pricing insurance risk

Pricing Insurance RiskModule C: Historical US Property-Casualty Profitability and Volatility

Stephen J. MildenhallCreated 2021-11-15 16:30:43.766628

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Table of Contents

Module C Contents

Section C.1 Premium to GDP Ratio, 1923-2020Section C.2 Surplus to GDP Ratio, 1931-2020Section C.3 Industry Volatility and Profitability Metrics, 1985-2020Section C.4 Direct and Net Volatility and Profitability by Major Line, 1992-2020Section C.5 Direct Premium Growth by Major Line, 1992-2020Section C.6 Implications





C.01. Premium to GDP Ratio,1923-2020

Premium to GDP Ratio

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

NW

P to

GD

P R

atio

Figure 1: The ratio of US statutory net written premium (NWP) to nominal gross domestic product (GDP) gives a good measureof the insurance market cycle. It measures the penetration of the insurance industry into the economy. GDP and NWP are bothare on a nominal basis; inflation cancels in the ratio. If GDP in 2020 had grown inline with 2019 over 2018, then premium toGDP ratio in 2020 would be unchanged. Source: NAIC US Statutory Compbined P&C Industry premium and GDP from FRED.





Premium to GDP Ratio: Cyclical Growth Between 1947 and 1997

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

NW

P to

GD

P R

atio

Figure 2: Secular growth from the end of WW2 through 1986 has given way to retrenchment and stabilization. The 1986watershed saw tax reform, which introduced loss reserve discounting for tax purposes, as well as the claims-made form andabsolute pollution exclusion. The period since 2008 is particularly stable.





Premium to GDP Ratio: 1968 Watershed

1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

NW

P to

GD

P R

atio

Great D

epression

Pearl Harbor

Oil C

risis

LMX Spriral

AndrewN

orthridge

WTC

KatrinaG

FC

HIM

After 1968, all years above 2.8%Until 1968, all years below 2.8%

Figure 3: The 2.8 percent level (green lines) separates 1968 and prior from all subsequent years. The ratio was less than 2.8percent in every year until 1968, while it has been greater than 2.8 percent in every year since. Significant insurance-relatedevents are called out on the x-axis.





Annual Change in Statutory Surplus, 1932 to 2020

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

-30%

-20%

-10%

0%

10%

20%

30%

40%

Cha

nge

in S

urpl

us

1974

2001

2008Change in PHSmean change 0.0785Upper CI z=2.3, SD=0.102Lower CI

Figure 4: The three most significant post-1968 surplus declines have coincided with significant asset value declines: 1974, 2001and 2008. 2000-02 is the only consecutive three year decline.





Annual Change in Statutory Surplus, 1932 to 2020 With 10- And 25-Year Rolling SD

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

-30%

-20%

-10%

0%

10%

20%

30%

40%

Cha

nge

in S

urpl

us

Change in PHSmean change 0.0785Upper CI z=2.3, SD=0.102

Lower CIRolling 10 year SDRolling 25 year SD

Figure 5: Rolling standard deviation reasonably steady over long-term history, and currently at historically low levels.





Multi-Year Change in Statutory Surplus, 1932 to 2020

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

-20%

-10%

0%

10%

20%

30%

1 Ye

ar C

hang

e in

Sur

plus

1 Year Change in Surplus, cagr=7.8%

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

-20%

0%

20%

40%

2 Ye

ar C

hang

e in

Sur

plus


1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

-20%

0%

20%

40%

60%

80%

3 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

20%

40%

60%

80%

100%

120%

4 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

25%

50%

75%

100%

125%

150%

5 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

50%

100%

150%

200%

6 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

50%

100%

150%

200%

7 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

50%

100%

150%

200%

250%

8 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

50%

100%

150%

200%

250%

300%

9 Ye

ar C

hang

e in

Sur

plus


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

50%

100%

150%

200%

250%

300%

10 Y

ear

Cha

nge

in S

urpl

us


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

50%

100%

150%

200%

250%

300%

350%

11 Y

ear

Cha

nge

in S

urpl

us


1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0%

100%

200%

300%

400%

500%

12 Y

ear

Cha

nge

in S

urpl

us


Figure 6: Surplus doubles every nine years, on average. Current period shows historically low long-term growth rates. Notadjusted for inflation.





Premium to Surplus Ratio, 1932 to 2020

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

2.5

2.75

3

NWP to Surplus RatioFive-year rolling average

Figure 7: Industry leverage ratios have been decreasing since their mid-1970s high of 2.7 to 1. They have been remarkablystable over the last decade. Current leverage ratios were also seen in the 1930s.





Premium to GDP vs. Suprlus to GDP

1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5%Surplus to GDP

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

Prem

ium

to G

DP

1968-69average

193119511968199220052020

Figure 8: Period since 1968, above the dotted line, has seen much greater swings in surplus to GDP (east west direction) thanthe earlier period. Current premium penetration is below historical highs but current surplus to GDP ratios are at historic highs.Note relatively high surplus levels in 1930s (yellow): the industry did not return to 1930s levels of relative capitalization until1995.





Three Phases of the Market 1931-2020

1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5%Surplus to GDP

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

Prem

ium

to G

DP

1931

19681969

1985

1986

20012020

Phase I

Phase IIPhase III

193119511968199220052020

Figure 9: Phase I, 1931-1968: establishment, depression, WW2, and recovery. Phase II, 1969-1985: growth and expansion,industry looking for ways to find coverage. Tax code and high interest rate favorable to casualty business. Phase III,1986-present: retrenchment and responsibility, secular decline in interest rates and revised tax code emphasize underwritingprofits, and growing casualty reserves increase capital intensity.





Market Dynamics Since 1986 Explained by Prior Year Surplus Levels

1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 4.5%Prior Year-End Surplus to GDP

2.8%

3.0%

3.2%

3.4%

3.6%

3.8%

4.0%

Prem

ium

to G

DP

1986

1992

2001

2005

2009

2018

2020

198620012020

Figure 10: Regression of premium to GDP on prioryear surplus to GDP. Anticlockwise cycle between1994 and 2008!

Results: Ordinary least squares===================================================================Model: OLS Adj. R-squared: 0.862Dependent Variable: PG AIC: -365.3573Date: 2021-11-15 14:51 BIC: -362.2466No. Observations: 35 Log-Likelihood: 184.68Df Model: 1 F-statistic: 214.0Df Residuals: 33 Prob (F-statistic): 5.54e-16R-squared: 0.866 Scale: 1.6216e-06--------------------------------------------------------------------

Coef. Std.Err. t P>|t| [0.025 0.975]--------------------------------------------------------------------Intercept 0.0474 0.0011 44.8331 0.0000 0.0453 0.0496pSG -0.4717 0.0322 -14.6297 0.0000 -0.5374 -0.4061-------------------------------------------------------------------Omnibus: 3.263 Durbin-Watson: 1.031Prob(Omnibus): 0.196 Jarque-Bera (JB): 2.006Skew: 0.368 Prob(JB): 0.367Kurtosis: 3.913 Condition No.: 150===================================================================

• Very strong correlation of premium penetration against prior year-end surplus ratio, regression R2 = 0.87• Suggests current premium levels will persist while industry capitalization remains strong





C.02. Surplus to GDP Ratio, 1931-2020

Surplus to GDP Ratio, 1931-2020

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

PHS

to G

DP

Rat

io

Figure 11: The surplus to GDP ratio shows that relative surplus levels have steadily increased since their recorded low in 1974 of1.1% (red dot). YE 2020 surplus estimated at 2 percent above Q3. Last year’s level is the all-time high of 4.6%.





The Surplus to GDP Ratio Has Increased During the Modern Period, 1968-2020

1930 1940 1950 1960 1970 1980 1990 2000 2010 2020Year

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

4.0%

4.5%

PHS

to G

DP

Rat

io

Figure 12: Linear regression has R2 = 0.892, though horrible error auto-correlation until the mid-2000s.





C.03. Industry Volatility and ProfitabilityMetrics, 1985-2020

Industry Net Volatility and Profitability Metrics, 1985-2020

Table 1: Industry operating and profitability metrics

Quantity Kind Full Name Definition

NEP USD000 Net earned premiumNIL USD000 Net incurred lossExp USD000 Expenses All underwriting expenses and other income, excluding LAEUWGain USD000 Underwriting gainNII USD000 Net Inv Inc Net investment income, excluding gain or lossesOP USD000 UW Operating result UW Gain plus net inveestment incomeGL USD000 Inv Gain or Loss Realized and unrealized investment gain, pre-tax 2005-19NI USD000 Net income Statutory net income, page 4DF USD000 Dividends and Fin. Dividends net of capital contributions (generally negative)PHS USD000 Polholder Surplus Policyholder surplus, page 4

NIIR Net Inv Income Ratio Net investment income to earned premiumLR, ER ratio Loss, Expense Ratio Loss and expense ratio, to earned premiumCR, OR ratio Combined, Operating Ratio UW Gain, operating result to earned pmreium

