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Theoretical underwriting profits and losses can be determined by the Capital Asset Pricing Model. The model developed by Biger and Kahane (1978) indicates that property and casualty insurers are subject to underwriting losses, assuming the underwriting beta is zero. In other words, P&C insurers have sufficient amount of investment earnings that are more than enough to offset underwriting losses. The fact is that individuals pay premiums in advance and losses occur throughout the year, so insurers can invest their earned premiums and loss reserves in securities. How much they can earn in investments depends upon the claim settlement period/fund-generating coefficients and bond yields since bonds are their primary investment holdings. This study uses the model and computes theoretical/equilibrium underwriting returns and compare those to actual/historical underwriting profits/losses. The excess/abnormal return for each year is the difference between actual and theoretical underwriting gain or loss. The study examined the excess/abnormal returns for 19 years from 1996 to 2014 and found that property and casualty insurers were able to have excess returns for 11 years, amounting 55.47% whereas the excess losses for 8 years were 31.75%. The whole industry was able to have the net excess return of 23.72% over the entire 19-year period. It implies that insurers paid too much premiums if the theory is right with zero underwriting beta.

Keywords: Underwriting results, investment earnings, excess underwriting gains/losse.


An insurer is a financial intermediary in a sense that an insurance company receives funds from the sale of insurance policies in the insurance market and invests the funds for investment earnings in the capital market. It is known that the insured pay premiums in advance, but losses occur throughout the year. The time lag between premiums collections and loss payments gives property and liability insurers an opportunity for generating investment income.

The fact is that insurance companies are largely depending upon investment income and often they are willing to sell policies at a loss. In other words, when bond yields are high and investment opportunities are good, property-casualty insurers seem to be willing to sacrifice underwriting profits to raise funds from the sale of insurance for expected investment returns. This is known as a cash-flow underwriting and there were many studies on the nature of cyclical underwriting profits/losses. The underwriting cycle is caused by interest rates and other investment opportunities in financial markets (Kang, 2007). There have been six-year cycles on underwriting returns caused by the cyclical interest rates. (Kang & Joaquin, 2012).

Historically, for most years, investment earnings have been increasingly a major source of income for property and casualty insurers because of the competitive nature of the underwriting business in insurance pricing. In 2015, for example, the aggregate net investment income was 49.32 billion dollars, whereas the underwriting gain was only 9.89 billion dollars for the US property and casualty insurance industry.

This proposed study presents a financial and economic model for the determination of underwriting profitability. It postulates that equilibrium profits may not be stable over time and that insurers collectively adjust toward changing equilibrium prices in a competitive market. An equilibrium rate of return on underwriting is derived from the Capital Asset Pricing Model (CAPM). This study computes equilibrium underwriting profits based on a theoretical model derived from the Capital Asset Pricing Model and compares them to actual/historical underwriting returns. The ultimate objective is to compute the excess underwriting returns and explain whether or not the insured pay reasonable amount of premiums in the property/casualty insurance.


There were many previous studies on the issue of underwriting returns based on the cash- flow underwriting practice (e.g., Kang, 2012; Wen & Born, 2005; Gron, 1994; Kang, 2012). The Kang's study was based on a negative relationship between interest rates and underwriting results. The linear and log-linear models of regression were estimated and the study's empirical result confirmed the negative relationship. The primary contribution of the study was the lag relationship between interest rates and underwriting results.

The Wen and Born study argued that premium rates and underwriting margins were affected by the combined competitive forces of both insurance and capital markets. Therefore, it is important to analyze how interest rates affect the underwriting business and underwriting results, considering the importance of investment earnings. In other words, we cannot separate the insurance business from investment activities, given the nature of insurance premium collection in advance. The practice offers a major advantage to insurance companies and also important policy implications on insurance regulation.

