Nanyang Business School Forum on Risk Management and Insurance
Marginal Cost of Risk-Based Capital and Risk Taking
Capital regulations serve to discourage financial institutions from excessive risk-taking and to prevent their insolvency by ensuring that these institutions hold adequate capital. However, their effectiveness in discouraging risk-taking behavior is debatable.
In this study, we show that particular interactions between the risk categories assumed in required capital calculations may encourage risk taking by lowering the marginal cost of undertaking additional risks. To illustrate this relationship analytically, we utilize the structure of the risk-based capital (RBC) calculation for U.S. insurance companies and show that the predetermined interactions underlying the square root rule of the RBC formula (i.e., the square root of the sum of the squared risk charges) explicitly assigns the marginal cost of each risk category.
Under the current U.S. RBC system, there are six risk categories for P&C insurance companies and each category is subjected to capital charges. As mentioned earlier on, the square root rule applied in the RBC calculation incorporates the assumption of independence between risk categories. Due to the nonlinearity of the square root rule, the marginal RBC cost of a risk category is inevitably dependent on other risk categories. Specifically, if a certain risk category contributes a lower proportion to the total risk charge, this will result in a lower capital cost for an additional dollar increase in this risk category, relative to other risk categories. When the marginal cost of risky investment is reduced, insurers may then take advantage of the opportunity to seek a higher profit at a lower capital cost. This illustrates a specific channel through which the built-in diversification benefits of the RBC system may have unintended consequences on the risk-taking behavior of insurance companies.
In our empirical analyses, we examine how the RBC formula affects P&C insurers’ risk-taking behavior in fixed-income (FI) security holdings, the largest portion of total investments by P&C insurers. Using a sample of U.S. P&C insurance companies from 2003 to 2010, we find that insurers with a lower marginal RBC cost of FI investments at the beginning of the year increase the amount of risk taken in their portfolio of FI investments for that year.
To mitigate the endogeneity concern, we examine the impact of an exogenous shock on the marginal RBC cost of FI security holdings. We investigate how insurers adjust their investment behavior after getting hit by the two costliest natural disasters in U.S. history, Hurricane Katrina and Hurricane Sandy. Both hurricanes caused affected insurers to amass huge loss reserves for their claimants and raised their capital requirement for reserve risk. This implies that for a given amount of risky FI investment, an increase in the capital charge of reserve risk translates to a decrease in RBC costs for acquiring additional units of risky FI securities. We document that insurers reporting higher coverage relevant to hurricane loss in severely affected states undertook more risk in their bond investments and purchased more risky bonds after those hurricanes. Our result is robust to controlling for shocks on capital adequacy.
Our analysis of the natural disasters highlights the unintended consequence of predetermined interactions between the risk categories incorporated within the square root rule of the RBC calculation. We document that insurers failed to control their overall risk where an increase in risky bond investment increases the firm’s volatility of return on assets (ROA) and overall insolvency probability as measured by the z-score. Our results call for caution in the design of capital regulations.
Assuming particular interactions between risk categories is a common practice in aggregating risks for the purpose of setting the minimum required capital for financial institutions. Our results and regulatory implications are thus not only limited to the U.S. insurance industry, but are also applicable to the broader regions of the banking and financial industry.
The complete paper is available for download https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2943371