rbounded.test: Random bounded portfolios
In rportfolios: Random Portfolio Generation

Description Usage Arguments Details Value Author(s) References See Also Examples

This function generates m portfolios of n investments where the weights are constrained to be within investment specificd lower and upper bounds. This function is used to evaluation the computational performance of the portfolio generation algorithm.

1	rbounded.test(m, n = 2, x.t = 1, x.l = rep(0, n), x.u = rep(x.t, n), max.iter = 1000)

`m`	An integer value for the number of portfolios to be generated
`n`	An integer value for the number of investments in the portfolio
`x.t`	Numeric value for the sum of the investment weights
`x.l`	Numeric vector for the lower bounds on the investment weights
`x.u`	Numeric vector for the upper bound on the investment weights
`max.iter`	An integer value for the maximum iteration in the acceptance rejection loop

The function executes the function random.bounded using the R function sapply. The result returned is the transpose of the matrix generated in the previous step.

A list with two named components.

`xmatrix`	An m \times n matrix of investment weights
`iters`	An m \times 1 vector with the number of iterations used to obtain the portfolios

Frederick Novomestky fn334@nyu.edu

Cheng, R. C. H., 1977. The Generation of Gamma Variables with Non-integral Sape Parameter, Journal of the Royal Statistical Society, Series C (Applied Statistics), 26(1), 71.

Kinderman, A. J. and J. G. Ramage, 1976. Computer Generation of Normal Random Variables, Journal of the American Statistical Association, December 1976, 71(356), 893.

Marsaglia, G. and T. A. Bray, 1964. A Convenient method for generating normal variables, SIAM Review, 6(3), July 1964, 260-264.

Ross, S. M. (2006). Simulation, Fourth Edition, Academic Press, New York NY.

Tadikamalla, P. R., (1978). Computer generation of gamma random variables - II, Communications of the ACM, 21 (11), November 1978, 925-928.

random.bounded

###
### standard long only portfolio
###
p.1.matrix <- rbounded.test( 400, 30, 1 )

###
### 3% lower bound for all investments
### 100% upper bound for all investments
###
x.lb.all.3 <- rep( 0.03, 30 )
x.ub.all.100 <- rep( 1, 30 )
p.2.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.all.3, x.u= x.ub.all.100 )
###
### 4% upper bound for all investments
### 3% lower bound for all investments
x.ub.all.4 <- rep( 0.04, 30 )
p.3.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.all.3, x.u = x.ub.all.4 )
###
### 2% lower bound for 1-10, 3% lower bound for 11-20, 2% lower bound for 21-30
### 100% upper bound for all investments
###
x.lb.2.3.2 <- c( rep( 0.02, 10 ), rep( 0.03, 10 ), rep( 0.02, 10 ) )
p.4.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.2.3.2, x.u = x.ub.all.100 )
###
### 3% lower bound for 1-10, 2% lower bound for 11-20, 3% lower bound for 21-30
### 100% upper bound for all investments
###
x.lb.3.2.3 <- c( rep( 0.03, 10 ), rep( 0.02, 10 ), rep( 0.03, 10 ) )
p.5.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.3.2.3, x.u = x.ub.all.100 )
###
### 2% lower bound for 1-10, 3% lower bound for 11-20, 2% lower bound for 21-30
### 4% upper bound for all investments
###
x.lb.2.3.2 <- c( rep( 0.02, 10 ), rep( 0.03, 10 ), rep( 0.02, 10 ) )
p.6.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.2.3.2, x.u = x.ub.all.4 )
###
### 3% lower bound for 1-10, 2% lower bound for 11-20, 3% lower bound for 21-30
### 4% upper bound for all investments
###
x.lb.3.2.3 <- c( rep( 0.03, 10 ), rep( 0.02, 10 ), rep( 0.03, 10 ) )
p.7.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.3.2.3, x.u = x.ub.all.4 )
###
### 3% lower bound for all investments
### 4% upper bound for 1-10 5% for 11-20 and 4% for 21-30
###
x.ub.4.5.4 <- c( rep( 0.04, 10 ), rep( 0.05, 10 ), rep( 0.04, 10 ) )
p.8.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.all.3, x.u= x.ub.4.5.4 )
###
### 3% lower bound for all investments
### 5% upper bound for 1-10 4% for 11-20 and 5% for 21-30
###
x.ub.5.4.5 <- c( rep( 0.05, 10 ), rep( 0.04, 10 ), rep( 0.05, 10 ) )
p.9.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.all.3, x.u= x.ub.5.4.5 )
###
### 3% lower bound for 1-10, 2% for 11-20, 3% for 21-30
### 4% upper bound for 1-10  5% for 11-20  4% for 21-30
###
p.10.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.3.2.3, x.u = x.ub.4.5.4 )
###
### 2% lower bound for 1-10, 3% for 11-20, 2% for 21-30
### 4% upper bound for 1-10  5% for 11-20  4% for 21-30
###
p.11.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.2.3.2, x.u = x.ub.4.5.4 )
###
### 3% lower bound for 1-10, 2% for 11-20, 3% for 21-30
### 5% upper bound for 1-10  4% for 11-20  5% for 21-30
###
p.12.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.3.2.3, x.u = x.ub.5.4.5 )
###
### 2% lower bound for 1-10, 3% for 11-20, 2% for 21-30
### 5% upper bound for 1-10  4% for 11-20  5% for 21-30
###
p.13.matrix <- rbounded.test( 400, 30, 1, x.l = x.lb.2.3.2, x.u = x.ub.5.4.5 )