Higgins (2000) argued that underwriting profits are affected by insurance capacity, meaning that cyclical underwriting profits are caused by the supply or capacity restrictions. However, when insurers are subject to capacity restraint problems, they cannot adjust to new market conditions instantaneously, producing interruption and cyclical business patterns. It implies that underwriting profits are related to how much insurers are able to sell policies. If they are able to write more polices, then they have to cut premiums and incur underwriting losses. On the other hand, when the insurance capacity is an issue, they cannot sell policies at a lower premium rate and are able to make profits in underwriting business.

Gron (1994) conducted a study on underwriting profits in relation to insurance capacity and found a negative relationship between underwriting returns and capacity (i.e. a reduction in capacity causes higher insurance prices and improved profitability). In other words, when insurance companies face capacity or supply limitation, insurers cannot sell a large volume of insurance policies. Under this situation, they have to raise insurance prices and underwriting profits can be increased.

On the other hand, when a plenty of reserves are available and insurance capacity is not restricted, insurers are able to sell more new policies. Under this situation, they have to cut insurance prices, causing underwriting losses. The Gron's empirical study found the insurance capacity had a significant negative relationship with underwriting returns.

A recent study (Kang & Domingo, 2012) on the capacity constraint indicated that the insurance supply was limited by the insurance capacity. The study's regression model was used to explain the cyclical underwriting profits in relation to interest rates.

Another study by Jawadi, Bruneau and Sghaier (2009) tested insurers' dependency to financial markets in five countries (Canada, France, Japan, the United Kingdom, and the United States) and found that a significant relationship between insurance business and financial markets. Their empirical study found a strong evidence of significant linkages between insurance and financial markets. Another study by Leng (2006) analyzed claim losses and tested whether the underwriting cycle exists in other foreign countries. The study found that the cycle was country-specific and there were different degrees of underwriting cycle.

A "fair" or competitive rate of return on underwriting was the study in relation to rate regulation by Biger and Kahane (1978). Biger and Kahane derived an equilibrium underwriting profit rates based on the Capital Asset Pricing Model (CAPM). Their study was based on an assumption that insurance companies pay no tax in a competitive insurance market and the fund- generating coefficient is one. The study asserted that insurers were supposed to lose money in the insurance business and offset the loss from investment earnings. The study presented a theoretical model based on no tax. Many other studies were conducted to overcome this strong assumption. Also, the fund-generating coefficient is much larger than one for liability lines. It measures the investable period and long-tail liability lines have a longer settlement period.

Fairley (1979) conducted a pioneer work on equilibrium underwriting returns and presented a model for estimating a "fair" returns on underwriting. Their study had a policy implications on insurance rate regulation. Hill and Fairley (1979) found that "fair" profit rates determined by the Capital Asset Pricing Model were close to historical profit rates than to traditional rule-of-thumb profit rates used in regulation. Their study had an important policy implication on insurance price regulation. Insurance premium is regulated in each state.


Biger and Kahane (1978) showed that the Capital Asset Pricing Model implies an equilibrium level of underwriting profits as follows:
E([R.sub.u]) = - a [R.sub.f] + [b.sub.u] [E([R.sub.m]) - [R.sub.f]],
               where (1)
E([R.sub.u]) = "fair" rate of return on underwriting.
a = fund-generating coefficient (FGC).
[R.sub.f] = risk-free interest rate.
[b.sub.u] = systematic risk of underwriting returns.
E([R.sub.m]) = expected rate of return on market portfolio.

The model indicates that a fair rate of return on underwriting is the negative of risk-free interest rate multiplied by the fund-generating coefficient "a"plus the risk premium of underwriting. The underlying ideal of the model is that insurance stock prices adjust until the expected rate of return on underwriting conforms to the equilibrium model. If the underwriting [b.sub.u] is zero, the "fair" rate of return on underwriting becomes E([R.sub.u]) = - a [R.sub.f]. The minus sign indicates that insurers end up taking underwriting losses in a competitive market, and the magnitude of the underwriting loss depends upon the fund-generating coefficient and interest rates.

