momentVote | R Documentation |

The first step computes mean, std.dev, skewness, kurtosis (kurt),and the Sharpe Ratio (mean/sd) representing risk-adjusted return where sd measures the risk. The input x must be a matrix having p columns (col.names recommended). and n rows as in the data. If data are missing for some columns, insert NA's. Thus x has p column of data matrix ready for comparison and ranking. For example, x has a matrix of stock returns. The output matrix produced by this function has p columns for each data column (i.e. for each stock being compared). The output matrix has twelve rows. Top five rows have the magnitudes of mean, sd, skew, kurt, Sharpe ratios. Output matrix rows 6 to 10 have respective ranks of moment stats. The output 11-th row reports a weighted sum of ranks with following weights mean=1,sd=-1,skew=0.5,kurt=-0.5,Sharpe Ratio=1. User has the option to change the weights. They measure relative importance.

```
momentVote(mtx, weight = c(1, -1, 0.5, -0.5, 1))
```

`mtx` |
n by p matrix of data, For example, n stock returns for p stocks. The mtx columns should have some names (ticker symbols) |

`weight` |
vector of reliability weights. default: mean=1, sd=1, skew=0.5,kurt=0.5,sharpe=1 |

Since skewness and kurtosis are measured relatively less reliably (have greater sampling variation due to higher powers) their weight is 0.5. Our ranking gives the smallest number 1 to the most desirable outcome. The 11-th line of the output matrix has weighted sum of ranks and we suggest higher portfolio weight be given to the column having smallest value (in the bottom line). The 12-th row of output matrix has ‘choice,’ where input weights give the number 1 is for the top choice column of data and all other choice numbers. The (p+1)-th column of the output matrix has the chosen weights. The argument weight to the ‘momentVote’ function allows one to change these weights.

a matrix with same number of columns as in the input matrix x and eleven rows. Top five rows have moment quantities, next five are their ranks the eleventh row has weighted sum of ranks with the input weights (see default) and the 12-th row has choice numbers (choice=1 is best)

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

```
x1=c(1,4,7,2,6)
x2=c(3,4,8,4,7)
momentVote(cbind(x1,x2))
```

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