NII_PHS ratio Net Inc Inc / PHS NII / PHSTIG_PHS ratio Total Inv Gain / PHS Total investment income and GL to PHS (tax mis-match)NI_PHS ratio Net Inc / PHS NI / PHS, quasi-ROE, includes realized gainsOP_PHS ratio Op Res / PHS Operating result to PHS, “operating-ROE”ROEci ratio Comp Inc / PHS Change in PHS net of dividends and financing / PHS, a

comprehensive income ci ROE





Insurance Volatility and Profitability Metrics Showing Underwriting and Operating

statistic

NetEarned

Premium

Net In-curredLoss Expenses

UndewritingGain

UW Op-eratingResult

Net InvIncomeRatio Loss Ratio

ExpenseRatio

CombinedRatio

OperatingRatio

min 133.342G 118.572G 39.761G -50.309G -11.448G 0.0832 0.652 0.263 0.929 0.8mean 363.201G 272.050G 103.009G -8.799G 33.397G 0.123 0.765 0.283 1.05 0.915max 643.004G 450.916G 187.661G 34.753G 88.101G 0.154 0.889 0.3 1.19 1.04sd 139.202G 91.640G 40.254G 17.410G 24.162G 0.0214 0.0587 0.00936 0.0591 0.0481cv 0.383 0.337 0.391 -1.98 0.723 0.174 0.0767 0.033 0.0564 0.0525growth -0.043 -0.0358 -0.0428 -0.507 1.09 0.0188 0.00867 847.159u 0.00612 0.00507r2 0.966 0.958 0.976 0.196 0.507 0.736 0.501 0.0588 0.441 0.139rse0 26.001G 19.077G 6.265G 15.837G 17.220G 0.0112 0.042 0.00921 0.0448 0.0453rse 26.418G 19.383G 6.366G 16.091G 17.496G 0.0113 0.0427 0.00936 0.0455 0.046slope 0.0358 0.0313 0.0367 -0.0832 0.0489 -0.0142 -0.00515 760.683u -0.00355 -0.00186year -25.642T -16.775T -7.458T -1.474T -3.235T 3.62 8.66 -0.148 8.51 4.32ar r2 0.991 0.966 0.993 0.255 0.517 0.839 0.428 0.6 0.425 0.238ar rse0 13.366G 16.574G 3.303G 15.331G 16.691G 0.00871 0.0426 0.00586 0.0422 0.0398ar rse 13.366G 16.574G 3.303G 15.331G 16.691G 0.0813 0.167 0.113 0.165 0.18ar slope 1.02 0.999 1.03 0.511 0.713 0.95 0.621 0.754 0.604 0.45ar intercept 8.584G 9.693G 1.316G -3.599G 11.277G 0.00436 0.285 0.0694 0.41 0.5

Table 2: statistics shown for the total US statutory industry. Columns are described on previous slide. Rows are described below.Source: S&P Global Market Intelligence, Statutory Accounts page 4.





Insurance Volatility and Profitability Metrics: Investments and Returns

statisticNet InvIncome

Inv Gainor Loss

NetIncome

Dividendsand Fin.

PolholderSurplus

Net IncInc / PHS

TotalInv Gain/ PHS

Net Inc/ PHS

Op Res/ PHS

Comp Inc/ PHS

Pre-TaxIncome

min 19.508G -98.513G -5.786G -36.665G 75.511G 0.0575 -0.0976 -0.0192 -0.0435 -0.0996 -5.882Gmean 42.196G 17.064G 31.102G -10.247G 411.178G 0.134 0.178 0.078 0.0819 0.089 37.886Gmax 56.981G 121.267G 70.061G 9.159G 929.932G 0.258 0.4 0.136 0.176 0.246 89.243Gsd 10.261G 34.761G 21.541G 14.922G 241.158G 0.0606 0.0974 0.0355 0.0476 0.0796 25.711Gcv 0.243 2.04 0.693 -1.46 0.587 0.451 0.547 0.455 0.581 0.894 0.679growth -0.0259 -1.92 0.147 0.0346 -0.0665 0.0477 0.0913 0.165 1.17 -0.681 -0.082r2 0.855 0.0817 0.562 0.752 0.965 0.903 0.501 0.0402 0.00436 270.752u 0.516rse0 3.967G 33.798G 14.468G 7.533G 45.602G 0.0191 0.0698 0.0353 0.0482 0.0808 18.148Grse 4.031G 34.340G 14.700G 7.654G 46.334G 0.0195 0.0709 0.0358 0.049 0.0822 18.439Gslope 0.0213 0.0553 0.0493 0.12 0.0547 -0.0407 -0.0368 -0.00865 -0.00364 0.00144 0.0463year -1.761T -1.871T -3.038T 2.450T -44.622T 11.07 13.28 1.43 0.68 -0.167 -3.472Tar r2 0.904 237.963u 0.483 0.748 0.983 0.969 0.293 0.0812 0.156 0.00665 0.45ar rse0 3.033G 35.777G 15.522G 7.549G 31.402G 0.0104 0.0776 0.0339 0.0402 0.0807 18.996Gar rse 3.033G 35.777G 15.522G 7.549G 31.402G 0.04 0.213 0.196 0.183 0.255 18.996Gar slope 0.896 -0.0158 0.696 0.888 1.04 0.944 0.5 0.276 0.353 0.0806 0.664ar intercept 5.334G 17.495G 10.889G -2.324G 10.202G 0.00192 0.0818 0.0579 0.0565 0.0797 14.413G

Table 3: Statistics shown for the total US statutory industry. Columns are described on above. Rows are described below.Source: S&P Global Market Intelligence, Statutory Accounts page 4.





Insurance Volatility and Profitability Metrics

Gloss for rows• growth is the average anuual growth rate• r2, rse0, slope, year are the R2, residual square error, slope and intercept for a regression of each variable

against time (year)• rse equals rse0 plus the standard error of the slope parameter, giving a better indication of uncertainty• ar_r2, ar_rse0, ar_rse, ar_slope, ar_intercept are the same statistics for an AR(1) autoregressive model





Time Series of Volatility and Profitability Metrics

1985 1990 1995 2000 2005 2010 2015 2020Year

0

100

200

300

400

500

600

×109Net Earned Premium; SD=1.39e+11linear fit, r2=0.966, rse0=2.6e+10

1985 1990 1995 2000 2005 2010 2015 2020Year

0

100

200

300

400

×109Net Incurred Loss; SD=9.16e+10

linear fit, r2=0.958, rse0=1.91e+10

1985 1990 1995 2000 2005 2010 2015 2020Year

0

25

50

75

100

125

150

175

×109Expenses; SD=4.03e+10


1985 1990 1995 2000 2005 2010 2015 2020Year

40

20

0

20

×109Undewriting Gain; SD=1.74e+10ar fit, r2=0.255, rse0=1.53e+10

1985 1990 1995 2000 2005 2010 2015 2020Year

0

20

40

60

80

×109UW Operating Result; SD=2.42e+10

ar fit, r2=0.517, rse0=1.67e+10

1985 1990 1995 2000 2005 2010 2015 2020Year

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

Net Inv Income Ratio; SD=0.0214ar fit, r2=0.839, rse0=0.00871

1985 1990 1995 2000 2005 2010 2015 2020Year

0.65

0.70

0.75

0.80

0.85

0.90

Loss Ratio; SD=0.0587linear fit, r2=0.501, rse0=0.042

1985 1990 1995 2000 2005 2010 2015 2020Year

0.265

0.270

0.275

0.280

0.285

0.290

0.295

0.300

Expense Ratio; SD=0.00936ar fit, r2=0.6, rse0=0.00586

1985 1990 1995 2000 2005 2010 2015 2020Year

0.95

1.00

1.05

1.10

1.15

1.20

Combined Ratio; SD=0.0591linear fit, r2=0.441, rse0=0.0448

1985 1990 1995 2000 2005 2010 2015 2020Year

0.80

0.85

0.90

0.95

1.00

Operating Ratio; SD=0.0481ar fit, r2=0.238, rse0=0.0398

1985 1990 1995 2000 2005 2010 2015 2020Year

0

10

20

30

40

50

×109Net Inv Income; SD=1.03e+10

ar fit, r2=0.904, rse0=3.03e+09

1985 1990 1995 2000 2005 2010 2015 2020Year

100

50

0

50

100

×109Inv Gain or Loss; SD=3.48e+10

linear fit, r2=0.0817, rse0=3.38e+10

1985 1990 1995 2000 2005 2010 2015 2020Year

0

10

20

30

40

50

60

70

×109Net Income; SD=2.15e+10


1985 1990 1995 2000 2005 2010 2015 2020Year

30

20

10

0

10×109

Dividends and Fin.; SD=1.49e+10linear fit, r2=0.752, rse0=7.53e+09

1985 1990 1995 2000 2005 2010 2015 2020Year

0

200

400

600

800

×109Polholder Surplus; SD=2.41e+11


1985 1990 1995 2000 2005 2010 2015 2020Year

0.050

0.075

0.100

0.125

0.150

0.175

0.200

0.225

0.250

Net Inc Inc / PHS; SD=0.0606linear fit, r2=0.903, rse0=0.0191

1985 1990 1995 2000 2005 2010 2015 2020Year

0.1

0.0

0.1

0.2

0.3

0.4

Total Inv Gain / PHS; SD=0.0974linear fit, r2=0.501, rse0=0.0698

1985 1990 1995 2000 2005 2010 2015 2020Year

0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Net Inc / PHS; SD=0.0355ar fit, r2=0.0812, rse0=0.0339

1985 1990 1995 2000 2005 2010 2015 2020Year

0.05

0.00

0.05

0.10

0.15

Op Res / PHS; SD=0.0476ar fit, r2=0.156, rse0=0.0402

1985 1990 1995 2000 2005 2010 2015 2020Year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25

Comp Inc / PHS; SD=0.0796ar fit, r2=0.00665, rse0=0.0807

Figure 13: Time series of the variables from the previous table. Declining investment income and increasing volatility of gainsand loss are particularly evident. See gloss on next slide.