The data on underwriting gains and losses, investment income, loss ratio, underwriting expense ratio, combined ratio, net premiums written, unearned premium reserves, and loss reserves were gathered from the Best's Aggregates and Averages--Property and Casualty. The fund-generating coefficient is computed by dividing the sum of unearned premium reserves and loss reserves by net premiums written. The data on interest rates were collected from the Economic Report of the President transmitted to the Congress. This study uses annual data from 1996 to 2014. All numbers in the table 4 were used to compute equilibrium underwriting profits or losses and excess returns.


Descriptive Statistics

Table 1 shows that the entire industry experienced an average annual underwriting loss of 11. 69 billion dollars during the period from 1992 to 2015. However, the average annual net invest income was about 45 billion dollars for the same period. It means that insurers are heavily depending upon the investment side of business and willing to accept underwriting losses or a very small amount of underwriting gains. This is known as a cash flow underwriting in the industry.

This study uses combined ratio to measure underwriting results. The ratio is a sum of loss ratio and expense ratio. As shown in Table 2, the average loss ratio is 76.04 percent during the period from 1992 to 2015, meaning that about 76 cents of one dollar premium were used for the payment of losses and loss adjustment expenses. On the other hand, the average underwriting expense ratio for the same period was about 28%, indicating that about 28 percent of premium dollars were used for all other expenses such as agent's commission, tax, administrative expenses, etc. The last column in Table 2 shows the combined loss and underwriting expense ratios. The average combined ratio of 102.89 means that the whole industry lost 2.89 percent in the underwriting business.

The fund-generating coefficient (FGC) in Table 3 is a measure of investable funds generated per dollar of premiums written. For example, the coefficient becomes larger for long-tail liability lines than property lines because the claim settlement period is longer for liability lines, so insurers have longer time to invest the premium dollars for those liability lines. For example, the medical malpractice insurance has a long court trial period, so insurers can invest premiums for a few years until claims are settled. The model indicates that insurers should lose more in underwriting business in liability than property lines. The fund-generating coefficient (FGC) variable is expressed as "a" in equation (1). Liability lines have a larger fund-generating coefficient, meaning more underwriting losses as indicated in the equilibrium model of equation (1). The model indicates that insurers are supposed to lose in insurance business since they have investment earnings on advanced premium payments. Note that the model of equilibrium underwriting profit/loss has a negative sign as shown in equation (1), meaning that a larger fund-generating coefficient (FGC) implies higher underwriting losses.

It is difficult to accurately measure the fund-generating coefficient. But, an approximate measurement of the coefficient can be obtained by dividing the sum of premium reserves and loss reserves by earned or written premiums. The coefficient for property lines is less than one, whereas the liability line's coefficient can be more than one, meaning a longer investment period and more investment earnings in liability lines. The implication is that the equilibrium rate of return on underwriting varies by line because the coefficient affects underwriting profitability when the capital market is in equilibrium. As mentioned before, the underwriting profit in this study is measured by a combined ratio that is a sum of the loss ratio and the expense ratio. The average fund-generating coefficient from 1996 to 2014 for all lines is 1.6822 as shown in Table 3.

Empirical outcomes

Table 4 shows equilibrium and actual underwriting profits/losses from year 1996 to 2014, assuming zero underwriting beta ([b.sub.u]). Two equilibrium/theoretical underwriting profits/losses are computed in the study. The variable, EUP1 is shown in equation (1). That is a negative of the product of the fund-generating coefficient multiplied by risk-free rates (INT3) with zero underwriting beta. In other words, EUP1 in Table 4 is obtained by multiplying FGC (fund-generating coefficient) by INT3 (risk-free rate) and adding a minus sign. The other equilibrium underwriting profit/loss variable, EUP2 is computed in the same way as shown in equation (1), but it is based on yields on municipal bonds (MUNI) rather than risk-free rates. The EUP2 variable in Table 4 is obtained by multiplying FGC (fund-generating coefficient) by MUNI (yield on municipal bonds) and adding a minus sign as indicated in the equilibrium model of equation (1). The variable INT3 in Table 4 is a yield on 3-month Treasury bill whereas the variable MUNI is a yield on high-grade municipal bonds. Note that insurers have a large amount of investments in tax-exempt municipal bonds.

