rportfolios (version 1.0-1)

random.equal.test: Random equal weighted portfolios

Description

This function generates a random portfolio of n investments in which there are only k positive equal weights. The sum of the weights is $x_t$. The function is used to evaluate the performance of the portfolio generation algorithm.

Usage

random.equal.test(n = 2, k = n, segments = NULL, x.t = 1)

Arguments

n

A positive integer for the number of investments in the portfolio

k

A positive integer for the number of investments with positive equal weights

segments

A vector or list of vectors that defines the portfolio segments

x.t

The sum of the investment weights

Value

A list with two named components.

Details

The R function sample is used to generate a simple random sample without replacement of k values from the integers $1,2, \ldots ,n$. These are the subscripts into an $n \times 1$ zero vector to assign the equal weight $x_t / k$.

References

Evans, J. and S. Archer, 1968. Diversification and the Reduction of Risk: An Empirical Analysis, Journal of Finance, 23, 761-767.

Upson, R. B., P. F. Jessup and K. Matsumoto, 1975. Portfolio Diversification Strategies, Financial Analysts Journal, 31(3), 86-88.

Elton, E. J. and M. J. Gruber, 1977. Risk Reduction and Portfolio Size: An Analytical Solution, Journal of Business, 50(4), 415-437.

Bird, R. and M. Tippett, 1986. Naive Diversification and Portfolio Risk - A Note, Management Science, 32(2), 244-251.

Statman, M., 1987. How many stocks make a diversified portfolio, Journal of Financial and Quantitative Analysis, 22, 353-363.

Newbould, G. D. and P. S. Poon, 1993. The minimum number of stocks needed for diversification, Financial Practice and Education, 3, 85-87.

O'Neal, E. S., 1997. How Many Mutual Funds Constitute a Diversified Mutual Fund Portfolio, Financial Analysts Journal, 53(2), 37-46.

Statman, M., 2004. The diversification puzzle, Financial Analysts Journal, 60, 48-53.

Benjelloun, H. and Siddiqi, 2006. Direct diversification with small stock portfolios. Advances in Investment Analysis and Portfolio Management, 2, 227-252.

Benjelloun, H., 2010. Evans and Archer - forty years later, Investment Management and Financial Innovation, 7(1), 98-104.

Examples

###
### equally weighted portfolio of 30 investments of which 5 are non-zero and
### the rest are zero.  the weights sum to 1.
###
result <- random.equal.test( 30, 5 )