Time Series of Volatility and Profitability Metrics

Title decoder: Net Earned Premium; SD=1.39e+11 linear fit, r2=0.966, rse0=2.6e+10• CR is the variable name, e.g., combined ratio• SD standard deviation• If the variable appears to have a linear trend show the R2 and residual standard error of a regression against

time• If it appears autoregressive ar show statistics for a fit against the lagged variable• Linear trend is selected if the linear model R2 is > 0.9 or is greater than the ar model R2

Line legend• Solid line is the statistic• Horizontal line is its mean value• Dotted line is the linear (straight) or ar fit (not straight, and appears lagging)

Interpretation• rse significantly less than SD suggests potentially explainable variation• Expenses (Exp) and surplus (PHS) have a much lower uncertainty than their SD suggests because they have a

clear trend• Almost all the variability in UWGain is unexpected• CR may have a slightly predictable component—corresponding to the autoregressive underwriting cycle





C.04. Direct and Net Volatility andProfitability by Major Line, 1992-2020

Direct and Net Calendar Year Loss Ratio Average, Standard Deviation, Coefficient of Variation,Skewness, and Kurtosis by Major Line

Direct Net DiffLine Average SD CV Skew Kurt Average SD CV Skew Kurt Average SD CV Skew KurtPersonal Auto 0.768 0.041 0.053 -0.416 0.889 0.765 0.040 0.052 -0.424 0.687 0.003 0.001 0.001 0.007 0.202total 0.752 0.065 0.087 0.475 0.484 0.753 0.057 0.075 0.529 0.153 -0.000 0.009 0.011 -0.054 0.331Other Comm 0.65 0.072 0.111 0.632 1.25 0.65 0.054 0.083 0.803 0.443 0.000 0.019 0.029 -0.171 0.81Comm Auto 0.751 0.081 0.108 -0.013 -0.946 0.75 0.073 0.097 -0.039 -1.005 0.002 0.008 0.010 0.026 0.059Inland Marine 0.551 0.082 0.149 0.664 -0.151 0.568 0.059 0.105 -0.016 -1.192 -0.018 0.022 0.044 0.68 1.04CMP 0.716 0.109 0.152 0.418 0.062 0.717 0.088 0.123 0.178 -0.874 -0.001 0.020 0.029 0.24 0.936Workers Comp 0.772 0.106 0.138 0.025 -0.472 0.768 0.1 0.13 -0.121 -0.558 0.005 0.006 0.007 0.146 0.086Homeowners 0.763 0.163 0.214 1.66 4.35 0.766 0.131 0.171 1.66 5.24 -0.003 0.033 0.044 0.003 -0.884Liability 0.857 0.16 0.187 0.703 -0.496 0.833 0.158 0.19 0.769 -0.593 0.024 0.002 -0.003 -0.066 0.097Med Mal 0.837 0.214 0.256 0.734 -0.265 0.834 0.2 0.24 0.825 0.044 0.003 0.014 0.016 -0.091 -0.309Comm Property 0.691 0.314 0.454 1.56 2.03 0.676 0.188 0.278 1.6 4.21 0.015 0.126 0.176 -0.042 -2.189Reinsurance nan nan nan nan nan 0.813 0.318 0.391 2.2 7.63 nan nan nan nan nanFin Guaranty 0.631 0.709 1.12 2.31 5.51 0.627 0.627 1 2.06 4.07 0.004 0.082 0.122 0.251 1.44

Table 4: The average, standard deviation, coefficient of variation, skewness and kurtosis of direct and net loss ratio, by majorline. Sorted by Net CV. Exact grouping of statutory lines shown on next slide. Source: Industry Combined Direct Statutory IEE,1996-2017.





Direct and Net Calendar Year Combined Ratio Average, Standard Deviation, and Coefficient ofVariation by Major Line

Direct Net DiffLine Average SD CV Average SD CV Average SD CVPersonal Auto 1.01 0.044 0.044 1.01 0.039 0.039 0.002 0.005 0.005Other Comm 0.937 0.073 0.078 0.973 0.046 0.048 -0.036 0.026 0.030total 1.02 0.068 0.067 1.04 0.057 0.055 -0.014 0.011 0.012Comm Auto 1.04 0.084 0.080 1.05 0.077 0.073 -0.007 0.007 0.008CMP 1.05 0.114 0.109 1.08 0.094 0.088 -0.027 0.020 0.021Inland Marine 0.854 0.092 0.108 0.918 0.081 0.089 -0.064 0.011 0.020Workers Comp 1.05 0.117 0.112 1.05 0.101 0.096 -0.007 0.016 0.016Homeowners 1.06 0.167 0.158 1.07 0.135 0.126 -0.016 0.032 0.032Liability 1.14 0.163 0.143 1.14 0.156 0.137 -0.001 0.007 0.007Med Mal 1.06 0.21 0.199 1.07 0.189 0.177 -0.015 0.021 0.022Comm Property 0.986 0.32 0.325 1.02 0.205 0.202 -0.029 0.116 0.123Reinsurance nan nan nan 1.16 0.37 0.319 nan nan nanFin Guaranty 0.818 0.889 1.09 0.923 0.601 0.65 -0.106 0.288 0.437

Table 5: The average, standard deviation, and coefficient of variation of direct combined ratio, by major line. For most linescombined ratio SD is higher than loss SD, indicating pro-cyclical expenses. LAE included with loss. Sorted by Net CV. Directminus net equals assumed minus ceded, and so does only proxies ceded. Broadly, expect net CR to be greater than direct,reflecting the cost of reinsurance, and SD to be lower, reflecting its volatility reduction. This is true for all lines execpt PersonalAuto. Personal Auto cessions tend to involve high loss ratio business ceded to residual market pools. Exact grouping of statutorylines shown on next slide. Source: Industry Combined Direct Statutory IEE, 1996-2017.





Direct and Net Average Loss Ratio and Combined Ratio by Line

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20Combined Ratio

Fin Guaranty

Inland Marine

Other Comm

Comm Property

Personal Auto

total

Comm Auto

Workers Comp

CMP

Homeowners

Med Mal

Liability

Reinsurance

DirectNet

0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90Loss Ratio

Fin Guaranty

Inland Marine

Other Comm

Comm Property

Personal Auto

total

Comm Auto

Workers Comp

CMP

Homeowners

Med Mal

Liability

Reinsurance

DirectNet

Figure 14: Lines sorted by descending net combined ratio.





Direct and Net Average Combined Ratio vs. Standard Deviation Combined Ratio

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40SD CR

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20Av

g D

irec

t CR Personal

Auto

OtherComm

total

CommAuto

CMP

InlandMarine

WorkersComp

Homeowners

Liability

MedMal

CommProperty

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40SD CR

0.80

0.85

0.90

0.95

1.00

1.05

1.10

1.15

1.20

Avg

CR

PersonalAuto

OtherComm

total

CommAuto

CMP

InlandMarine

WorkersComp

Homeowners

Liability

MedMal

CommProperty

Reinsurance

DirectNet

Figure 15: Left: direct, right: direct and net, with joining line. Expect imppact of reinsurance to be in the northwest direction:lower standard deviation but higher combined ratio. This is the case for most lines. Risk benefit most evident for commercialproperty.





Mapping Statutory Lines to Major Lines

US Statutory lines grouped as follows• CMP

• Commercial Multiple Peril (Liability Portion), Commercial MultiplePeril (Non-Liability Portion)

• Comm Auto• Commercial Auto Liability, Commercial Auto Physical Damage

• Comm Property• Allied Lines, Earthquake, Fire, Glass

• Fin Guaranty• Financial Guaranty, Mortgage Guaranty

• Homeowners• Farmowners Multiple Peril, Federal Flood, Homeowners Multiple Peril

• Inland Marine• Inland Marine

• Liability• Other Liability, Other Liability - Claims-Made, Other Liability -

Occurrence, Products Liability

• Med Mal• Medical Professional Liability

• Other Comm• Aggregate Write-Ins For Other Lines Of Business, Aircraft (All Perils),

Boiler And Machinery, Burglary And Theft, Credit, Credit A & H,Fidelity, Group A&H, International, Multiple Peril Crop, Ocean Marine,Other A&H, Private Crop, Surety, Warranty

• Personal Auto• Private Passenger Auto Liability, Private Passenger Auto Physical

Damage

• Reinsurance• Reinsurance-Nonproportional Assumed

• Workers Comp• Excess Workers’ Compensation, Workers’ Compensation

• total• Totals (Lines 1 Through 34)

• Federal Flood included with Homeowners• Liability computed as total minus all other lines owing

to Occurrence vs. Claims Made coding change inoriginal data source

• Earthquake with Comm Property: Northridge was apersonal lines event but the CEA greatly reducedpersonal lines quake premium