The variable, AUP shows actual/historical underwriting profits/losses based on the combined ratio. The combined ratio as shown in Table 2 is a sum of loss ratio and underwriting expense ratio. The loss ratio is claim payments divided by written premiums. The expense ratio is underwriting expenses divided by written premiums. For example, if the loss ratio is 80% and the expense ratio is 20%, the actual underwriting profit/loss (AUP) is zero since 80 cents are used for claim payments and 20 cents are used for expenses on every dollar of premium income. If the combined ratio is 110%, The AUP is minus 10% (10% underwriting loss) since the combined claim and expense payment is 10% more than premium income. If the combined ratio is 90%, the actual underwriting profit (AUP) is 10% since the combined claim and expense payment is 10% less than premium income. Note that the numerator of the combined ratio is cash outflow and the denominator is cash inflow. Therefore, the variable, AUP is computed as 100% minus the combined ratio. It is a commonly used method of computing underwriting returns in insurance industry. The last variable called Excess is the difference between actual/historical and theoretical/equilibrium underwriting profits/losses.

The Excess variable in Table 4 is the difference between AUP (actual underwriting profit) and EUP1 (equilibrium underwriting profit based on risk-free rate) in percent. It is computed as AUP minus EUP1. The positive values of the Excess variable indicate abnormal returns, while the negative values of the variable indicate abnormal losses in underwriting business. For some years insurers were able to make additional profits over equilibrium while other years they were behind. The excess return variable based on EUP2 (equilibrium underwriting profit based on municipal bonds) is not included in this study since it is not expected to make much differences in theory and practice.


The study examined the excess returns for 19 years from 1996 to 2014 and found that P&C insurers were able to have excess/abnormal returns for 11 years, amounting to 55.47%, whereas the excess/abnormal losses for 8 years were 31.75%. The whole industry was able to have the net excess return of 23.72% over the entire19-year period. This implies that the insured paid too much premiums over the period if the theory is right with zero underwriting beta. One can argue that the underwriting beta is low, not zero. Then, equilibrium/theoretical underwriting returns become higher due to risk premiums, resulting in higher equilibrium underwriting returns and smaller excess returns. In this case it is possible that the total excess return over the years can be close to zero.


Future research can estimate the underwriting beta and compute the excess return based on the value of beta. The estimation of excess underwriting return in this study is based on an assumption that the underwriting beta is zero. The correlation between insurance business and the general economy is supposed to be low, but may be not zero. The risk premium associated with the underwriting beta can have a substantial effect on the excess return. This research should have some implications with regard to insurance price regulation. Insurance price is regulated in each state and the study of equilibrium underwriting profit can have an important impact on rate regulation.


Biger, N., & Yehuda, K. (1978) Risk Consideration in Insurance Ratemaking, the Journal of Risk and Insurance. 45, 121-132.

Fairley, William B. (1979). Investment Income and Profit Margins in Property-Liability Insurance: Theory and Empirical Results, Bell Journal of Economics, 10, 192-210.

Gron, A. (1994) Capacity Constraints and Cycles in Property - Casualty Insurance Markets, RAND Journal of Economics, 25 (1), 110-127.

Higgins, M. L., & Thistle, P.D. (2000). Capacity Constraints and the Dynamics of Underwriting Profits. Economic Inquiry, 38 (3), 442.

Hill, R. D. (1979). Profit Regulation in Property-Liability Insurance, Bell Journal of Economics, 10, 172-191.

