This worksheet has been designed and tested using Netscape 3.0. It should work with later versions of Netscape's browsers but will not work with other browsers. It uses only JavaScript for computations and should cause no problems when used with the appropriate browsers. The operative word here is "should" -- the author cannot guarantee fault-free operation.

You should be able to use the worksheet when not connected to
the internet. Save the program file (ws_***.htm) and the
accompanying instruction file (wi_***.htm) on your disk using the
browser's command to **F**ile **S**ave.
At a later time you may retrieve the file using the browser's **F**ile
**O**pen file command; you may then use the page as
you would if you were on the network.

When using the worksheet, you may change any inputs. To do so, click inside the appropriate box, then make your changes. When finished, click any area outside the boxes on the form.

You may copy inputs from other sources such as spreadsheets,
word processing documents, and other worksheets in this series,
then paste the results into the appropriate boxes on this form.
To copy an area from an Excel spreadsheet, select it, then select
**E**dit **C**opy. In the browser,
select a position in the input box, then select **E**dit
**P**aste. To copy an area from a box in the browser
to an Excel spreadsheet, select the text in the browser and
select **E**dit **C**opy. In the Excel
spreadsheet, select a position, then select **E**dit
**P**aste. This brings each row into the spreadsheet
as text. To convert to a matrix, select the column in which the
information is located (the left-most one shown), then select **D**ata
**T**ext-to-columns. Choose **Delimited**
and **Spaces** as delimiters and the information
will appear in the requisite number of cells.

When you save a page on your own disk (using the browser's **F**ile
Save **A**s command), only the original material in
the form will be saved. There are two ways to save and retrieve
this worksheet information. You can copy the information you wish
to save to some other document, such as a spreadsheet, word
processing document or text file. You can also load the source
(ws_***.htm) file in a word processor and edit it to include your
inputs. You will find the default information in blocks marked
TEXTAREA and in the VALUE attributes of INPUT tags. Simply
replace the default values with your information, then save the
page as a file on your disk under any desired name.

Whenever you change an input, the output area will be cleared
to avoid having old outputs appear simultaneously with new
inputs. To produce new outputs, click the **PROCESS**
button.

The **Inputs** box should contain the data
observations, with each observation in a separate row. For each
observation the first column contains the month (preferably in
form YYYYMM); it is not used in the computations. The remaining
entries in each row give the monthly returns (as percentages --
thus 2.34 for 2.34% in that month).All returns must be separated
by one or more spaces and/or tabs. The top row should contain
column identifiers for the return series. 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.

The first series should give the returns a **one-month
riskless asset**. The second should give the returns on a **benchmark
portfolio**. The remaining series should give the returns
on one or more funds for which historic performance is to be
evaluated.

The **Risk Tolerance **parameter is used in the
computation of mean-variance utility measures (described below).
The **Relative Disutility **parameter is used An be
used in the computation of linear utility measures (also
described below).

The output is in the form of a table with a columns for the benchmark portfolio and all the funds for which returns were provided. All statistics are based on the historic returns provided, with all observations weighted equally.

The first row provides **cumulative returns**,
based on the ratio of the ending value to the beginning value,
assuming that returns are compounded throughout the period. Thus
a cumulative return of 50% would indicate that $1 invested at the
beginning of the period would have grown to $1.50 by the end of
the period.

The block labeled **Monthly Rtn** contains
statistics computed from the monthly total returns, with the
results expressed in terms of return per month. The first is the **mean
monthly return**, computed by summing all the monthly
returns and then dividing by the number of months. The second
statistic gives the **monthly standard deviation of return**.
This is computed by averaging the squared differences of the
monthly returns from their mean, then taking the square root. No
correction is made for degrees of freedom, so this can be
considered as a "population" standard deviation or
descriptive statistic. The third statistic is t**he
geometric mean monthly return**. This is the monthly
return that, if earned every month, would compound to give the
same cumulative value as did the investment in question.

