Strategic Risk and Performance management by Strategy@Risk Ltd. The modern approach to improving business forecasts.

1.
Foreca
asting sa
ales and
d foreca
asting u
uncerta
ainty
Introdu
uction
There aree a large numbber of methods used for fo
orecasting ran
nging from juudgmental (ex xpert forecasting
etc.) thru expert system
ms and time s
series to caus
sal methods ( nalysis etc.)1.
(regression an
Most are used to give single point fforecast or at most single p
point forecasts for a limite
ed number of f
scenarios. We will in the following take a look at
t the unusefuulness of such
h single point forecasts.
As exampple we will usee a simple for
recast ‘model
l’ for net sales multinational company. It turns
s for a large m
out that there is a good linear relati
ion between the company y’s yearly net sales in millio
on euro and
growth raates (%) in wo
orld GDP:
with a corrrelation coef
fficient R= 0.9
995. The relat
tion thus accoounts for alm
most 99% of th
he variation in
n the
sales data
a. The observe ed data is given as green d
dots in the gra
aph below, and the regresssion as the g
green
line. The ‘
‘model’ explaains expected sales as consstant equal 16638M and with 53M in inc creased or
decreased d sales per pe
ercent increas se or decrease in world GDDP:
The Intern
national Mon netary Fund (IMF) that kinddly provided tthe historical GDP growth rates also giv
ves
forecasts for expected future chang ge in World G 2 ‐ for the next five yea
GDP ars. When we put these
forecasts into the ‘moddel’ we ends up with foreccasts for net s
sales for 2012
2 to 2016 as d
depicted by th
he
yellow do
ots in the grap
ph above.
1
Gardner, D & Tetlock, P
P., (2011), Over
rcoming Our Aversion to Ackknowledging Our Ignorance, h
http://www.caato‐
unbound.o org/2011/07/11/dan‐gardner r‐and‐philip‐tetlock/overcom
ming‐our‐aversion‐to‐acknow
wledging‐our‐
ignorance/ /
2
World Economic Outloo ok Database, AApril 2012 Edition;
http://www w.imf.org/exteernal/pubs/ft/wweo/2012/01/ /weodata/indeex.aspx
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2.
So m
mission accom
mplished! … O
Or is it really?
?
We know that the prob bability for ge
etting a singlee‐point foreca
ast right is zero‐ even whe
en assuming tthat
ast of the GDP growth rate
the foreca e is correct ‐ s
so the forecas
sts we so far have will cert
tainly be wro
ong,
but how wwrong?
So
ome even persist in using forecasts that are manifesstly unreliable
e, an attitudee encounteredd by
th
he future Nob
bel laureate K
Kenneth Arrow w when he w was a young st ring the Second
tatistician dur
World War. W
W When Arrow di iscovered tha
at month‐long g weather for recasts used bby the army wwere
worthless, he w
w warned his suuperiors again
nst using them
m. He was rebuffed. "The Commanding g
General is well aware the fo
orecasts are n
no good," he was told. "Hoowever, he ne eeds them fo
or
planning purpooses." (Gardn
ner & Tetlock,, 2011)
Maybe we
e should take
e a closer look
k at possible f
forecast error
rs, input data
a and the final forecast.
The pre
ediction ba
and
Given the
e regression wwe can calcula t band for fut ure observations of sales g
ate a forecast given forecas
sts of
the future
e GDP growth h rate. That is the region w
where we with h a certain pr
robability will expect new
values of net sales to fall. In the gra
aph below thee green area ggive the 95% forecast band:
Since the variance of the predictionns increases th
he further ne
ew forecasts ffor the GDP ggrowth rate lie
es
from the mean of the s sample values (used to compute the re egression), the
e band will wwiden as we m
move
to either s
side of this m
mean. The bannd will also wi
iden with dec
creasing correelation (R) an
nd sample sizee (the
number o of observation ns the regress
sion is based on).
So even iff the fit to the
e data is good
d, our regress
sion is based o
on a very sma all sample givving plenty of
f
room for prediction errors. In fact a a 95% confideence interval f
for 2012, with an expected GDP growth
rate of 3.5
5%, is net salees 1824M plu us/minus 82MM. Even so the e interval is st
till only appro
ox. 9% of the
expected value.
Now we hhave shown thhat the mode confidence interval(s) and
el gives good forecasts, callculated the c
shown tha
at the expect
ted relative er
rror(s) with high probabilitty will be sma
all!
