alg_PAMR: Passive Aggressive Mean Reversion Algorithm (PAMR)
In ngloe/olpsR: Algorithms and functions for On-line Portfolio Selection

Description Usage Arguments Details Value Note References Examples

computes the Passive Aggressive Mean Reversion algorithm by Li et al. 2012

1	alg_PAMR(returns, epsilon = 0.5)

`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).
`epsilon`	sensitivity parameter

The idea of PAMR is to exploit the mean-reversion property of asset prices. Based on a loss function PAMR passively maintains the last portfolio if the loss is zero and otherwise aggressively aproaches a new portfolio that can force the loss to be zero.

As the algorithm can lead to negative portfolio weights which are not permitted by the definition of on-line portfolio selection a simplex projection step is needed. The simplex projection is implemented according to Duchi et al. 2008 (see also projsplx).

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.

Li, B.; Zhao, P.; Hoi, S. C. H. & Gopalkrishnan, V. PAMR: Passive aggressive mean reversion strategy for portfolio selection, Machine Learning, 2012

Duchi, J.; Shalev-Shwartz, S.; Singer, Y. & Chandra, T. Efficient projections onto the l 1-ball for learning in high dimensions, Proceedings of the 25th international conference on Machine learning, 2008

# load data
data(NYSE)
# select stocks
x = cbind(kinar=NYSE$kinar, iroqu=NYSE$iroqu)

# compute PAMR algorithm
PAMR = alg_PAMR(x, epsilon=0.5)
plot(PAMR)