Expert Commentary

# Determining the Optimal Combination of Risk Retention and Risk Transfer

If you are a risk manager for a large company or simply purchase the insurance for your firm, chances are you also have deductibles and/or self-insured retentions (SIRs), also referred to as retained risk. If you retain significant amounts of risk, your company incurs a capital charge for retaining such risk, regardless of whether the company recognizes the charge on its balance sheet.

Calculating this charge has proven to be a challenge, even to the most finance-savvy risk manager. If a capital charge for retained insurance risk is the Holy Grail, we can construct a methodology that will get us partially there.

Insurance is nothing more than a form of contingent capital—the insurance company is willing to provide, for a premium cost, access to a considerable amount of funds in the event you have a loss. Access to the insurance proceeds is contingent on experiencing an insurable loss. This begs the question: Is insurance an efficient use of capital? The answer is dependent on several factors, not the least of which is the cost of the insurance relative to the value of retaining the risk. Of course, some insurance purchases cannot be avoided; those for catastrophic loss, for example, but unless a company can identify the actual cost of retaining risk, the question of whether insurance premiums constitute an efficient use of capital will remain unanswered.

Up to this point you only know two things: (1) insurance premiums purchase off-balance sheet risk protection, and risk you retain, either through deductibles or self-insured retentions, remain on the balance sheet. The eternal question then becomes what is the optimal combination of risk retention and risk transfer? Most companies not only do not understand that retaining risk has a capital impact, but they have no financial metrics for comparing competing retention/transfer scenarios. They also have no way of determining if the risk transfer premiums represent economic value.

Many externalities contribute to the confusion surrounding this question. Pure economic factors do not usually drive the price of excess insurance; the markets do. This means that in most years, the cost of the protection bears little resemblance to your individual risk profile. Risk retention conventions such as the $250,000 per occurrence loss limit is practically institutional (thousands of companies retain this figure through large deductibles, retroactive plans or captives, but few actually know whether it is the right one!).

Another factor that contributes to the lack of understanding of the financial impacts of this decision is the role of insurance companies. When an insurer promulgates rates for excess risk transfer, it does so at convenient dollar amount intervals. For example, $100,000, $250,000, and $500,000 are quite popular retention amounts. In the absence of any economic reason why they should use any other figure, you get what they offer.

There is a way to calculate the costs of retained risk and risk transfer,
similar to how your company calculates its internal rate of return (IRR), and
the relationship between the IRR associated with your risk management decisions
and your weighted average cost of capital (WACC). It doesn't alleviate the
endemic problems of negotiating the cost of excess insurance, but you will have
a better idea of what the coverage *should* cost.

## The Weighted Average Cost of Capital (WACC)

The WACC is what it costs your firm to maintain its capital base. It is comprised of the cost of issuing common and preferred stock, the cost of issuing debt, and in come cases the cost of retained earnings.

Every company has a *capital structure*—a general understanding of
what percentage of debt comes from common stocks, preferred stocks, and bonds.
By taking a weighted average, we can see how much interest the company has to
pay for every dollar it borrows. This is the weighted average cost of capital.
While most people agree on what the WACC represents, few agree on a
standardized method of calculation. For example, some companies express a cost
for retained earnings, while others do not consider retained earnings as a
source of capital, just funds "left over" after the equity and debt
capital are optimally employed.

The following is a highly simplified example of what constitutes the WACC.

Capital Component | Cost | Multiplied By | % of Capital Structure | Total |

Common Stocks | 11% | X | 10% | 1.10% |

Preferred Stocks | 9% | X | 15% | 1.35% |

Bonds | 6% | X | 50% | 3.00% |

TOTAL |
5.95% |

## Internal Rate of Return (IRR)

The internal rate of return (IRR) is the discount rate that makes the net present value of periodic cash flows equal to zero. It is the return a company would earn if it invested in itself rather than investing elsewhere. In standard capital budgeting exercises, the IRR of a venture or project must surpass the company's WACC. If it falls beneath the WACC, the project has no value to the company. Theoretically, a company's overall IRR must exceed its WACC or it would not remain in business very long—its cost of borrowing would exceed its ability to pay for it.

The internal rate of return formula assumes a series of positive and
negative cash flows, resulting in a positive or negative percentage result. A
negative outcome usually suggests that the project or business is a bad bet. As
explained, a result that does not meet or exceed the company's WACC may
also qualify for the trash heap. So the challenge we face is to find a way to
mimic the value of the IRR calculation for the "investment" in risk
retention and insurance. The next question, then, is what combination of
retention and insurance produces the highest internal rate of return? Another
way to think of this is what combination of retention and insurance produces
the *least* opportunity costs? (This analysis does not take into account
a potentially positive reduction in losses though specific risk control
activities, which is a capital budgeting problem.)

While the calculation may be straightforward, estimating the variables is not. Since each "payment," whether for retained loss or insurance premiums, is a cash outflow, we need one or more assumed inflows to complete the calculation. We begin by assuming that we transfer all (hazard) risk to an insurance company for a premium. This is only true in the smallest of companies, of course, but it gives us a baseline from which to begin the calculation. We then deconstruct the insurance premium into its constituent parts based on multiple levels of risk retention. The following word formula illustrates this concept.

- Pre-tax standard insurance premium without retaining any risk whatsoever,
*Minus*

- Pre-tax premium reduction resulting from retained risk (pick any
amount)—once this figure is subtracted from the standard premium, the result
is mostly insurer expenses—this is the figure used in the IRR calculation
*Minus*

- Tax benefit resulting from purchasing insurance excess of the retention,
*Plus*

- The aggregate, discounted, after-tax cost of the retained risk—(over the appropriate payout period including investment income)

The following simple numeric example follows the above progression:

## Table 1

For simplicity's sake, in this example the premium credit for risk retention and the expected losses are the same figure. This means that the insurance underwriter and the actuary agree.

Using the above example, we can then calculate an internal rate of return
for this particular combination of risk retention and transfer, being careful
to enter the cash inflows and outflows in the sequence in which they occur. The
resultant IRR of one scenario has some value as it relates to the company's
cost of capital. But if the IRR does not meet or exceed your company's
WACC, you do not have the option of doing nothing. You must make a choice among
competing alternatives, so performing an IRR calculation on several
combinations of risk retention/transfer reveals the option with the most
*relative* value.

This technique doesn't give us a specific capital charge, but it provides a financial metric for comparing any combination of retention and transfer.

Opinions expressed in Expert Commentary articles are those of the author and are not necessarily held by the author's employer or IRMI. Expert Commentary articles and other IRMI Online content do not purport to provide legal, accounting, or other professional advice or opinion. If such advice is needed, consult with your attorney, accountant, or other qualified adviser.

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