Jawadi, F., Bruneau, C., & Sghaier, N. (2009). Nonlinear Cointegration Relationships Between Non-Life Insurance Premiums and Financial Markets. Journal of Risk and Insurance, 76 (3), 753-783.

Kang, H. B. (2007). Investment Returns and the Insurance Price Cycle: Industry vs. Stock. International Journal of Business, Accounting, and Finance, 1, 1.

Kang, H, & Joaquin, D. (2012). Interest Rates, Insurance Capacity and Cyclical Underwriting Profits Revisited, The International Journal of Business, Accounting, and Finance, 6, (1), 132-141.

Kahane, Y. (1978). Generation of Investable Funds and the Portfolio Behavior of the Non-Life Insurers, The Journal of Risk and Insurance, 45 (1), 65-77.

Leng, C. (2006). Stationarity and Stability of Underwriting Profits in Property-Liability Insurance: Part I and II. The Journal of Risk Finance, 7(1), 38-49.

Wen, M, & Born, P. (2005). Firm-Level Data Analysis of the Effects of Net Investment Income on Underwriting Cycles: An Application of Simultaneous Equations, The Journal of Insurance issues, 28, 14-32.

Han B. Kang

Illinois State University

About the Authors:

Han B. Kang is a professor in the Department of Finance, Insurance and Law, Illinois State University, Normal, Illinois. He authored and coauthored many articles in real estate appraisal, insurance fraud, service quality in automobile insurance, redlining, insurance distribution systems, insurance premiums comparisons, economies of scale, and underwriting profit cycles. He has published in several scholarly journals including Journal of Banking and Finance, CPCU Journal, Journal of Insurance issues, Managerial Finance, Journal of Business Case Studies, Midwest Review of Finance and Insurance, Southern business Review, Journal of International Insurance, Journal of Real Estate Research, Journal of American Real Estate and Urban Economic Association, International Journal of Business, Accounting and Finance among many other journals. He has presented papers in many academic conferences including the IABPAD Conference.
Table 1
Underwriting Gains/Losses and Investment Income
(In Millions)

Year     Underwriting Gains/Losses  Net Investment Income

1992          -36,260                    33,734
1993          -18,094                    32,645
1994          -22,083                    33,687
1995          -17,375                    36,834
1996          -17,162                    37,962
1997           -6,030                    41,499
1998          -17,669                    41,097
1999          -24,750                    40,071
2000          -32,145                    42,650
2001          -52,692                    39,849
2002          -32,347                    41,099
2003           -5,230                    41,147
2004            1,692                    41,776
2005           -6,676                    51,879
2006           34,141                    54,826
2007           18,779                    58,054
2008          -21,809                    54,412
2009             -195                    50,912
2010          -10,365                    49,855
2011          -35,201                    51,397
2012          -13,846                    50,064
2013            16280                     49530
2014            8,663                    55,210
2015            9,887                    49,323
Average       -11,685                    44,944

Source: Best's Aggregates & Averages, 2016

Table 2
Underwriting Profitability measured by Combined Ratio

Year     Loss Ratio  Underwriting   Combined
                     Expense ratio  Ratio

1992        88.1        26.5        114.6
1993        79.5        26.2        105.7
1994        81.1        26          107.1
1995        78.9        26.1        105
1996        78.4        26.3        104.7
1997        72.8        57.1         99.9
1998        76.5        27.6        104.1
1999        78.9        27.9        106.7
2000        81.4        27.4        108.8
2001        88.4        26.5        114.9
2002        81.5        25.1        106.6
2003        75.0        24.6         99.6
2004        73.5        24.9         98.4
2005        75.5        25.4        100.9
2006        65.5        26.1         91.6
2007        67.8        27.1         94.9
2008        77.1        27.5        104.6
2009        72.0        28.0        100
2010        73.7        28.2        101.9
2011        79.4        28.2        107.7
2012        74.3        28.1        102.5
2013        67.2        28.0         95.2
2014        69.1        27.5         96.6
2015        69.3        28.0         97.3
Average     76.04       28.10       102.89

