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					       Performance Measurement
          The 3 Traders Case
To get your “money’s worth” from this class,
 you should have:

• Read 3 traders case and performed some
  basic calculations
• understood z-scores
• practiced basic formulas and dragging.
• Done some DIY’s
        Performance Measurement
              Comparing several sets of data


Detecting changes or differences between
2 samples or groups

• Customer satisfaction for males and females
• Weekly complaints last year versus this year
• Number of defectives per shipment using old
  process versus new process




Same performance measure – two groups
        Performance Measurement
              Comparing several sets of data


Detecting changes or differences between
several samples or groups

• Expenditure of different age-groupings
• Default rates and amounts of low, medium and
  high risk borrowers.
• Revenue across the different days of the week.
• Profit performance of three or more currency
  traders.


Same performance measure – several groups
           Topics Covered
Excel and data presentation
• Stacking and Unstacking data (AWZ p99, 443)
• Using mean/stdev to compare performance
• Multiple Boxplots            (AWZ 3.8, p443,447)
• z-scores (again)
Some finance concepts
• Risk and return
• Sharp ratio



ILLUSTRATED USING CALL CENTRE DATA AS
      WELL AS THE 3 TRADERS CASE.
   Stacked and Unstacked Data

Several Samples of data – can come in two
forms: unstacked or stacked

Unstacked data – each data set is in a
separate column (with column labels
describing each sample.
Stacked data – all the data is in a single
column. A second column of labels says
which sample each data point is from.
Stacked and Unstacked Data
         Stacked data – all the data is in a
         single column. A second column
         carries labeling saying which
         sample each data point is from.
         Take rating as variable and gender
         as label.
                 Unstacked data – each data
                 set is in a separate column
                 (with column labels describing
                 each sample). Here we want
                 two separate columns of
                 ratings for M’s and F’s.
                 Slidesdata/call_centre1.xls

Stacked and Unstacked Data



             Unstacked data – each data
             set is in a separate column
             (with column labels describing
             each sample). Here we want
             two separate columns of
             ratings for M’s and F’s.
              Use StatproGo
                Data Utilities
                     Stack Variables…
                     Unstack Variables…
           Topics Covered
Excel and data presentation
• Stacking and Unstacking data
• Using mean/stdev to compare samples
• Multiple Boxplots
• z-scores (again)
Some finance concepts
• Risk and return
• Sharp ratio
                           Slidesdata/call_centre1B.xls


 Comparing Means and Std.Devs
Data distribution is largely summarised by
sample mean and standard deviation
Unstacked data: Use StatproGo then
Summary Stats then One-variable. Select all
variables you wish to summarise. You can also
use ordinary Excel.
Stacked data: Use Pivotables. Break down
data by coding variable. Select Mean and
Std.Dev as summary statistics.
           Topics Covered
Excel and data presentation
• Stacking and Unstacking data
• Using mean/stdev to compare samples
• Multiple Boxplots
• z-scores (again)
Some finance concepts
• Risk and return
• Sharp ratio
                                      slidesdata\3traders.xls
Example. The three currency traders

You have 26 weeks of growth data from three
traders, Neville, Ann and Brian.

5 minute breakout
• Use StatproGo to get means and stdev.
• What aspects of performance do the mean and
  standard deviation measure?
• Who seems to deserve promotion and why?
• Who cares about risk?
• What other statistics might be useful? How
  about the median?
            Don’t look at next slides!
                                        slidesdata\3traders.xls
Example. The three currency traders

You have 26 weeks of growth data from three
traders, Neville, Ann and Brian.

                  Neville       Ann          Brian
       Mean       0.242%       0.310%       0.303%
       Stdev      0.050%       0.083%       0.017%
       Min        0.173%       0.188%       0.262%
       Max        0.348%       0.506%       0.320%
       Range      0.175%       0.318%       0.058%
       Growth     6.490%       8.380%       8.190%


   Do we really care about risk (stdev)? Isn’t growth
   the bottom line?
Example. The three currency traders

Let’s take a vote. Who would you promote?

Open https://qp.e.unimelb.edu.au/clloyd and save to favs

A = Ann
B = Brian
C = Neville
                                      slidesdata\3traders.xls
Example. The three currency traders (Class prep chart)
                                      slidesdata\3traders.xls
Example. The three currency traders

You have 26 weeks of growth data from three
traders, Neville, Ann and Brian.


