Instructions for Weighted Statistics Worksheet

Inputs

The Values box should contain the data observations, with each observation in a separate row. For each observation the first column contains an identifier (or row label) that is not used in the computations. An identifier may use any characters, but no spaces. The remaining entries in each row give the data values. These must be valid numbers using only digits and an optional decimal point. All entries must be separated by one or more spaces and/or tabs. The top row should contain column identifiers for the data values. Each should use six or fewer characters (of any type), but no spaces. Blank rows may be included in the table and it is not necessary for your data to "line up" in columns as long as it conforms to the rules given above.

To avoid excessive processing time (and potentially running out of virtual memory) it is strongly recommended that you use a minimum number of spaces to separate entries in the values box.

The Half-life value controls the weightings used in the analysis. If the value entered here is zero, each observation is assigned the same weight. If another value is entered, each observation is assign a weight equal to 2 ^ ( 1 / h ) times the prior observation, where h is the indicated half-life. This has the characteristic that the value h periods prior to the present period will receive half the weight assigned the present period (hence the name).

The Scale factor can be used to annualize monthly or quarterly data. Mean values are multiplied by this factor, while standard deviations are multiplied by the square root of the factor. A scale factor of 1 will, in effect, provide no scaling.

You may choose any of three different Output formats. If you want a table showing only the statistics, select the first. If you wish the output to be in a format ready to be used as input for the reverse optimization worksheet, select the second. To obtain output in a format ready to be used as input for the optimization worksheet, select the third.

Output

The output is in the form of a table with columns for computed statistics and, optionally, other information needed for further analysis.

Each Mean is an arithmetic mean for the data series, using the selecting weighting scheme and scale factor.

Each Standard Deviation (StdDev) uses the selected weighting scheme and scale factor. No adjustment is made for "degrees of freedom", even when equal weights are assigned to the observations.

Each of the Correlation Coefficients uses the selected weighting scheme; the scale factor need not be applied, since it does not affect correlation. The correlation coefficients are given in columns labelled c: *** where *** stands for the name of the asset class.

Notes

You may enter any desired text in this box to describe the source of the input data, etc...