Loss Ratio Correlation by Major Line

name CMPCommAuto

CommProperty

FinGuaranty

Home-owners

InlandMarine Liability

MedMal

OtherComm

PersonalAuto

WorkersComp total

CMP 1 0.539 0.731 -0.213 0.754 0.668 0.586 0.65 0.538 0.312 0.416 0.898Comm Auto 0.539 1 0.306 -0.480 0.021 0.213 0.285 0.544 0.39 0.599 0.080 0.407Comm Property 0.731 0.306 1 -0.196 0.634 0.741 0.35 0.347 0.354 0.224 0.121 0.712Fin Guaranty -0.213 -0.480 -0.196 1 0.018 -0.083 -0.373 -0.539 -0.228 -0.072 0.116 -0.059Homeowners 0.754 0.021 0.634 0.018 1 0.639 0.385 0.306 0.279 0.069 0.313 0.769Inland Marine 0.668 0.213 0.741 -0.083 0.639 1 0.237 0.283 0.47 0.052 0.213 0.632Liability 0.586 0.285 0.35 -0.373 0.385 0.237 1 0.809 0.534 0.249 0.492 0.703Med Mal 0.65 0.544 0.347 -0.539 0.306 0.283 0.809 1 0.662 0.279 0.517 0.662Other Comm 0.538 0.39 0.354 -0.228 0.279 0.47 0.534 0.662 1 0.222 0.509 0.596Personal Auto 0.312 0.599 0.224 -0.072 0.069 0.052 0.249 0.279 0.222 1 0.418 0.486Workers Comp 0.416 0.080 0.121 0.116 0.313 0.213 0.492 0.517 0.509 0.418 1 0.614total 0.898 0.407 0.712 -0.059 0.769 0.632 0.703 0.662 0.596 0.486 0.614 1

Table 6: Pearson correlation coefficient between direct loss ratios by major line.

name CMPCommAuto

CommProperty

FinGuaranty

Home-owners


MedMal

OtherComm

PersonalAuto

Reinsur-ance

WorkersComp total

CMP 1 0.539 0.637 -0.147 0.793 0.764 0.615 0.559 0.598 0.385 0.353 0.343 0.852Comm Auto 0.539 1 0.32 -0.489 0.132 0.283 0.113 0.441 0.307 0.644 -0.020 -0.134 0.358Comm Property 0.637 0.32 1 -0.091 0.522 0.557 0.443 0.195 0.27 0.248 0.488 -0.015 0.59Fin Guaranty -0.147 -0.489 -0.091 1 0.189 0.236 -0.305 -0.542 -0.311 -0.166 -0.194 0.226 0.023Homeowners 0.793 0.132 0.522 0.189 1 0.675 0.573 0.332 0.39 0.28 0.383 0.479 0.855Inland Marine 0.764 0.283 0.557 0.236 0.675 1 0.358 0.201 0.361 0.159 0.367 0.332 0.663Liability 0.615 0.113 0.443 -0.305 0.573 0.358 1 0.649 0.724 0.26 0.679 0.369 0.75Med Mal 0.559 0.441 0.195 -0.542 0.332 0.201 0.649 1 0.881 0.339 0.39 0.409 0.597Other Comm 0.598 0.307 0.27 -0.311 0.39 0.361 0.724 0.881 1 0.329 0.445 0.557 0.692Personal Auto 0.385 0.644 0.248 -0.166 0.28 0.159 0.26 0.339 0.329 1 -0.063 0.313 0.582Reinsurance 0.353 -0.020 0.488 -0.194 0.383 0.367 0.679 0.39 0.445 -0.063 1 0.196 0.465Workers Comp 0.343 -0.134 -0.015 0.226 0.479 0.332 0.369 0.409 0.557 0.313 0.196 1 0.598total 0.852 0.358 0.59 0.023 0.855 0.663 0.75 0.597 0.692 0.582 0.465 0.598 1

Table 7: Pearson correlation coefficient between net loss ratios by major line.





Loss Ratio, Premium Change, and Loss Change Correlation

CMPComm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Workers Comp

total

CMP

Comm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Workers Comp

total

Direct Loss Ratio

CMPComm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Workers Comp

total

CMP

Comm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Workers Comp

total

Direct Premium Change

CMPComm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Workers Comp

total

CMP

Comm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Workers Comp

total

Direct Loss Change

CMPComm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Reinsurance

Workers Comp

total

CMP

Comm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Reinsurance

Workers Comp

total

Net Loss Ratio

CMPComm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Reinsurance

Workers Comp

total

CMP

Comm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Reinsurance

Workers Comp

total

Net Premium Change

CMPComm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Reinsurance

Workers Comp

total

CMP

Comm Auto

Comm Property

Fin Guaranty

Homeowners

Inland Marine

Liability

Med Mal

Other Comm

Personal Auto

Reinsurance

Workers Comp

total

Net Loss Change

0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

0.2

0.0

0.2

0.4

0.6

0.8

1.0

Figure 16: Premium and loss change is year over year change in total losses. It is another measure of the degree to which thecycle for a line is correlated with the overall market. Numerical values given below. Direct and net views.





Correlation Between Annual Change in Losses, by Major Line

name CMPCommAuto

CommProperty

FinGuaranty

Home-owners


MedMal

OtherComm

PersonalAuto

WorkersComp total

CMP 1 0.303 0.814 0.312 0.867 0.721 0.164 0.103 0.46 0.13 0.38 0.903Comm Auto 0.303 1 0.181 -0.231 0.138 0.216 0.256 0.517 0.43 0.513 0.145 0.41Comm Property 0.814 0.181 1 0.266 0.733 0.752 0.136 -0.087 0.355 0.122 0.118 0.78Fin Guaranty 0.312 -0.231 0.266 1 0.319 0.226 -0.015 -0.147 0.124 -0.237 -0.128 0.311Homeowners 0.867 0.138 0.733 0.319 1 0.694 0.022 -0.146 0.307 0.091 0.332 0.862Inland Marine 0.721 0.216 0.752 0.226 0.694 1 0.209 -0.063 0.424 -0.019 0.333 0.753Liability 0.164 0.256 0.136 -0.015 0.022 0.209 1 0.549 0.102 0.011 0.169 0.31Med Mal 0.103 0.517 -0.087 -0.147 -0.146 -0.063 0.549 1 0.366 0.228 0.41 0.176Other Comm 0.46 0.43 0.355 0.124 0.307 0.424 0.102 0.366 1 0.238 0.217 0.527Personal Auto 0.13 0.513 0.122 -0.237 0.091 -0.019 0.011 0.228 0.238 1 0.111 0.346Workers Comp 0.38 0.145 0.118 -0.128 0.332 0.333 0.169 0.41 0.217 0.111 1 0.427total 0.903 0.41 0.78 0.311 0.862 0.753 0.31 0.176 0.527 0.346 0.427 1

Table 8: Pearson correlation between annual change in direct losses, by major line.

name CMPCommAuto

CommProperty

FinGuaranty

Home-owners


MedMal

OtherComm

PersonalAuto

Reinsur-ance

WorkersComp total

CMP 1 0.186 0.668 0.368 0.812 0.666 0.379 0.214 0.274 -0.067 0.547 0.41 0.817Comm Auto 0.186 1 -0.004 -0.302 0.046 0.055 0.249 0.322 0.36 0.505 0.204 0.083 0.343Comm Property 0.668 -0.004 1 0.294 0.627 0.556 0.071 -0.147 0.125 -0.074 0.577 -0.049 0.62Fin Guaranty 0.368 -0.302 0.294 1 0.45 0.564 0.112 -0.106 0.131 -0.282 0.094 -0.108 0.34Homeowners 0.812 0.046 0.627 0.45 1 0.68 0.324 0.003 0.189 0.016 0.544 0.366 0.836Inland Marine 0.666 0.055 0.556 0.564 0.68 1 0.366 -0.123 0.316 -0.095 0.497 0.184 0.639Liability 0.379 0.249 0.071 0.112 0.324 0.366 1 0.299 0.34 -0.011 0.46 0.18 0.478Med Mal 0.214 0.322 -0.147 -0.106 0.003 -0.123 0.299 1 0.28 0.143 -0.100 0.451 0.213Other Comm 0.274 0.36 0.125 0.131 0.189 0.316 0.34 0.28 1 0.277 0.317 0.044 0.459Personal Auto -0.067 0.505 -0.074 -0.282 0.016 -0.095 -0.011 0.143 0.277 1 -0.090 0.148 0.318Reinsurance 0.547 0.204 0.577 0.094 0.544 0.497 0.46 -0.100 0.317 -0.090 1 0.002 0.616Workers Comp 0.41 0.083 -0.049 -0.108 0.366 0.184 0.18 0.451 0.044 0.148 0.002 1 0.407total 0.817 0.343 0.62 0.34 0.836 0.639 0.478 0.213 0.459 0.318 0.616 0.407 1

Table 9: Pearson correlation between annual change in net losses, by major line.





