pricing uncertainty: ignore volatility at your perilthe combination of a dozen or more models could...
TRANSCRIPT
01/05/2013
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Pricing uncertainty: Ignore volatility at your peril
Current Issues in General Insurance2nd May 2013
About the presenters
Sherdin Omar is a senior manager with Ernst & Young’s European actuarial services practice. He has significant technical and commercial motor insurance pricing experience building predictive models for motor and home pricing as well as managing the pricing structures for one the UKand home pricing as well as managing the pricing structures for one the UK leading motor brands. He has advised a number of leading motor brands on a wide range of projects ranging from getting value out of data and elasticity.
Dr. Ji Yao is a manager with Ernst & Young’s European actuarial services practice. He has extensive experience in various modelling for pricing with a solid background in mathematics and statistics. He has extensive first-hand gexperience in risk models, demand models and price optimisation. Recently, he has worked on elasticity modelling for a large insurance-related company.
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Agenda
Background
D ibi i i t i t d dDescribing pricing uncertainty and adequacy
Quantifying pricing uncertainty
Applications of pricing uncertainty
Summary
Q&A
3 Pricing uncertainty: Ignore volatility at your peril
Background
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Pricing is the primary lever that affects revenue and ultimately profitability
Pricing: Sets maximum available profit
y s
available profit(includes ancillary income)
sInvestment returns
nal
es
Po
licy
proc
es
5
Once a policy is written, there are limited levers an insurer can use to influence the final profit for that business
Cla
impr
ocesResidual profits
Pricing uncertainty: Ignore volatility at your perilO
pera
tioex
pens
e
The UK insurance market is one of the most competitive markets in the world
80%
90%
o
Motor Home
100%
110%
120%
130%
Rep
ort
ed n
et c
om
bin
ed r
atio
6
Source: S&P and Ernst & Young interpretation
Year
Please note all results are before ancillary income and investment returns
Pricing uncertainty: Ignore volatility at your peril
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140%
150%
3,000,000
3,500,000
Case study: A UK motor insurerCompany maintained premium volume but grew customer numbers, while the performance deteriorated
The company maintained premium volume but
90%
100%
110%
120%
130%
500,000
1,000,000
1,500,000
2,000,000
2,500,000
Rep
ort
ed n
et c
om
bin
ed r
atio
Gro
ss w
ritt
en p
rem
ium
(£k
)
pgrew customer numbers, while the results deteriorated
80%02005 2006 2007 2008 2009 2010 2011
Year
Gross written premium Reported net combined ratio
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Source: S&P and Ernst & Young interpretation
Pricing uncertainty: Ignore volatility at your peril
Any company’s data only represents a small proportion of the market
►Remember that the best estimate is only a point estimate from the sample of the total
Company A10%
Company B8% Company C
20%Company D
6%
market
►Typically, the standard error of predicted values is related to the sample size
►where s is the sample standard d i ti
Whole market
%
C ACompany B
Company C
Company A has grown by moving into new customer segments where it has no
historical data. Its pricing decisions have been based on extrapolation
deviation
►n is the number of observations
8
Whole market
Company A20%
6%Company C
18%
Company D6%Can Company A be sure it has grown in
a sustainable fashion with accurate pricing?
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Looking at multiple factors at once, there is limited data to support pricing in the potential growth segments
►30% of book is non-core segments2500
3000
3500
cies
Distribution of age by car age by NCD
Non-core customer segmentsPotential growth customer segments
Core customer segments
g►Under-pricing these segments by 5% will lead to 1.5% increase in loss ratio of total book
► Pricing models will extrapolate the experience from the core customer segments into the potential growth customer segments and non-core segments
0
500
1000
1500
2000
Nu
mb
er o
f p
oli
c
Age by car age by NCD
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► The less data available in these segments, the greater the uncertainty in the predicted values► For example the pricing models become increasingly unreliable as we consider the customer segments
to the right► The key issue is how much reliance is placed on these predicted values?
► For smaller companies, these issues could arise in some two way interactions.
Pricing uncertainty: Ignore volatility at your peril
Creating a rating structure is a combination of science and art
► Typically we use science (statistical models) to set the relativities for the technical price
► And overlay ‘art’ to set the future claims and premium assumptions to calculate ‘street price’
► However are we considering the volatility in our models?
► Is that volatility significant ?
► What could we do about it?
