Many of us have bought life insurance, but what about buying shares in life insurance companies? The industry is a black hole to investors who struggle to see how such companies create value and make money. Because the insurance industry feels current - and complex - accounting rules do not accurately portray long-term performance (policies can last 50 years), so companies publish customised performance indicators to help their evaluation. Yet bewildered investors tend to shun or conservatively price life insurance stocks. Life insurers regularly protest that they pay too much for capital (that is, they believe themselves undervalued). Despite this, growth prospects for the sector in Asia - where income is rising and insurance penetration low - appear bright. Richard Li Tzar-kai recently agreed to buy ING's life insurance operations in Hong Kong, Macau and Thailand for more than US$2.1 billion, or 24.3 times estimated 2012 earnings and 1.9 times book value. Given the number and size of Hong Kong-listed international and mainland insurers, the sector is worth a closer look. First let's look at how they work. Insurers operate on the concept of shared risks, under which only a portion of policies sold result in a claim. If an insurer takes HK$1,000 each from 100 customers, five of whom make claims of HK$15,000 each, it makes a profit of HK$25,000. The premium charged for policies is calculated by actuaries using sophisticated statistics that consider investment yields, costs, policyholder returns (if there is an investment feature), morbidities (probability of sickness or disability) and mortalities (chance of death). As premiums include a profit element and cover expected claims and costs, by screening applications - known as underwriting - insurance companies can make profitable risk and return trade-offs. It is more profitable for insurers if customers renew their policies: new customers are expensive to acquire and renewal premium is the largest cash-flow contributor. The persistency ratio measures the percentage of policies renewed. Premiums collected are invested to cover costs, meet future claims and generate profits. Life insurance companies are among the world's biggest institutional investors. Claims provisions - typically an insurer's largest liability - are regularly reviewed and adjusted by actuaries to ensure they meet future claims, as the assumptions beneath their premium calculations may change (a process called liability adequacy testing). Any increase results in higher claim expenses. Life insurers typically do not make excessive underwriting margins due to competition and have become increasingly reliant on investment income. However, they are exposed to interest rate risks if they can't match invested assets with liabilities. Say, an insurer assumes an annual investment return of 3 per cent to cover its 30-year liability; if it buys a 30-year bond with 3 per cent yield, it will cover the claim. Because of the scarcity of long-dated bonds in Asia, if it is only able to buy a 15-year bond at, say 2.5 per cent, (shorter term bonds often have lower yields), not only will it fail to meet its target, but it also runs the risk yields may be even lower when it reinvests after the bond matures. Many life insurers are having difficulty meeting returns in the current low interest rate and weak equity market environment, since their portfolios are full of long-term fixed-income investments and some equities as a return kicker. AIA reported profit before tax of US$2.2 billion last financial year, of which US$2 billion was investment income (representing a 2 per cent return because of equity losses). If investment income (boosted by equity gains) was excluded in the previous financial year, it would have swung into a loss due to higher claims provisions. Life insurers need to meet certain required minimum solvency margins (available capital divided by required capital), which measures their ability to settle claims. The profit of an insurance contract is the same over its lifespan - premiums plus investment income, less claims and costs. But because insurance contracts have long maturities, complications arise over which revenues and costs to recognise in each financial year. For example, customer acquisition costs (such as commission and policy issue expenses) are capitalised and spread over the life of the contract, thereby distorting net asset values (excess of assets over liabilities) and cash flows. AIA reported US$12.8 billion of such deferred costs last financial year, compared with US$21.3 billion of equity. As a result, life insurers routinely disclose relevant sector-specific measures to help investors value them and fend off hostile takeovers. Sales of new policies are measured by annualised new premium (all first year premiums and 10 per cent of single premiums) while the value and profitability of new contracts are captured by the value of new business (VNB), which is the present value of the future after-tax profits of new policies sold during the year. Total weighted premium income comprising renewal and new premiums gives a more accurate reflection of total annual revenue. Many investors value life insurers like banks, using price-earnings and price-to-book (market value over net asset value) ratios. Due to the possible limitations of reported accounting data, analysts increasingly supplement their evaluation with embedded value (EV), the economic value of the existing life insurance businesses (not future new business) determined by an actuary. EV is the sum of the adjusted net asset value (adjusted by marking assets and liabilities to market and deducting unrealised gains and deferred acquisition costs) and the present value of the future after-tax profits from its existing policies (called in-force value). It is thought to be a better value indicator because it includes all the cash flows in the life of the insurance contracts (accounting data provides a one-year snapshot). As EV is very sensitive to the choice of assumptions such as discount rate (the rate which converts future cash flows to today's value), investment returns, costs and probabilities, life insurers can flatter this figure (although the same also applies to accounting data). As insurers usually disclose the sensitivity of the EV to key assumptions, investors could adjust this number using their own assumptions. As EV is equivalent to the market value of the equity of life insurers, investors commonly use the ratio of share price to EV to value them. The economic earning of a life insurer is the periodic change in EV before taking into account capital increases and dividend distribution (called EV profit). The ratio of price to EV profit is similar to the traditional price earnings multiple. Let's use AIA, Prudential and China Life, life insurance companies listed in Hong Kong, to illustrate these concepts (see table). Besides price to EV and price to EV profit, market capitalisation can be expressed as a multiple of VNB, which is how many times the value created by one year of new business the firm is worth. At the first look, China Life seems most expensive among the three based on traditional price-earnings and price-to-book ratios. Its price-to-EV multiple is also the highest. China Life deserves a good price-to-EV rating as it generates superior economic returns (EV profit divided by EV) primarily because of its more efficient cost base. But AIA is trading at around twice its price-to-EV-profit ratio due to AIA's higher growth. AIA's VNB for the first half of this year grew by 28 per cent, compared with China Life's 2.5 per cent. AIA's prospects have also been enhanced by its recently announced US$1.7 billion acquisition of ING Malaysia, which would make it the country's largest life insurer when completed. This is also why markets think AIA is worth about 46 times the value of one year of new business. Prudential, on the other hand, is trading close to its EV, which means investors see little value in its future business or think its EV is overstated. If Prudential's EV is fair, then it may look like good value. It is trading at a lower price-to-EV-profit ratio than China Life despite having stronger growth. Moreover, it is worth only 9.5 times the value created by one year's business, compared with more than 21 years for China Life. So China Life is not as expensive as it first looks, AIA seems to have been rewarded for its growth prospects, and Prudential could potentially be of good value.