outOFsamp function

Compare out-of-sample portfolio choice algorithms by a leave-percent-out method.

This function randomly leaves out 5 percent (pctOut'=5 by default) data and finds portfolio choice by seven different portfolio selection algorithms using the data on the remaining 95 percent (say). The randomization removes any bias in time series definitions of out-of-sample' data. For example, the input to outOFsamp(.) named mtx' is a matrix with p columns for p stocks and n returns. Also, let the maximum number of stocks admitted to belong in the portfolio be four, or maxChosen=4'. Now outOFsamp function computes the returns earned by the seven portfolio selection algorithms, called "SD1", "SD2", "SD3", "SD4", "SDAll4", "decile," and "moment," where SDAll4 refers to a weighted sum of SD1 to SD4 algorithms. Each algorithm provides a choice ranking of p stocks with choice values 1,2,3,..,p where stock ranked 1 should get the highest portfolio weight. The outOFsamp function then calls the function rank2return,' which uses these rank choice numbers to the selected maxChosen' stocks. The allocation is linearly declining. For example, it is 4/10, 3/10, 2/10, and 1/10, with the top choice stock receiving 4/10 of the capital. Each choice of pctOut' rows of the mtx' data yields an outOFsamp return for each of the seven portfolio selection algorithms. These outOFsamp return computations are repeated reps times. A new random selection of pctOut' rows (must be 2 or more) of data is made for each repetition. We set reps=20 by default. The low default is set to save processing time in early phases, but we recommend reps=100+. The final choice of stock-picking algorithm out of seven is suggested by the one yielding the largest average out-of-sample return over the reps' repetitions.Its standard deviation measures the variability of performance over the reps' repetitions.

outOFsamp(mtx, pctOut = 5, reps = 10, seed = 23, maxChosen = 2, verbo = FALSE)

Arguments

• mtx: matrix size n by p of data on n returns from p stocks
• pctOut: percent of n randomly chosen rows left out as out-of-sample, default=5 percent. One must leave out at least two rows of data
• reps: number of random repetitions of left-out rows over which we average the out-of-sample performance of a stock-picking algorithm, default reps=20
• seed: seed for random number generation, default =23
• maxChosen: number of stocks (out of p) with nonzero weights in the portfolio
• verbo: logical, TRUE means print details, default=FALSE

Returns

a matrix called `avgRet' with seven columns for seven stock-picking algorithms "SD1","SD2","SD3","SD4","SDAll4","decile",and "moment," containing out-of-sample average returns for linearly declining allocation in a portfolio. The user needs to change rank2return() for alternate portfolio allocations.

Note

The traditional time-series out-of-sample leaves out the last few time periods, and estimates the stock-picking model using part of the data time periods. The pandemic of 2019 has revealed that the traditional out-of-sample would have a severe bias in favor of pessimistic stock-picking algorithms. The traditional method is fundamentally flawed since it is sensitive to the trends (ups and downs) in the out-of-sample period. The method proposed here is free from such biases. The stock-picking algorithm recommended by our outOFsamp() is claimed to be robust against such biases.

Examples

## Not run:

x1=c(2,5,6,9,13,18,21,5,11,14,4,7,12,13,6,3,8,1,15,2,10,9)
x2=c(3,6,9,12,14,19,27,9,11,2,3,8,1,6,15,10,13,14,5,7,4,12)
x3=c(2,6,NA,11,13,25,25,11,9,10,12,6,4,3,2,1,7,8,5,15,14,13)
mtx=cbind(x1,x2,x3)
mtx=mtx[complete.cases(mtx),]
os=outOFsamp(mtx,verbo=FALSE,maxChosen=2, reps=3)
apply(os,2,mean)
## End(Not run)

See Also

rank2return

Author(s)

Prof. H. D. Vinod, Economics Dept., Fordham University, NY