Correlation Between Annual Change in Premium, by Major Line

name CMPCommAuto

CommProperty

FinGuaranty

Home-owners


MedMal

OtherComm

PersonalAuto

WorkersComp total

CMP 1 0.757 0.745 0.149 0.664 0.768 0.753 0.793 0.025 0.503 0.575 0.913Comm Auto 0.757 1 0.421 0.093 0.306 0.696 0.626 0.512 0.016 0.706 0.474 0.841Comm Property 0.745 0.421 1 0.212 0.408 0.496 0.604 0.774 0.166 0.215 0.157 0.646Fin Guaranty 0.149 0.093 0.212 1 0.264 0.141 0.103 0.161 0.433 0.193 -0.111 0.257Homeowners 0.664 0.306 0.408 0.264 1 0.305 0.498 0.58 -0.130 0.369 0.359 0.614Inland Marine 0.768 0.696 0.496 0.141 0.305 1 0.479 0.523 0.176 0.482 0.564 0.746Liability 0.753 0.626 0.604 0.103 0.498 0.479 1 0.561 -0.108 0.335 0.472 0.788Med Mal 0.793 0.512 0.774 0.161 0.58 0.523 0.561 1 0.086 0.477 0.271 0.742Other Comm 0.025 0.016 0.166 0.433 -0.130 0.176 -0.108 0.086 1 0.091 -0.121 0.142Personal Auto 0.503 0.706 0.215 0.193 0.369 0.482 0.335 0.477 0.091 1 0.262 0.717Workers Comp 0.575 0.474 0.157 -0.111 0.359 0.564 0.472 0.271 -0.121 0.262 1 0.606total 0.913 0.841 0.646 0.257 0.614 0.746 0.788 0.742 0.142 0.717 0.606 1

Table 10: Pearson correlation between annual change in direct premium, by major line.

name CMPCommAuto

CommProperty

FinGuaranty

Home-owners


MedMal

OtherComm

PersonalAuto

Reinsur-ance

WorkersComp total

CMP 1 0.718 0.711 0.11 0.752 0.535 0.466 0.725 -0.001 0.506 0.257 0.644 0.886Comm Auto 0.718 1 0.343 0.060 0.434 0.563 0.331 0.403 0.18 0.72 0.023 0.547 0.818Comm Property 0.711 0.343 1 0.247 0.567 0.386 0.486 0.682 -0.132 0.322 0.299 0.257 0.647Fin Guaranty 0.11 0.060 0.247 1 0.231 0.308 0.596 0.127 0.328 0.222 -0.012 -0.071 0.215Homeowners 0.752 0.434 0.567 0.231 1 0.378 0.381 0.592 -0.163 0.474 -0.091 0.569 0.686Inland Marine 0.535 0.563 0.386 0.308 0.378 1 0.437 0.475 0.165 0.493 0.317 0.451 0.677Liability 0.466 0.331 0.486 0.596 0.381 0.437 1 0.418 0.013 0.36 0.341 0.252 0.558Med Mal 0.725 0.403 0.682 0.127 0.592 0.475 0.418 1 -0.003 0.365 0.57 0.405 0.723Other Comm -0.001 0.18 -0.132 0.328 -0.163 0.165 0.013 -0.003 1 0.042 0.031 -0.115 0.114Personal Auto 0.506 0.72 0.322 0.222 0.474 0.493 0.36 0.365 0.042 1 -0.076 0.437 0.77Reinsurance 0.257 0.023 0.299 -0.012 -0.091 0.317 0.341 0.57 0.031 -0.076 1 0.055 0.288Workers Comp 0.644 0.547 0.257 -0.071 0.569 0.451 0.252 0.405 -0.115 0.437 0.055 1 0.669total 0.886 0.818 0.647 0.215 0.686 0.677 0.558 0.723 0.114 0.77 0.288 0.669 1

Table 11: Pearson correlation between annual change in net premium, by major line.





Direct Loss Ratio Statistics by Major Line of Business

index CMPCommAuto

CommProperty

FinGuaranty Homeowners

InlandMarine Liability Med Mal

OtherComm

PersonalAuto

WorkersComp total

min 0.543 0.624 0.365 0.0791 0.565 0.393 0.678 0.548 0.522 0.663 0.577 0.639mean 0.716 0.751 0.691 0.631 0.763 0.551 0.857 0.837 0.65 0.768 0.772 0.752max 0.964 0.897 1.59 3.21 1.33 0.74 1.24 1.34 0.853 0.853 0.993 0.921sd 0.109 0.0808 0.314 0.709 0.163 0.082 0.16 0.214 0.0723 0.0409 0.106 0.0653cv 0.152 0.108 0.454 1.12 0.214 0.149 0.187 0.256 0.111 0.0533 0.138 0.0868growth 573.984u 0.00221 0.126 0.208 0.00546 0.0224 -0.00404 -0.00346 0.00437 -0.00479 -0.0126 -0.0046r2 0.281 0.00215 0.0793 0.0174 0.168 0.0329 0.546 0.272 0.118 0.0185 0.324 0.342rse0 0.094 0.0822 0.307 0.715 0.152 0.0821 0.11 0.186 0.0692 0.0413 0.0891 0.0539rse 0.0961 0.084 0.314 0.731 0.155 0.0839 0.112 0.19 0.0707 0.0422 0.0911 0.0551slope -0.00678 -439.525u -0.0104 0.011 -0.00787 -0.00175 -0.0139 -0.0131 -0.00292 -654.337u -0.00711 -0.00448year 14.32 1.63 21.51 -21.42 16.55 4.06 28.72 27.17 6.51 2.08 15.03 9.75ar r2 0.262 0.78 4.630u 0.471 0.00922 0.00367 0.663 0.79 0.272 0.434 0.69 0.226ar rse0 0.0878 0.0393 0.323 0.534 0.126 0.0826 0.0949 0.0994 0.0633 0.0319 0.0589 0.055ar rse 0.24 0.131 0.517 0.676 0.272 0.283 0.207 0.187 0.229 0.202 0.169 0.216ar slope 0.464 0.883 0.00213 0.686 0.0716 -0.062 0.804 0.866 0.517 0.758 0.836 0.443ar intercept 0.376 0.0888 0.682 0.203 0.688 0.581 0.161 0.104 0.313 0.183 0.116 0.414

Table 12: Direct calendar year Loss ratio statistics by major line of business. See below for gloss.





Net Loss Ratio Statistics by Major Line of Business

index CMPCommAuto

CommProperty

FinGuaranty

Home-owners

InlandMarine Liability Med Mal

OtherComm

PersonalAuto

Reinsur-ance

WorkersComp total

min 0.568 0.633 0.387 0.0657 0.589 0.451 0.623 0.574 0.575 0.662 0.374 0.582 0.653mean 0.717 0.75 0.676 0.627 0.766 0.568 0.833 0.834 0.65 0.765 0.813 0.768 0.753max 0.895 0.873 1.33 2.77 1.24 0.658 1.17 1.32 0.787 0.838 2.05 0.971 0.884sd 0.0884 0.0728 0.188 0.627 0.131 0.0595 0.158 0.2 0.0538 0.0399 0.318 0.1 0.0567cv 0.123 0.0971 0.278 1 0.171 0.105 0.19 0.24 0.0827 0.0521 0.391 0.13 0.0754growth -0.00217 964.957u 0.0511 0.217 -0.00478 0.00924 -0.002 -999.599u -0.00182 -0.00512 0.0612 -0.0145 -0.00612r2 0.388 0.00228 0.0611 0.0124 0.273 0.112 0.474 0.218 0.346 0.0644 0.0798 0.282 0.405rse0 0.0704 0.0741 0.186 0.635 0.113 0.0571 0.117 0.18 0.0443 0.0393 0.311 0.0863 0.0446rse 0.072 0.0757 0.19 0.649 0.116 0.0584 0.12 0.184 0.0452 0.0401 0.318 0.0882 0.0456slope -0.00647 -408.233u -0.00546 0.0082 -0.00802 -0.00233 -0.0128 -0.011 -0.00372 -0.00119 -0.0105 -0.00624 -0.00424year 13.69 1.57 11.62 -15.82 16.86 5.25 26.52 22.84 8.11 3.15 21.97 13.29 9.26ar r2 0.466 0.746 0.0144 0.441 0.125 0.0368 0.479 0.731 0.663 0.447 0.0597 0.683 0.368ar rse0 0.0618 0.038 0.192 0.487 0.0904 0.0593 0.114 0.105 0.0321 0.0306 0.318 0.0538 0.0422ar rse 0.194 0.137 0.385 0.633 0.221 0.254 0.251 0.204 0.145 0.198 0.507 0.161 0.185ar slope 0.63 0.864 0.119 0.664 0.252 0.194 0.668 0.833 0.807 0.766 0.243 0.802 0.555ar intercept 0.259 0.102 0.591 0.211 0.556 0.456 0.268 0.132 0.124 0.175 0.609 0.14 0.329

Table 13: Net calendar year Loss ratio statistics by major line of business. See below for gloss.





Loss Ratio Statistics by Major Line of Business

Key• min, mean, max, sd, and cv are the minimum, mean, maximum, standard deviation and coefficient of variation of

loss ratio• growth is the arithmetic average annual growth rate• r2, rse0, slope, and year are the R2, residual standard error, slope coefficient and year (time) coefficient for a

regression of loss ratio against time; rse equals rse0 plus the standard error of the slope parameter• ar r2, ar rse0, ar intercept, and ar slope are the R2, residual standard error, slope coefficient and year

(time) coefficient for an autoregression with lag 1; ar rse equals ar rse0 plus the standard error of the autoregressive parameter





Direct Loss Ratio Time Series by Major Line

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9

CMP; SD=0.109 (0.0645), cor=0.898ar fit, r2=0.262, rse0=0.0878

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9

Comm Auto; SD=0.0808 (0.0507), cor=0.407ar fit, r2=0.78, rse0=0.0393

1995 2000 2005 2010 2015 2020year

0.25

0.50

0.75

1.00

1.25

1.50

Comm Property; SD=0.314 (0.154), cor=0.712ar fit, r2=4.63e-06, rse0=0.323

1995 2000 2005 2010 2015 2020year

0

1

2

3

Fin Guaranty; SD=0.709 (0.561), cor=-0.0588ar fit, r2=0.471, rse0=0.534

1995 2000 2005 2010 2015 2020year

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Homeowners; SD=0.163 (0.106), cor=0.769ar fit, r2=0.00922, rse0=0.126

1995 2000 2005 2010 2015 2020year

0.4

0.5

0.6

0.7

Inland Marine; SD=0.082 (0.0425), cor=0.632ar fit, r2=0.00367, rse0=0.0826

1995 2000 2005 2010 2015 2020year

0.75

1.00

1.25

Liability; SD=0.16 (0.126), cor=0.703ar fit, r2=0.663, rse0=0.0949

1995 2000 2005 2010 2015 2020year

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Med Mal; SD=0.214 (0.159), cor=0.662ar fit, r2=0.79, rse0=0.0994

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

Other Comm; SD=0.0723 (0.0419), cor=0.596ar fit, r2=0.272, rse0=0.0633

1995 2000 2005 2010 2015 2020year

0.7

0.8

Personal Auto; SD=0.0409 (0.0266), cor=0.486ar fit, r2=0.434, rse0=0.0319

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9

1.0

Workers Comp; SD=0.106 (0.0695), cor=0.614ar fit, r2=0.69, rse0=0.0589

1995 2000 2005 2010 2015 2020year

0.7

0.8

0.9

total; SD=0.0653 (0.0429), cor=1ar fit, r2=0.226, rse0=0.055

Figure 17: Direct calendar year Loss ratio time series by major line. See gloss below.