• Are any of these traders any good?
• How could you check?

5 minute breakout
• Who are the best traders? Who are the worst?
• Produce a plot that displays the relative
  performance of all the traders. (Remember the
  academic appraisal case?)
                                      slidesdata\3traders.xls
Example. The three currency traders
           Topics Covered
Excel and data presentation
• Stacking and Unstacking data
• Using mean/stdev to compare samples
• Multiple Boxplots
• z-scores (again)
Some finance concepts
• Risk and return
• Sharp ratio
                              Big 15 stocks (from class 17)

                    Sharp ratio
For any investment the return (daily, weekly, monthly)
    is uncertain. It has a distribution with two features:
(1) Mean return which you want to be high
(2) Stdev (called volatility) which you want to be low.

• How can you combine risk and return into a single
  number?




• How about using z-scores?
                                      slidesdata\3traders.xls
Example. The three currency traders

5 minute breakout
• How good is Brian? He obviously stands out.
  How far does he stand out? Give a number!
           Topics Covered
Excel and data presentation
• Stacking and Unstacking data
• Using mean/stdev to compare samples
• Multiple Boxplots
• z-scores (again)
Some finance concepts
• Risk and return
• Sharp ratio
    Boxplots – A simpler Display

Describes the overall distribution of a set of
numbers but is simpler than a histogram.
Useful when comparing several samples
because too many histograms on one graph
would be both crowded and confusing.
Also produces useful display with small data
sets. Histograms require at least 40 data
values for a reliable picture.
    Boxplots – A simpler Display

S=smallest, L=Largest, M=median
Q1=lower quartile, Q3=upper quartile
         Watch the Movie!

 Boxplots – A simpler Display
Add the sample mean as red diamond.
Points too far from centre displayed
separately (as aberrant points)
                                      slidesdata\3traders.xls
Example. The three currency traders


You have 26 weeks of growth data from three
traders, Neville, Ann and Brian.

Brian’s returns are unusually consistent – the
  stdev is very low.
Q: Are there any more subtle differences in the
  pattern/shape/profile of Brian, or indeed of the
  other traders?
                                      slidesdata\3traders.xls
Example. The three currency traders
                                      slidesdata\3traders.xls
Example. The three currency traders


Who would your promote?




               Neville
               Ann
               Brian
          Your Dream Job(???)

• Suppose you got a
  job betting on the
  outcome of the toss
  of a fair coin.
• 66 hour week –
    1 toss per hour
You Always Bet $1 on Heads
                After a week

• Your boss concludes
  that you do not have
  any expertise at coin
  tossing investment
  and suggests that
  your talents could be
  better employed
  elsewhere.
              Sitting at the bar..

• Jim, an experienced
  trader, explains how to
  play the coin toss
  game.
• “Whenever you lose,
  double plus one.”
• “When you win, go
  back to one.”
              How it works:

Bet   Outcome        Payoff                Cumulative
1     Heads          1                     1
1     Tails          -1                    0
3     Tails          -3                    -3
7     Heads          7                     4
1     Tails          -1                    3
3     Heads          3                     6
1     Heads          1                     7
1     Heads          1                     8
1     Tails          -1                    7
                              John Bilson - Financial Risk Management
Weekly record : (11 tosses x 6 days)
          Wow!!! Says the Boss
• Out of 66 bets, you
  made 65 dollars!
• You sure know how to
  pick a coin toss!
• I really liked the way
  that you traded
  yourself out of
  adverse positions.
• Would you like to be
  head trader in charge
  of currency options?
Record over many weeks
Record over many weeks
Record over many weeks
         Moral of this Case

If you expect people to make large
   consistent sums of money from an
   efficient market, you have to
   assume that there is a small
   probability of a very large loss.
KEY TAKE AWAYS CLASSES 1-3
• Data can come in stacked or unstacked form.
• Comparing data sets
  Numeric:
         sample mean, std. dev and z-scores can reveal much
  Graphical
         large data sets:         data dist or histograms
         many small data sets: boxplots (any number)
• Excel:
    – Stacking and unstacking (StatproGo)
    – Pivot tables for comparing samples
    – Multiple Boxplots (StatproGo)
    – COUNTIF, templates
• Finance
    – risk, return, Sharp ratio and RFR

				
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posted:7/5/2013
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