**Alfons Brodschelm explains why return on equity is a useful way to measure an insurer’s financial strength.**

In general, a company's success is measured by its return on equity (ROE). However, this measure is rarely used as a performance benchmark for insurance companies. Instead, the combined ratio (CR) is used as the benchmark for technical performance, where claims expenditure and operating expenses are compared with premium. But the CR does not consider the variance in risk for individual insurance companies, for classes of business, or the sources of return and expenditure.

Given that the CR has limitations, we should consider whether the ROE may be an alternative for measuring an insurance company's success, and whether it could even be used as a tool for calculating premium rates.

Limitations of the CR

If capital is to be invested in an insurance company, the return is often measured using the CR. However, the CR does not consider all sources of return, such as the investment yield from existing capital. It also disregards the timing of the premiums, claims, and expenses, essentially ignoring the return on the interim investment of cashflow.

Furthermore, the CR may not adequately describe the profitability of a business class. For instance, a CR of 115% might suggest a loss. But for a long-tail class, the cumulative return on the investment often compensates for initial losses. For short-tail businesses, such as household insurance, a CR of 115% indicates a loss since claim settlement is quick without any appreciable return made on the interim premium investments. Table 1 shows some examples of CRs based on risk and cashflow.

These examples also illustrate another problem with the CR: it does not recognise the relationship between classes of business or between types of insurance. Using a reinsurance example, in most years the CR in proportional reinsurance is higher than that in non-proportional or excess of loss reinsurance. But this does not mean that excess of loss reinsurance is more profitable. Since excess of loss reinsurance is normally associated with a higher risk, a loss can lead to an extremely high CR.

In short, the CR would not help investors to assess profitability. This is where the ROE comes in.

The advantages of the ROE

In simple terms, the ROE shows the relationship between the operating result of a company and its equity. It can be used to compare investment in insurance companies with other types of investment, to compare insurance companies within a market, and to compare an individual class of business with others within the same company.

Insurers can also use the ROE to determine the capacity for individual business classes and units.

How equity mitigates risk

Equity must absorb all unforeseen negative financial occurrences, whether these are based on insurance risks or other risks not specific to insurance. In estimating the capital required for underwriting, insurers adhere to a series of standard methods:

- Europe Minimum solvency margin, Solvency II, equalisation reserve, and ruin theory.

- USA Standard & Poor's (S&P) capital factors, risk-based capital, statutory leverage ratios, and the liquidation basis formula.

- Additional method Dynamic financial analysis, in which the impact of certain underwriting and investment risks are tested in a computer model.

European insurers are the most familiar with the minimum solvency margin and the associated leverage ratios. The minimum solvency margin indicates how much equity an insurer must have for an existing or future portfolio, and this is calculated according to a specified model taken from a comparison of premium and claims indices.

In the American market, leverage ratios of at least 50% are required that is, at least $1 equity per $2 written net premium. In Germany, a leverage ratio of 20% is considered a rule-of-thumb for the minimum capital and surplus requirements of a property and casualty insurer.

Some insurance companies work with equity allocation according to S&P standards. The allocation of equity is effected through the application of capital factors published in S&P tables.

A reinsurer must have equity available to take on ceded risks. This means the capital requirements for the primary insurer should be lower. A good reinsurance programme cuts risk and removes catastrophe exposure. It should ensure that the volatility after reinsurance and equity are substantially lower than the volatility before reinsurance. Here the primary insurer can thanks to the reinsurer save capital costs. Its ROE improves if the capital savings are greater than the reduction on the gross result through the reinsurance premium.

The capital market is international and efficient. There is no reason why, for the same risk, the capital market should make capital available at a cheaper rate for a reinsurer as it does for a primary insurer. Nevertheless, there is still a saving effect. Normally the additional risk potential the reinsurer needs to take on compared to the cedant's risk is lower than the risk potential the cedant saves. This is because the reinsurer has a worldwide diversified portfolio in many classes of business so that new risks accepted create more balance. The difference between risk capital saved by the cedant and the risk capital required by the reinsurer is the economic value of reinsurance. This becomes even greater the more efficiently the reinsurance programme reduces the volatility of the primary insurer's portfolio and the more diversified the reinsurer.

Technical details

How is the ROE calculated for an insurance company? The elements can be described by a few formulae based on some simplified assumptions.

ROE =

This shows the operating result of a class of insurance business divided by the equity allocated to the class. The operating result is defined as the underwriting result (ie premiums less claims and expenses) plus interest on cashflow and capital investments. This formula can be rearranged:

ROE = + ROC

where the leverage ratio is the ratio of equity to net premium and CFUR (cashflow underwriting result) is the ratio of the underwriting result including cashflow interest to net premium. The ratio of the return on capital investments to equity will be referred to as return on capital (ROC). This formula contains income, but the CR does not, hence the two cannot be directly compared with each other.

Calculating premium rates

An insurer can also use the ROE to calculate premiums. For example, if the pure rate of an insurer is 1.05â° and is paid in one lump sum one year after receipt of premium and expenses incurred, then, allowing for an interest rate of 5%, the discounted pure rate will be 1.0â° of the sum insured. This represents an investment of 1.0â° of the sum insured at an interest rate of 5%, which results in the amount accruing to 1.05â° by the time of the claim settlement:

Discounted pure rate =

However, if we assume expenditure of 35% for commission and internal expenses, as well as a CFUR of 4%, the pure rate of 1.0â° results in an original premium rate of 1.64â°:

Original premium rate =

= = 1.64â°

The 1.64â° represents 101% CR [=100%/4%+5%", but what is the corresponding ROE? Assuming the business requires a 50% leverage ratio and the current market interest rate is 2% ROC, the ROE is 10%, as calculated using the following formula:

ROE = +ROC

Similar assumptions are made in the next example, but with a leverage ratio of 125% instead of 50% and with claims paid in one lump sum five (not one) years after receipt of premium; interest earned is equivalent to 27.6% [=(1+5%)51". Unlike the first example, this class of business has a higher risk and requires more capital. The discounted pure rate amounts to 0.82â° [=1.05â°/(1+5%)5" and assuming a CFUR of 15%, the original premium rate is again 1.64â° [=0.82â°/(100%/35%/15%)", but the CR is 112.6% [=100%/15% +27.6%" and the corresponding ROE is still 10%.

In both examples the ROE is 10% with an original premium rate of 1.64â°. However, additional profit is necessary in the second example because of the increased risk and additional capital requirements. But longer cashflow will account for a higher part of the return than before.

These simplified examples show that use of ROE makes investing in insurance companies easier to understand. As a benchmark, ROE can provide more information about an insurance company's return and profitability than a CR formula. This is essentially because the ROE accounts for more forms of income and expenditure.