading days)
`MDD`	maximum draw down (downside risk)
`SR`	Sharpe ratio
`CR`	Calmar ratio

see also print.OLP, plot.OLP

The print method for OLP objects prints only a short summary.

Cover & Ordentlich 1991, Universal Portfolios. Mathematical Finance, 1991, 1, 1-29

Ishijima 2001, Numerical Methods for Universal Portfolios http://www.business.uts.edu.au/qfrc/conferences/qmf2001/Ishijima_H.pdf

# load data
data(NYSE)
# select stocks
returns = cbind(comme=NYSE$comme, kinar=NYSE$kinar)

# compute Universal Portfolio algorithm
UP_rnd = alg_UP(returns, method="rand", samplings=1000); UP_rnd
UP_approx = alg_UP(returns, method="approx", step=0.05); UP_approx
plot(UP_rnd, UP_approx)
plot(UP_approx$Weights[,1], type="l")