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An insurer that understands the volatility in their pricing models should be able to gain a long term competitive advantage
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Describing pricing uncertainty and adequacy
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Key discussion point is to identify and apply pricing uncertainty into the pricing decision
Hypothesis► Each insurer’s own experience is only a sample of the overall market experience for any risk► The smaller the sample the higher the risk of mispricing► Over-pricing: potentially profitable business is lostp g p y p► Under-pricing: has the potential to be a significant issue, especially on a price comparison
websiteChallenges► Competitors may have lots of data for a
specific segment, but you do not► How much to adjust the basic risk price by
customer segment to allow for sample error.► Checking that the under-pricing risk across
the portfolio is within the insurer’s risk
Risk premium calculated by insurer A
Insurer B estimates the risk cost to be less than insurer A.However there is a 45% chance that the actual risk cost is greater than insurer
Risk premium calculated by i B the portfolio is within the insurer s risk
appetite.► Putting in place real-time portfolio
management.
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A’s view.Is Insurer B under pricing?
Potential range of expected risk cost
insurer B
45%
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A typical approach to risk cost modelling ignores the uncertainty associated with each component model
Risk premiumThe important thing is to quantify the uncertainty when the component models are combined to aid the pricing decision
AD BC
AD Freq
AD Sev
Large BI BC
LBIFreq
LBI Sev
Small BI BC
SBIFreq
SBISev
TPPD BC
TPPD Freq
TPPDSev
WS BC
WSFreq
WSSev
F&T BC
F&TFreq
F&TSev
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q q q q q q
► Each model (frequency and severity) has some uncertainty associated with it► Typically this uncertainty is ignored► The combination of a dozen or more models could lead to some very uncertain point
estimates
Pricing uncertainty: Ignore volatility at your peril
Result of bootstrapping: the estimated burning cost can have significant variation
200
250
360
380
400
2% difference Where there is less data, the variance is
50
100
150
200
240
260
280
300
320
340
360
Nu
mb
er o
f p
olic
ies
(th
ou
san
ds)
Bu
rnin
g c
ost
9% difference
significantly larger
0200
220
0-1 2 3-4 5-6 7-8 9+
No Pols Selected 95th percentile 5th percentil
14
Tenure
5th percentile
Pricing uncertainty: Ignore volatility at your peril
Number of policies
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In our potential growth segment our estimate
How does the range of the prediction intervals vary with the number of policies?
40
50
60
ere
nti
le –
5th
ti
ca
l po
lic
ies
Graph showing the variation of risk premium
Non-core customer segments
Potential growth customer segments
Core customer segments
gcould differ by in excess of ± £10, which will make a difference in highly elastic marketsFor non-core customer segments the results are highly uncertain
0
10
20
30
40
521
282
070
239
844
239
121
819
534
981
401
355
249
221
197
140
129
100
93 85 21 19 10 6 5
Bu
rnin
g c
ost
ran
ge
(95t
h p
ep
erce
nti
le)/
nu
mb
er o
f id
en
Range
Graph showing the variation of risk premium when there is sparse data
15
The potential growth customer segments have enough uncertainty to skew predicted results significantly, while the non-core customer segments have a wide uncertainty on predicted results
195
112 40 32 28 12 11 8 5 9 4 3 2 2 1 1 1 1
Number of identical policies
Pricing uncertainty: Ignore volatility at your peril
The scope to reduce price in potential growth customer segments is limited by pricing uncertainty
Core customer segments Potential growth customer segments
9,00010,000
8 0009,000
10,000Best estimate of burning cost
Best estimate of burning cost
Range of best estimateRange of best estimate
01,0002,0003,0004,0005,0006,0007,0008,000
400 450 500 550 600 650 700
Dem
and
Premium (£)
01,0002,0003,0004,0005,0006,0007,0008,000
400 450 500 550 600 650 700
Dem
and
Premium (£)
Current price
burning cost burning cost
Current price
►Price is set with a margin to the burning cost
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►Price is set with a margin to the burning cost but is already competitive►To increase sales in this segment efficiently, a combination of price, product and marketing is needed
and the price is not competitive►A small change in price is expected to grow volumes significantly►Due to the uncertainty of the burning cost we need to understand for which customers within the segment we can reduce the margin
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The uncertainty around the burning cost prediction can be explicitly calculated
► Let and be the linear predictors of the frequency and severity models, respectively.
► The 95% confidence interval of the burning cost is defined as:
► The covariance is computationally difficult to calculate, so let
► So the 95% confidence interval is simplified to
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The simplification holds true against the results from the bootstrap exercise► We can ‘measure‘ the uncertainty around the burning cost using confidence
intervals with a simplification for independence.
► The results are similar to those obtained from the bootstrap, except when the
uncertainty is very large in which case we over estimateuncertainty is very large, in which case we over-estimate.