Table 3
Funds-Generating Coefficient (FGC)
All Industry(1996-2014)

           UPR            LR           NPW        FGC

2014     233,413,000  614,509,000  507,522,062  1.67070
2013     220,453,891  596,711,138  481,705,445  1.69640
2012     210,941,096  603,179,216  460,968,626  1.76611
2011     203,260,938  600,707,917  441,997,964  1.81894
2010     199,291,899  569,505,045  426,252,627  1.80362
2009     197,674,829  564,277,773  423,128,170  1.80076
2008     201,422,115  567,397,802  440,382,756  1.74580
2007     204,165,491  544,213,598  446,968,640  1.67434
2006     201,721,585  523,854,257  448,932,081  1.61623
2005     193,687,581  512,504,119  426,794,517  1.65464
2004     185,931,470  471,089,274  425,391,932  1.54451
2003     174,429,337  430,618,052  404,342,450  1.49637
2002     156,298,711  400,060,199  367,580,872  1.51357
2001     134,734,920  377,160,621  320,763,809  1.59586
2000     122,607,155  362,379,916  296,788,133  1.63412
1999     118,574,112  367,226,056  286,343,349  1.69657
1998     113,781,174  368,865,278  279,765,130  1.72518
1997     109,761,605  367,653,926  275,984,295  1.72986
1996     105,213,551  368,920,314  268,385,434  1.76662
Average  169,663,970  477,573,583  384,582,013  1.68219

UPR: Unearned Premium Reserve; LR: Loss &Loss Adjustment Expense
NPW: Net Premiums Written;

Table 4
Equilibrium Underwriting Profits/Losses (EUP) vs. Actual Underwriting
Profit/Losses (AUP)

(1996-2014 in percent)
      FGC      INT3  MUNI  EUP1        EUP2       AUP   Excess

2014  1.67070  0.03  3.78  -0.05012   -6.31525    2.9     2.95
2013  1.69640  0.06  3.96  -0.10178   -6.71774    3.51    3.72
2012  1.76611  0.09  3.14  -0.15895   -5.54559   -3.28   -3.12
2011  1.81894  0.06  4.29  -0.10914   -7.80325   -8.01   -7.9
2010  1.80362  0.14  4.16  -0.25251   -7.50306   -2.61   -2.36
2009  1.80076  0.16  4.64  -0.28812   -8.35553   -0.46   -0.17
2008  1.74580  1.48  4.80  -2.58378   -8.37984   -5.10   -2.42
2007  1.67434  4.41  4.42  -7.38384   -7.40058    4.49   11.87
2006  1.61623  4.73  4.42  -7.64477   -7.14374    7.19   14.83
2005  1.65464  3.16  4.29  -5.22866   -7.09841   -0.84    4.39
2004  1.54451  1.38  4.63  -2.13142   -7.15108    1.49    3.62
2003  1.49637  1.01  4.73  -1.51133   -7.07783   -0.16    1.35
2002  1.51357  1.62  5.05  -2.45198   -7.64353   -7.39   -4.94
2001  1.59586  3.45  5.19  -5.50572   -8.28251  -15.73  -10.22
2000  1.63412  5.84  5.77  -9.54326   -9.42887  -10.16   -0.62
1999  1.69657  4.66  5.43  -7.90602   -9.21238   -7.88    0.03
1998  1.72518  4.81  5.12  -8.29812   -8.83292   -5.66    2.64
1997  1.72986  5.07  5.55  -8.77039   -9.60072   -1.63    7.14
1996  1.76662  5.02  5.75  -8.86843  -10.15807   -5.84    3.03
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Author:Kang, Han B.
Publication:International Journal of Business, Accounting and Finance (IJBAF)
Article Type:Report
Date:Sep 22, 2017

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