The block labeled **Annualized Rtn** contains
annualized versions of the statistics in the first block. The **annualized
mean monthly return** is simply the mean monthly return
times 12. The **annualized monthly standard deviation of
return** equals the monthly standard deviation of return
times the square root of 12. The **annualized geometric
mean return **is that return that, if earned every year,
would compound to give the same cumulative value as did the
investment in question. More precisely, if 1+ga raised to the
number of years covered will equal one plus the cumulative
return.

The **Monthly ER** block contains statistics
computed using monthly excess returns. The **excess return **for
a benchmark or fund in a given month equals its return minus that
of the risk-free asset. The first two statistics for an
investment provide its **mean monthly excess return**,
computed by summing all the monthly excess returns and then
dividing by the number of months and the **monthly standard
deviation of excess return,** computed by averaging the
squared differences of the monthly excess returns from their
mean, then taking the square root. As before, no correction is
made for degrees of freedom, so this can be considered as a
"population" standard deviation or descriptive
statistic. The third statistic is the **monthly Sharpe
Ratio**, computed by dividing the mean monthly excess
return by the monthly standard deviation of excess return.

The **Annualized ER** block contains statistics
that are annualized versions of those in the prior block. The **annualized
mean monthly excess return** is simply the mean monthly
excess return times 12. The **annualized monthly standard
deviation of excess return** equals the monthly standard
deviation of excess return times the square root of 12. The **annualized
Sharpe Ratio **is computed by dividing the annualized mean
monthly excess return by the annualized monthly standard
deviation of excess return. Equivalently, the annualized Sharpe
Ratio equals the monthly Sharpe Ratio times the square root of
12.

The subsequent block, labeled **Mthly ER, **provides
statistics calculated separately for months in which excess
returns were positive and those in which excess returns were
negative. The first statistic (**Prop >= 0**)
indicates the proportion of months in which the fund's excess
return was positive or zero. The next row shows the mean monthly
return in all such months. The next row (**Prop < 0**)
shows the proportion of months in which the fund's excess return
was negative, with the following row showing the mean monthly
return in all such months.

The **Utility** block provides measures of
utility based on both the funds' historic performances and the
parameters specified in the form. The first calculation uses the
annualized mean total return (am) and annualized standard
deviation of total return (asd) to compute a mean-variance
utility of the form:

u = am - ( asd^2) / t

where t is the risk-tolerance specified in the form.

The second calculation in the utility block is based on a piecewise linear utility function. Every positive excess return is given a utility equal to the excess return, while every negative excess return is given a utility equal to rd times its excess return, where rd is the relative disutility specified in the form. The resulting monthly utility values are averaged, then multiplied by 12 to give an annualized monthly utility. Thus:

u = 12 * average

_{t}( u( er_{t}) )where:

u ( er

_{t }) = k*er_{t}

with:

k = 1 if er >0

k = rd if er < 0

The next block, labeled **ER Regression**,
provides the results obtained by performing standard regression
analyses in which the benchmark excess return is the independent
variable and each of the fund' excess returns is, in turn, the
dependent variable. The **Bet**a value is the slope
coefficient and the **Monthly Alpha** value the
intercept. The **Monthly Residual Standard Deviation**
(**RSD**) is the standard deviation of the residuals
from the regression. In this calculation, there is no adjustment
for degrees of freedom; it may thus be considered a
"population estimate" or descriptive statistic.

The final block (labeled **Annualized**) provides
annualized performance measures derived from the excess return
regression analysis. The **Annualized Alpha **value
is equal to 12 times the monthly alpha value. The **Annualized
Alpha/Beta** ratio equals the annualized alpha divided by
the beta value. The value labeled RSD is the **Annualized
Monthly Residual Standard Deviation**. It equals the
Monthly Residual Standard Deviation times the square root of 12.
The final value, **Alpha/RSD**, is the ratio of the
Annualized Alpha divided by the Annualized Monthly Residual
Standard Deviation. Otherwise stated, this is the **Sharpe
Ratio of the Residual**.

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

This version May 1, 1997