Net Loss Ratio Time Series by Major Line

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9


1995 2000 2005 2010 2015 2020year

0.7

0.8


1995 2000 2005 2010 2015 2020year

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Comm Property; SD=0.188 (0.154), cor=0.59ar fit, r2=0.0144, rse0=0.192

1995 2000 2005 2010 2015 2020year

0

1

2

Fin Guaranty; SD=0.627 (0.561), cor=0.0228ar fit, r2=0.441, rse0=0.487

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9

1.0

1.1

1.2


1995 2000 2005 2010 2015 2020year

0.5

0.6


1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9

1.0

1.1


1995 2000 2005 2010 2015 2020year

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3


1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8


1995 2000 2005 2010 2015 2020year

0.7

0.8


1995 2000 2005 2010 2015 2020year

0.25

0.50

0.75

1.00

1.25

1.50

1.75

2.00

Reinsurance; SD=0.318 (0.268), cor=0.465ar fit, r2=0.0597, rse0=0.318

1995 2000 2005 2010 2015 2020year

0.6

0.7

0.8

0.9


Figure 18: Net calendar year Loss ratio time series by major line. See gloss on next slide.





Loss Ratio Time Series by Major Line

Title decoder: CMP; SD=0.109 (0.0645), cor=0.898 ar fit, r2=0.262, rse0=0.0878• Line; standard deviation• Down-side semi-deviation is shown in parenthsis (explain)• Correlation of the line with total on the first line• (second line) shows the R2 and residual standard error of an autoregressive loss ratio model

Interpretation• When the rse is much lower than SD it suggests the market cycle is predictable• Tends to occur in casualty lines (e.g., commercial auto, medical malpractice, private passenger auto, and workers

compensation)• The cycle for property lines tends to be idiosyncratic, for obvious reasons.

Line Legend• Thin gray line in each plot shows the total loss ratio, for context• The horizontal lines show the mean (thicker) and mean ±Φ−1(22/23) = ±1.71 standard deviations

• If the loss ratios were normally distributed we expect all observations from 22 years (1996-2017) to fall within thesetram lines

• They provide a surprisingly good estimate of the range of loss ratio, except for Financial Lines (which uses adifferent tick spacing, note).





Total Loss Ratio Time Series, Direct and Net

1995 2000 2005 2010 2015 2020year

0.7

0.8

0.9

Total Direct and Net; SD=0.0567 (0.0429), cor=1ar fit, r2=0.368, rse=0.185

viewDirectNet

Figure 19: Average direct loss ratio is 0.752 with standard deviation 0.065. Average net loss ratio is 0.753 with standarddeviation 0.057. Remember gross equals direct plus assumed minus ceded, so the difference between direct and net is not thesame as ceded.





Direct Loss Ratio Time Series by Major Line, Loss Ratio Scale 0 to 150 Percent

1995 2000 2005 2010 2015 2020year

46.7%

71.6%

96.6%


1995 2000 2005 2010 2015 2020year

56.6%

75.1%

93.7%


1995 2000 2005 2010 2015 2020year

69.1%

141.0%


1995 2000 2005 2010 2015 2020year

63.1%


1995 2000 2005 2010 2015 2020year

38.8%

76.3%

113.7%


1995 2000 2005 2010 2015 2020year

36.3%

55.1%

73.9%


1995 2000 2005 2010 2015 2020year

49.1%

85.7%

122.4%


1995 2000 2005 2010 2015 2020year

34.6%

83.7%

132.9%


1995 2000 2005 2010 2015 2020year

48.4%

65.0%

81.6%


1995 2000 2005 2010 2015 2020year

67.5%76.8%86.2%


1995 2000 2005 2010 2015 2020year

52.9%

77.2%

101.6%


1995 2000 2005 2010 2015 2020year

60.3%

75.2%

90.2%


Figure 20: Same as the previous plot, but using the same y axis scale on all plots, to emphasize inter-line behavior.





Net Loss Ratio Time Series by Major Line, Loss Ratio Scale 0 to 150 Percent

1995 2000 2005 2010 2015 2020year

51.5%

71.7%

92.0%


1995 2000 2005 2010 2015 2020year

58.3%

75.0%

91.7%


1995 2000 2005 2010 2015 2020year

24.5%

67.6%

110.7%


1995 2000 2005 2010 2015 2020year

62.7%


1995 2000 2005 2010 2015 2020year

46.6%

76.6%

106.5%


1995 2000 2005 2010 2015 2020year

43.2%

56.8%

70.5%


1995 2000 2005 2010 2015 2020year

47.0%

83.3%

119.6%


1995 2000 2005 2010 2015 2020year

37.6%

83.4%

129.3%


1995 2000 2005 2010 2015 2020year

52.7%65.0%77.3%


1995 2000 2005 2010 2015 2020year

67.4%76.5%85.6%


1995 2000 2005 2010 2015 2020year

8.5%

81.3%


1995 2000 2005 2010 2015 2020year

53.8%

76.8%

99.7%


Figure 21: Same as the previous plot, but using the same y axis scale on all plots, to emphasize inter-line behavior.





Some Lines Are More Volatile Than Others. . .

1995 2000 2005 2010 2015 2020year

46.7%

71.6%

96.6%


1995 2000 2005 2010 2015 2020year

56.6%

75.1%

93.7%


1995 2000 2005 2010 2015 2020year

69.1%

141.0%


1995 2000 2005 2010 2015 2020year

63.1%


1995 2000 2005 2010 2015 2020year

38.8%

76.3%

113.7%


1995 2000 2005 2010 2015 2020year

36.3%

55.1%

73.9%


1995 2000 2005 2010 2015 2020year

49.1%

85.7%

122.4%


1995 2000 2005 2010 2015 2020year

34.6%

83.7%

132.9%


1995 2000 2005 2010 2015 2020year

48.4%65.0%81.6%


1995 2000 2005 2010 2015 2020year

67.5%76.8%86.2%


1995 2000 2005 2010 2015 2020year

52.9%

77.2%

101.6%


1995 2000 2005 2010 2015 2020year

60.3%75.2%90.2%


Figure 22: Same as the previous plot, but not clipping loss ratios at 150 percent for Commercial Property, Liability and FinGuaranty.





Reinsurance More Effective for Some Lines Than Others. . .

1995 2000 2005 2010 2015 2020year

51.5%

71.7%

92.0%


1995 2000 2005 2010 2015 2020year

58.3%

75.0%

91.7%


1995 2000 2005 2010 2015 2020year

24.5%

67.6%

110.7%


1995 2000 2005 2010 2015 2020year

62.7%


1995 2000 2005 2010 2015 2020year

46.6%

76.6%

106.5%


1995 2000 2005 2010 2015 2020year

43.2%56.8%70.5%


1995 2000 2005 2010 2015 2020year

47.0%

83.3%

119.6%


1995 2000 2005 2010 2015 2020year

37.6%

83.4%

129.3%


1995 2000 2005 2010 2015 2020year

52.7%65.0%77.3%


1995 2000 2005 2010 2015 2020year

67.4%76.5%85.6%


1995 2000 2005 2010 2015 2020year

8.5%

81.3%


1995 2000 2005 2010 2015 2020year

53.8%

76.8%

99.7%


Figure 23: Reinsurance on Commercial Property, typically excess, reduces volatility very effectively whereas net loss more volatilefor liabiltiy lines, often protected with quota shares.





Direct Premium and Loss Dynamics

1995 2000 2005 2010 2015 2020

15

20

25

30

35

40

45

×109 CMPEP, rse=0.0688linear, r2=0.937IL, rse=0.115linear, r2=0.759

1995 2000 2005 2010 2015 2020

15

20

25

30

35

40

45

×109 Comm AutoEP, rse=0.06ar, r2=0.956IL, rse=0.0683ar, r2=0.951

1995 2000 2005 2010 2015 2020

5

10

15

20

25

30

35×109 Comm Property

EP, rse=0.115linear, r2=0.925IL, rse=0.385linear, r2=0.425

1995 2000 2005 2010 2015 2020

0

5

10

15

20

25

30

×109 Fin GuarantyEP, rse=0.123ar, r2=0.889IL, rse=1.29ar, r2=0.376

1995 2000 2005 2010 2015 2020

20

40

60

80

100

×109 HomeownersEP, rse=0.05linear, r2=0.989IL, rse=0.199linear, r2=0.817

1995 2000 2005 2010 2015 2020

5

10

15

20

25

×109 Inland MarineEP, rse=0.118linear, r2=0.936IL, rse=0.207linear, r2=0.822

1995 2000 2005 2010 2015 2020

20

30

40

50

60

70

80

×109 LiabilityEP, rse=0.146linear, r2=0.874IL, rse=0.129ar, r2=0.851

1995 2000 2005 2010 2015 2020

5

6

7

8

9

10

11

12

×109 Med MalEP, rse=0.075ar, r2=0.916IL, rse=0.139ar, r2=0.746

1995 2000 2005 2010 2015 2020

10

15

20

25

30

35

40

×109 Other CommEP, rse=0.1linear, r2=0.845IL, rse=0.155ar, r2=0.646

1995 2000 2005 2010 2015 2020

75

100

125

150

175

200

225

250

×109 Personal AutoEP, rse=0.0708linear, r2=0.943IL, rse=0.0681linear, r2=0.944

1995 2000 2005 2010 2015 2020

20

25

30

35

40

45

50

55

×109 Workers CompEP, rse=0.113linear, r2=0.805IL, rse=0.0785ar, r2=0.832

1995 2000 2005 2010 2015 2020

200

300

400

500

600

700

×109 totalEP, rse=0.0623linear, r2=0.963IL, rse=0.0827linear, r2=0.917

Figure 24: See below for gloss. rse is residual standard error without parameter uncertainty, normalized by the mean.





