# UNDERWRITING PROFITS IN PROPERTY AND CASUALTY INSURANCE: EQUILIBRIUM VERSUS ACTUAL.

ABSTRACTTheoretical 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.

INTRODUCTION

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.

PREVIOUS RESEARCH ON UNDERWRING PROFITTS, LOSSES AND INVESTMENT INCOME

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.

METHODOLOGY AND THE EQUILIBRIUM MODEL

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.

RESULTS

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.

CONCLUSION AND IMPLICATION

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.

RECOMENDATION FOR FUTURE RESEARCH

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.

REFERENCES

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 (1992-2015) (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 (1992-2015) 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 Reserve; NPW: Net Premiums Written; FGC: (UPR + LR) / NPW 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. |
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Publication: | International Journal of Business, Accounting and Finance (IJBAF) |

Article Type: | Report |

Date: | Sep 22, 2017 |

Words: | 4206 |

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