300
400
500
un
cert
ain
ty
Theoretical vs empirical uncertainty
0
100
200
0 50 100 150 200 250 300 350 400 450 500
Th
eore
tica
l
Empirical uncertainty
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Applications of price uncertainty
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We reserve to a defined percentile. Should we also manage our prices actively to a level of adequacy?► Let’s define Pricing Adequacy (PA) for a policy as
where,
P i th i f th i kP is the price for the risk
PL is the lower bound of the burning cost estimate
PU is the upper bound of the burning cost estimate
Example
► The current price for this risk is £300
► For a nominal 10% increase we can increase the pricing adequacy substantially while minimally affecting 40%
60%
80%
100%
120%
140%
160%
180%
200
300
400
500
600
uac
y &
pro
bab
ility
of
con
ver
sio
n
Pri
ce
20
the probability to convert
► The challenge is to analyse the portfolio and understand where price increases could be established to gain margin and fund segments where the uncertainty is greater
Pricing uncertainty: Ignore volatility at your peril
-40%
-20%
0%
20%
40%
-
100
200
225 248 273 300 330 363 399 439 483
Pri
ce a
deq
c
Range of prices
price Price adequacy Probabilty of conversion
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► A price increase across the whole portfolio is unlikely to increase the price adequacy efficiently as only the cheapest quotes are accepted
Th t i k i t id tif t t th t t i
The pricing adequacy measure may help to provide a consistent basis to adjust quoted premiums
► The trick is to identify customer segments that can carry a rate increaseFlat increase Use pricing uncertainty
1%
2%
3%
4%
5%
6%
7%
8%
rob
abil
ity
den
sity
fu
nct
ion
Accept distribution moves to the right but is still on average around 50%
1%
2%
3%
4%
5%
6%
7%
8%
rob
abil
ity
den
sity
fu
nct
ion
Distribution of ‘accepts’ is now centred around 65%
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A flat increase will marginally improve the accept distribution of price adequacy
Price changes are made to maximise the pricing adequacy
0%0% 20% 40% 60% 80% 100%
Pr
Pricing adequacy
Distribution of quotes Distribution of accepts
Pricing uncertainty: Ignore volatility at your peril
0%0% 20% 40% 60% 80% 100%
Pr
Pricing adequacy
Distribution of quotes Distribution of accepts
Does pricing uncertainty lead to anti-selection?
► Recall each insurer has a distribution of price points:► In a highly competitive market, such as a price
comparison site, generally only the cheapest (underpriced?) risk is sold
Risk premium calculated by insurer A
Insurer B estimates the risk cost to be less than insurer A.However there is a 45% chance that the actual risk cost is
Ri k i( p )
► This effect is known as the winner’s curse
► Key question is what to do with this information?
Quotes with high pricing 4%
5%
6%
7%
8%
sity
fu
nct
ion
Distribution of pricing adequacy for quotes and accepts
actual risk cost is greater than insurer A’s view.Is Insurer B under pricing?
Potential range of expected risk cost
Risk premium calculated by insurer B
45%
adequacy rarely convert because the quoted premium is uncompetitive in the market place
22
0%
1%
2%
3%
4%
0% 20% 40% 60% 80% 100%
Pro
bab
ility
den
Pricing adequacy
Distribution of quotes Distribution of accepts
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Which way are you heading?How strong are your prices?
46% 46%34%
80% 60%
66%
Having the information to justify deviances from plan and to spot potential opportunities
Customer segment Target volume
Actual volume Current priceadequacy
Price adequacy to meet target volume
Young drivers 10% 9% 60% 60%
4WD drivers 30% 20% 53% 26%
Over 55s 30% 25% 72% 62%
Urbanites 5% 7% 66% 66%
Commuters 5% 7% 58% 60%
Young couples 20% 32% 45% 57%
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Total 100% 100% 57% 50%
► Assume a price adequacy target of 60%
► The “4WD drivers” segment is behind its target volumes but the cost to get to target is too high, if considering the price adequacy
► The “Over 55s” segment volume is also behind target but there is scope to reduce prices and still maintain a healthy price adequacy
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25
30
Conversion model monitoring
Understanding the model’s confidence intervals can indicate when a model needs refreshing
► Confidence intervals can be calculated based on the previously defined
Traditionally we would refresh a demand model
Data the conversion model was built on
0
5
10
15
20
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53C
on
ver
sio
n (
%)
Week
Best estimate Lower bound of 95% CI
the previously defined formulae
► Check whether the observation is within the confidence interval► At the 95% confidence
level it is expected that 19
every six months
Best estimate Lower bound of 95% CI
Upper bound of 95% CI Actuallevel, it is expected that 19 out of 20 times, actual observations are within confidence interval
25
The actual experience is outside the CI once in couple of weeks, so the model is still okay
Here the actual experience is consistently outside the CI, so we conclude the model needs to be refreshed
Pricing uncertainty: Ignore volatility at your peril
Summary
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Knowing how to use pricing uncertainty is crucial for sustainable growth in a competitive market
► Rate setting for high volume business has to be automated
► However all statistical models have an error term associated
► Understanding customer segments where the error term is uncertain will help to make different pricing decisions
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Price setting is not a science, the key is to understand how to blend science and judgment in a cost effective matter
Q&A
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