Net Premium and Loss Dynamics

1995 2000 2005 2010 2015 2020

15

20

25

30

35

40

×109 CMPEP, rse=0.0663linear, r2=0.94IL, rse=0.0819linear, r2=0.858

1995 2000 2005 2010 2015 2020

15

20

25

30

35

40×109 Comm Auto

EP, rse=0.0573ar, r2=0.951IL, rse=0.0701ar, r2=0.935

1995 2000 2005 2010 2015 2020

5

10

15

20

25

×109 Comm PropertyEP, rse=0.0939linear, r2=0.946IL, rse=0.242linear, r2=0.694

1995 2000 2005 2010 2015 2020

0

5

10

15

20

25×109 Fin Guaranty


1995 2000 2005 2010 2015 2020

20

40

60

80

100×109 Homeowners


1995 2000 2005 2010 2015 2020

2

4

6

8

10

12

14

×109 Inland MarineEP, rse=0.0962linear, r2=0.929IL, rse=0.136linear, r2=0.851

1995 2000 2005 2010 2015 2020

20

30

40

50

60

70

80

×109 LiabilityEP, rse=0.136linear, r2=0.883IL, rse=0.121ar, r2=0.865

1995 2000 2005 2010 2015 2020

4

5

6

7

8

9

10

×109 Med MalEP, rse=0.0656ar, r2=0.938IL, rse=0.143ar, r2=0.705

1995 2000 2005 2010 2015 2020

10

15

20

25

30

35

×109 Other CommEP, rse=0.0663ar, r2=0.899IL, rse=0.111ar, r2=0.743

1995 2000 2005 2010 2015 2020

75

100

125

150

175

200

225

250×109 Personal Auto


1995 2000 2005 2010 2015 20204

6

8

10

12

14

16

×109 ReinsuranceEP, rse=0.152linear, r2=0.217IL, rse=0.268ar, r2=0.337

1995 2000 2005 2010 2015 2020

20

25

30

35

40

45

50×109 Workers Comp


Figure 25: See below for gloss. rse is residual standard error without parameter uncertainty, normalized by the mean.





Direct Premium and Loss Dynamics

CMPCommAuto

CommProperty

FinGuaranty

Home-owners

InlandMarine

index EP IL EP IL EP IL EP IL EP IL EP ILcv 0.270 0.231 0.285 0.306 0.413 0.499 0.385 1.586 0.470 0.458 0.456 0.482cvlr 0.149 0.149 0.106 0.106 0.446 0.446 1.103 1.103 0.211 0.211 0.146 0.146r2 0.937 0.759 0.740 0.688 0.925 0.425 0.447 0.036 0.989 0.817 0.936 0.822rse 0.069 0.115 0.148 0.174 0.115 0.385 0.291 1.585 0.050 0.199 0.118 0.207ar r2 0.982 0.661 0.956 0.951 0.969 0.132 0.889 0.376 0.998 0.700 0.987 0.826ar rse 0.036 0.138 0.060 0.068 0.073 0.476 0.123 1.292 0.021 0.257 0.053 0.205

Liability Med MalOtherComm

PersonalAuto

WorkersComp total


Table 14: See below for gloss.





Net Direct Premium and Loss Dynamics

CMPCommAuto

CommProperty

FinGuaranty

Home-owners

InlandMarine


Liability Med MalOtherComm

PersonalAuto

Reinsur-ance

WorkersComp


Table 15: See below for gloss.





Premium and Loss Dynamics

• Loss ratio uncertainty combines loss uncertainty and premium uncertainty• Loss uncertainty = event risk, catastrophes, unexpected trends, estimation error, etc.• Premium uncertainty = market or cycle uncertainty; ability to charge technical rate in market• rse is residual standard error without parameter uncertainty

• Looking at premium and loss time series separately illuminates the particular dynamics of each line• Each plot shows premium and loss time series (thicker) and a linear or AR(1) fit (thinner)

• Cat-driven loss dynamics stand-out for CMP, Comm Property, Homeowners, Other Commercial and to a lesserextent, Inland Marine

• Non-cat losses tend to be smoother, as events bleed in through development: Comm Auto and Workers Comp

• A priori expect premium in most lines to grow smoothly, approximately with GDP, as seen in Homeowners• However, most lines exhibit excess premium volatility

• Personal Auto and Workers Comp premium are more uncertain than loss as measured by regression residual standarderror

• Comm Auto premium exhibits huge cyclic behavior

• Loss ratio uncertainty is a multifaceted and subtle pheneomenon





Calm Surface Masks Inner Turmoil

1992 1996 2000 2004 2008 2012 2016 2020year

0.20%

0.22%

0.24%

0.26%

0.28%

CMP

1992 1996 2000 2004 2008 2012 2016 2020year

0.16%

0.18%

0.20%

0.22%

0.24%

0.26%

Comm Auto

1992 1996 2000 2004 2008 2012 2016 2020year

0.10%

0.11%

0.12%

0.13%

0.14%

0.15%

0.16%

0.17%Comm Property

1992 1996 2000 2004 2008 2012 2016 2020year

0.02%

0.03%

0.04%

0.05%

0.06%

0.07%

Fin Guaranty

1992 1996 2000 2004 2008 2012 2016 2020year

0.35%

0.40%

0.45%

0.50%

0.55%

Homeowners

1992 1996 2000 2004 2008 2012 2016 2020year

0.08%

0.09%

0.10%

0.11%

0.12%

Inland Marine

1992 1996 2000 2004 2008 2012 2016 2020year

0.20%

0.25%

0.30%

0.35%

0.40%

0.45%

Liability

1992 1996 2000 2004 2008 2012 2016 2020year

0.05%

0.06%

0.07%

0.08%

0.09%

Med Mal

1992 1996 2000 2004 2008 2012 2016 2020year

0.20%

0.22%

0.24%

0.26%

0.28%

0.30%

0.32%

Other Comm

1992 1996 2000 2004 2008 2012 2016 2020year

1.10%

1.15%

1.20%

1.25%

1.30%

1.35%

Personal Auto

1992 1996 2000 2004 2008 2012 2016 2020year

0.25%

0.30%

0.35%

0.40%

0.45%

0.50%

0.55%Workers Comp

1992 1996 2000 2004 2008 2012 2016 2020year

3.00%

3.10%

3.20%

3.30%

3.40%

3.50%

3.60%

3.70%

total

Figure 26: Direct premium to GDP by major line shows a wide variety of behaviors. Broadly, property has increased, whileliability coverages have decreased.





The Underwriting Cycle Is Driven by Commercial Lines

1992 1996 2000 2004 2008 2012 2016 2020year

1.2%

1.4%

1.6%

1.8%

2.0%

2.2%Personal

1992 1996 2000 2004 2008 2012 2016 2020year

1.2%

1.4%

1.6%

1.8%

2.0%

2.2%Commercial

1992 1996 2000 2004 2008 2012 2016 2020year

3.0%

3.2%

3.4%

3.6%

3.8%

total

Figure 27: Premium to GDP for personal lines vs. commerical shows the cycle is more driven by commercial. All y axes have thesame range but different locations. Personal lines (blue) shown on commerical plot to compare relative sizes. Commercial lineshas been bigger than personal since 2001





Direct and Net Premium and Loss

1992 1996 2000 2004 2008 2012 2016 2020

15

20

25

30

35

40

45

×106 CMPDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 202010

15

20

25

30

35

40

45

×106 Comm AutoDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

5

10

15

20

25

30

35×106 Comm Property

Direct premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

0

5

10

15

20

25

30

×106 Fin GuarantyDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

20

40

60

80

100

×106 HomeownersDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

5

10

15

20

25

×106 Inland MarineDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

20

30

40

50

60

70

80

×106 LiabilityDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

4

6

8

10

12

×106 Med MalDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

10

15

20

25

30

35

40

×106 Other CommDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

75

100

125

150

175

200

225

250

×106 Personal AutoDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 202015

20

25

30

35

40

45

50

55

×106 Workers CompDirect premiumDirect lossNet premiumNet loss

1992 1996 2000 2004 2008 2012 2016 2020

200

300

400

500

600

700

×106 totalDirect premiumDirect lossNet premiumNet loss

Figure 28: Direct and net premium and loss by major line.