So finally th d! … Or is it really?
he mission is accomplished
The forecasts we have made is base
ed on forecas
sts of future w
world GDP gro but how certain
owth rates, b
are they?
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3.
The GD
DP forecast
ts
Forecastin
ng the future growth in GD DP for any country is at be
est difficult an
nd much more e so for the G
GDP
growth foor the entire w
world. The IMMF has therefoore supplied tthe baseline fforecasts with a fan chart3
picturing the uncertainnty in their es
stimates.
This fan chart4 shows a
as blue colore
ed bands the uncertainty a
around the W
WEO baseline forecast with
h 50,
70, and 900 percent con rvals5.
nfidence inter
There is also another b
band on the cchart, implied but un‐seen,
, indicating a 10% chance of something g
“unpredicctable”. The fan chart thus
s covers only 9
90% of the IM
MF's estimatees of the futur
re probable
growth raates.
The table below shows s the actual fi
igures for the
e forecasted G
GDP growth (%
%) and the lim
mits of the
confidenc
ce intervals:
Lower Baseline Uppe
er
90% 70% 50%
% % 50% 70% 90%
%
2012 2.5
5 2.9 3.1
1 3.5 3.8 4.0 4.3
2013 2.1
1 2.8 3.3
3 4.1 4.8 5.2 5.9
The IMF h wing comments to the figures:
has the follow
3
The Inflat
tion Report Proojections: Understanding the e Fan Chart By Erik Britton, Paaul Fisher and John Whitley,
Quarterly B Bulletin, Febru
uary 1998, pagees 30‐37.
The MPC's s Fan Chart Inflation Report, May 2002, pag ges 48‐49.
Assessing t the MPC's Fan Charts By Rob b Elder, George Tim Taylor and Tony Yates, Q
e Kapetanios, T Quarterly Bullet
tin,
Autumn 20 005, pages 3266‐48
4
Figure 1.1
12. from:, Worrld Economic OOutlook (April 22012), Internat
tional Monetar ry Fund, Isbn 9
978161635246 62.
5
As shown n, the 70 perce
ent confidence interval includdes the 50 perc
cent interval, a and the 90 perccent confidencce
interval inccludes the 50 a
and 70 percent t intervals. See
e Appendix 1.2 in the April 20009 World Economic Outlook k for
details.
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4.
Risks around the WEO pro
“R ojections havee diminished, consistent w with market in
ndicators, butt they
re
emain large and tilted to the downside. . The various indicators do
o not point in a consistent
direction. Infla
ation and oil p
price indicato
ors suggest doownside risks to growth. The term spread
nd S&P 500 o
an options pricess, however, pooint to upside
e risks.”
Our appro
oximation of t
the distribution that can h art for 2012 as given in the
have produce d the fan cha e
World Eco
onomic Outloook for April 2
2012 is shownn below:
This distribution has: mmean 3.43%, standard dev viation 0.54, m
minimum 1.2 22 and maximmum 4.70 – it is
skewed w with a left tail.
. The distribut
tion thus also
o encompasse es the implied
d but un‐seen
n band in the
chart.
Now
w we are read
dy for serious forecasting!
The final sales forecasts
By employying the samee technic that
t we used to calculate the forecast bannd we can by Monte Carlo
simulation
n compute thhe 2012 distribution of nett sales forecas e distribution of GDP grow
sts, given the wth
rates and by using the expected varriance for the
e differences b
between fore ecasts using the regression
n and
new obseervations. The
e figure below
w describes thhe forecast prrocess:
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5.
We however are not only using the 90% interval for The GDP growth rate or the 95% fo orecast band,, but
the full range of the distributions. T
The final fore
ecasts of net s
sales are given as a histogr
ram in the gra
aph
below:
This distribution of forecasted net s
sales has: me 0M, standard
ean sales 1820 d deviation 81
1, minimum s
sales
1590M an nd maximum sales 2055M – and it is slightly skewed d with a left ta
ail.
So what a
added informa
ation have we got from th
he added effo
ort?
Well, we nnow know that there is on nly a 20% probability for ne
et sales to be
e lower than 1
1755 or above e
1890. The e interval from
m 1755M to 11890M in net sales will theen with 60% pprobability co
ontain the act
tual
sales in 20
012 ‐ se graphh below giving the cumula
ative sales dis tribution:
know that we with 90% pro
We also k obability will see actual ne
et sales in 20112 between 1 1720M and
1955M.Buut most impoortant is that w
we have visua alized the unccertainty in th
he sales forec
casts and that
contingen
ncy planning f
for both low aand high sales should be p performed.