Direct and Net Combined Ratio and Loss Ratio by Line by Year

1992 1996 2000 2004 2008 2012 2016 2020

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

CMPDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 20200.6

0.7

0.8

0.9

1.0

1.1

1.2

Comm AutoDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

Comm PropertyDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

2

1

0

1

2

3

Fin GuarantyDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.6

0.8

1.0

1.2

1.4

1.6

HomeownersDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Inland MarineDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 20200.6

0.8

1.0

1.2

1.4

LiabilityDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.6

0.8

1.0

1.2

1.4

1.6Med Mal

Direct CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 20200.5

0.6

0.7

0.8

0.9

1.0

1.1

Other CommDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.7

0.8

0.9

1.0

1.1

Personal AutoDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Workers CompDirect CRDirect LR

Net CRNet LR

1992 1996 2000 2004 2008 2012 2016 2020

0.7

0.8

0.9

1.0

1.1

1.2total

Direct CRDirect LR

Net CRNet LR

Figure 29: Direct and Net Combined Ratio and Loss Ratio by Line by Year.





Net Operating Results

nameAvg UWMargin

WtdAvg UWMargin

SD UWMargin

Avg OpMargin

Wtd AvgOp Margin

SD OpMargin Avg II MSD

Adj OpMargin

Med Mal -0.072 -0.044 0.189 0.117 0.128 0.181 0.188 0.644 0.155Inland Marine 0.082 0.096 0.081 0.104 0.117 0.080 0.023 1.308 0.156Workers Comp -0.053 -0.037 0.101 0.088 0.100 0.097 0.141 0.911 0.123Liability -0.140 -0.103 0.156 0.037 0.058 0.148 0.177 0.250 0.053Fin Guaranty 0.077 -0.030 0.601 0.035 -0.106 1.052 -0.042 0.033 0.018Personal Auto -0.007 -0.004 0.039 0.027 0.028 0.040 0.034 0.676 0.035total -0.036 -0.026 0.057 0.025 0.030 0.060 0.061 0.418 0.035Comm Property -0.016 0.015 0.205 0.018 0.047 0.203 0.034 0.090 0.019Reinsurance -0.161 -0.136 0.370 0.013 0.033 0.341 0.174 0.038 -0.574Comm Auto -0.052 -0.048 0.077 0.009 0.010 0.072 0.061 0.129 0.013Other Comm 0.027 0.030 0.046 -0.003 -0.011 0.512 -0.030 -0.006 -0.009CMP -0.076 -0.059 0.094 -0.008 0.003 0.079 0.068 -0.106 -0.014Homeowners -0.071 -0.038 0.135 -0.041 -0.012 0.129 0.030 -0.320 -0.061

Table 16: Insurance operating result, with allocated investment income from policyholder funds, by major line. Weighted Wtdaverage margins are higher than straight Avg averages because bad results are followed by increasing rates and volume, thusgood years receive relatively greater weight. Weighted also biases towards the most recent year. The straight average is a moreappropriate measure of average achieved profitability. Sorted by descending average operating margin, most profitable first. AvgII shows implied investment income. MSD shows (straight) average to standard deviation ratio for operating margin. Adj OpMargin shows the operating margin adjusted for average expenses in the line.





Average Margins, All Lines Combined

Historical average margins

index UW Margin Op MarginIEE Op

Ins Funds IEE Total Op

Inc StmtPre-Tax To-tal Return Adj Op Margin

Average -0.0366 0.0905 0.0276 0.106 0.108 0.126Wtd Avg -0.0259 0.0951 0.0313 0.111 0.112 0.133Drag 0.0107 0.00459 0.00367 0.0052 0.00387 0.00641

1992 1996 2000 2004 2008 2012 2016 2020Year

0.20

0.15

0.10

0.05

0.00

0.05

0.10

0.15

0.20

UW MarginOp Margin

IEE Op Ins FundsIEE Total Op

Inc Stmt Pre-Tax Total Return

Figure 30: Average margins over time, all lines combined

Target average margins• Table shows historical average pre-tax

margin to earned premium• UU margin, with no investment income• Op margin, with income but no gains• IEE margin, with investment gains on

insurance funds• IEE margin, wtih all invsetment gains• Income statement, with all gains• THe last two should be the same

• Weighted return greater than averagebecause of cycle effect

• Adj Op Margin adjusts for expenses





C.05. Direct Premium Growth by MajorLine, 1992-2020

Average Direct Premium Growth Rates by Line (Percent)

index Mean SD CAGR AdjWorkers Comp 1.53 6.62 1.33 1.32Med Mal 2.82 8.14 2.53 2.49CMP 3.30 3.86 3.23 3.23Comm Auto 3.67 5.73 3.52 3.51Personal Auto 3.82 2.90 3.78 3.78Other Comm 3.97 7.29 3.73 3.70total 4.03 3.30 3.98 3.98GDP 4.28 2.19 4.25 4.25Inland Marine 5.62 5.22 5.49 5.48Liability 5.63 12.26 5.00 4.87Comm Property 5.70 9.07 5.34 5.28Homeowners 6.14 2.70 6.11 6.11Fin Guaranty 6.86 14.73 5.96 5.77

Table 17: Average direcet premium growth rates by line of business, with (nominal) GDP included for reference. Lines sortedfrom slowest to fastest growth. Insurance grows broadly with the economy, as the premium to GDP analysis showed. Since 1992,premium growth has slightly lagged GDP growth. Mean shows the average annual growth rate and SD its standard deviation.CAGR is the compound average growth rate. Adj shows the arithmetic mean adjusted for volatility using the lognormal µ+ σ2/2formula. It is very close to the actual compound rate. Source: GDP from FRED.





Annual Change in Direct Premium by Line

1995 2000 2005 2010 2015 2020year

0.2

0.1

0.0

0.1

0.2

0.3

0.4

prem

ium

, pct

cha

nge

CMPComm_AutoComm_PropertyHomeowners

Inland_MarineLiabilityMed_MalOther_Comm

Personal_AutoWorkers_ComptotalGDP

Figure 31: Change by line correlated to the economy (GDP), but displays considerable variation by line.





Annual Change in Direct Premium Detailed by Line

1995 2000 2005 2010 2015 2020year

0.025

0.000

0.025

0.050

0.075

0.100

0.125

0.150CMP

CMPtotalGDP

1995 2000 2005 2010 2015 2020year

0.05

0.00

0.05

0.10

0.15

Comm_Auto

1995 2000 2005 2010 2015 2020year

0.1

0.0

0.1

0.2

0.3

Comm_Property

1995 2000 2005 2010 2015 2020year

0.2

0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6Fin_Guaranty

1995 2000 2005 2010 2015 2020year

0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14Homeowners

1995 2000 2005 2010 2015 2020year

0.05

0.00

0.05

0.10

0.15

Inland_Marine

1995 2000 2005 2010 2015 2020year

0.2

0.1

0.0

0.1

0.2

0.3

0.4

Liability

1995 2000 2005 2010 2015 2020year

0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Med_Mal

1995 2000 2005 2010 2015 2020year

0.05

0.00

0.05

0.10

0.15

0.20

Other_Comm

1995 2000 2005 2010 2015 2020year

0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

Personal_Auto

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

Workers_Comp

1995 2000 2005 2010 2015 2020year

0.02

0.00

0.02

0.04

0.06

0.08

0.10

0.12

total

Figure 32: Degree of correlation to the economy (GDP) varies by line.





Annual Change in Direct Premium by Line Common Scale

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25CMP

CMPtotalGDP

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Comm_Auto

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Comm_Property

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Fin_Guaranty

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Homeowners

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Inland_Marine

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Liability

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Med_Mal

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Other_Comm

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Personal_Auto

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25Workers_Comp

1995 2000 2005 2010 2015 2020year

0.10

0.05

0.00

0.05

0.10

0.15

0.20

0.25total

Figure 33: Magnitude of premium changes varies considerably by line.





Premium and GDP Growth Since 1992 (1992=1.0)

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

Workers CompWorkers ComptotalGDPEMP

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

Med Mal

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

CMP

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

Comm Auto

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

Personal Auto

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

Other Comm

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

total

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Inland Marine

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

3.5

4.0Liability

1995 2000 2005 2010 2015 2020year

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Comm Property

1995 2000 2005 2010 2015 2020year

1

2

3

4

5

Homeowners

1995 2000 2005 2010 2015 2020year

1

2

3

4

5

6

7

8Fin Guaranty

Figure 34: Lines sorted from slowest to fastest average growth rate, since 1992. The workers compensation plot includes theoverall level of employment EMP from the FRED series CE16OV. WC premium has declined as productivity has improved. Broadly,labor inputs have become less important in higher-risk segments of the economy. Commercial auto is particularly interesting.Pricing Insurance Risk Course by Stephen J Mildenhall is licensed under Creative Commons Attribution 4.0 International 56




C.06. Implications

Implications

Loss ratio and margin expectations• Adjusted Insurance Operating Ratios averages 13%

• Net basis• Pre-tax• Including all investment income

• Considerable variation in underlying loss ratio by line

• By line asymptotic (large portfolio) direcet loss ratioCVs range from 5% for personal auto to 45% forcommercial property

• Smaller portfolios will have larger CVs• Total industry loss ratio CV is 9% direct and 8% net

Margin expectations• Average historical pre-tax, net margin based on

industry data 1992 to 2020• -4% underwriting income to net earned premium• 9% excluding capital gains and• 11% including all capital gains

• Over period, investment income declined from over20% to less than 10% of net earned premium

• A pricing model producing a gross margin of 8 to 10%is consistent with realized experience 1996-2020





pricing insurance risk

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