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6.
An unce
ertain pas
st
The Bank of England’s fan chart from 2008 show wed a wide ra nge of possibble futures, bu
ut it also show
wed
the uncerrtainty about where we we ere then ‐ see
e that the blac
ck line showing National SStatistics data
a for
the past h
has probabilit
ty bands arou
und it:
ates that the values for pa
This indica ast GDP growt th rates are u
uncertain (sto
ochastic) or co
ontains
measurem ment errors. TThis of course
e also holds fo
or the IMF his
storic growthh rates, but th
hey are not
supplying this type of i
information.
wth rates can
If the grow n be considereed stochastic the results a bove will still l hold, if the c
conditional
distributio
on for net sales given the G
GDP growth r rate still fulfil ls the standard assumptio ons for using
regressionn methods. Iff not other meethods of estimation must t be consider
red.
Black Swans
y was still not enough to co
But all this uncertainty ontain what w
was to becom
me reality – sh
hown by the r
red
line in the
e graph abovee.
How wron
ng can we be? Often more
e wrong than we like to thiink. This is go
ood ‐ as in use
eful ‐ to know
w.
`“
“As Donald Ru
umsfeld once
e said: it's not only what w e don't know
w ‐ the known unknowns ‐ it's
what we don't
w t know we don't know.”
While stattistic methodds may lead us to a reasonably understa anding of som me phenomen non that doess not
always tra
anslate into aan accurate prractical prediction capabil ity. When thaat is the case,
, we find ours
selves
talking ab
bout risk, the likelihood tha
at some unfav vorable or favvorable event will take plaace. Risk
assessment is then nec cessitated and we are left only with pro obabilities.
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7.
A final w
word
Sales for
recast models are an integrated part of our enterp
o prise simulat
tion models - as parts of the
f
models predictive an
p nalytics. Pred
dictive analy
ytics can be d
described as statistic mo
odeling enablling
the prediction of futu events or results6, usi present a past info
ure r ing and ormation and data.
d
In today’ fast movin and highly uncertain markets, for
’s ng y m recasting hav become th single mo
ve he ost
importan element of the manage
nt f ement proces The abilit to quickly and accura
ss. ty y ately detect
changes in key extern and inter variable and adjust tactics acco
i nal rnal es t ordingly can make all the
e
differenc between su
ce uccess and failure:
f
1. Forecasts must integrate both externa and interna drivers of business an the financ
b al al f nd cial
re
esults.
2. Absolute fore
A ecast accurac (i.e. small confidence intervals) is less import than the
cy l e s tant e
in
nsight about how current decisions and likely fut
t a ture events w interact to form the
will
re
esult
3. Detail does not equal accu
D uracy with respect to for
r recasts
4. The forecast is often less important th the assum
T i han mptions and variables th underpin it –
d hat
th
hose are the things that should be tra
s aced to provi advance warning.
ide
5. Never relay on single poi or scenari forecastin
N o int io ng
The foreccasts are usuually done in three stages first by for
n s, recasting the market for that particu
e r ular
product(s then the firm’s marke share(s) en
s), f et nding up wit a sales for
th recast. If the firm has
e
activities in different geographic markets the the exerci se has to be repeated in each market
s t en t,
having in mind the co
n orrelation be
etween markkets:
1. All uncertaint about the different ma
A ty arket sizes, m
market share and their c
es correlation wwill
fi
inally end up contributin to the unc
p ng certainty in th forecast f the firm’s total sales.
he for
2. This uncertain combine with the uncertainty fr
T nty ed u from other fo
orecasted varriables like
in
nterest rates, exchange ra
ates, taxes et will even
tc. ntually be ma
anifested in t probability
the
distribution fo the firm’s equity valu
or s ue.
The ‘mod we have been using in the exam have nev been test out of sa
del’ e mple ver ted ample. Its
usefulnes as a foreca model is therefore sti debatable
ss ast ill e.
Referen
nces
Gardner, D & Tetlock, P., (2011) Overcomin Our Aver
), ng rsion to Ack
knowledging Our Ignora
g ance,
http://ww
ww.cato-unbound.org/20011/07/11/daan-gardner-a
and-philip-tet
tlock/overco
oming-our-
aversion-
-to-acknowle
edging-our-iignorance/
World Ecconomic Ouutlook Databa April 20 Edition;
ase, 012
http://ww
ww.imf.org/e
external/pubs/ft/weo/201
12/01/weoda
ata/index.asp
px
6
In this cas
se the probabi
ility distribution of future net
t sales.
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