Risk and Return

There are no universally true statements about risk.

Risk, Skill, and Luck

Years ago I asked economist Robert Shiller, who won the Nobel Prize in economics, “What do you want to know about investing that we can’t know?” “The exact role of luck in successful outcomes,” he answered. The Psychology of Money, Morgan Housel (2020)

Judge the process or the outcome?

Pay for skill, don’t pay for luck.

Question the model if the outcome deviates from expected too often.


Posterior assessment of skill given a bad outcome: depends on strength of prior. With weak convictions, skill sours with few observations.

Process risk influences margin primarily through the amount of capital (driven by regulatory capital standard) then through the unit cost (target return). Management gets caught in the middle, not wanting to look a fool to owners and judging insureds, in part, on the basis of “how likely is this insured to make me look bad?” Those insureds get the higher price. Total foots to overall cost of capital x amount.

That all makes sense. High param risk = diffuse prior, which “collapses” more with less information - bigger change in view. The WC uw who says “my book is good” can point to pricing relative to NCCI to give confidence to their principal. The XS Casualty uw can say only “trust me”. It’s not really explainability per se. And, with cat, the fact everyone is in the same boat really helps. Your excess WC loss is likely to be idiosyncratic. Your FL wind loss, not.

What is Return

Expected margin at inception: expected premium less expected loss and expense payments. In property casualty, premium is generally fixed—unlike life insurance. Expenses are split between acquisition, underwriting and processing expenses that are incurred in year 1, and loss-related expenses that can be modeled with claims.

Expected return at inception compares margin to capital deployed. And there the troubles start. What is the appropriate hurdle rate? What tenor of capital commitment?

Step back and look at insurance market participants.

Insurance market participants

Figure 1 shows relationships between the four players in the insurance market: insureds, insurers, investors, and regulators.

Insureds face a mandatory or quasi-mandatory insurance requirement—up to 60% of premium (Aon Benfield (2015)) is required in some way. The mandate is for third-party protection and insureds often do not care about insurer solvency provided their policy satisfies the mandatory requirement. Insureds are pure price buyers, do not see capital-driven quality differences.

Solvency regulation is necessary to ensure that mandatory insurance effective (Cummins (1988)). Regulatory capital standard risk functionals focus on one-year process risk, often using Value at Risk (VaR) or tail value at risk. They are calibrated from historical results.

Investors bear the risk. They charge for all risks: process, parameter, informational, agency, frictional. In a simple model, the market price of capital explained by a distortion risk measure \(\rho\). \(ρ(X)\) gives market (ask) price to assume a loss distribution given by a random variable \(X\). DRMs are coherent, can be expressed as a weighted average of TVaRs, and are law invariant. Price of risk only depends on the probability of loss. This view appears to focus exclusively on process risk, through \(X\).

Insurance companies intermediate between insureds and investors. They exist to economize on costly capital by allowing unrelated insureds to pool their risks together. Insureds assume solvency risk through limited liability, which tends to fall most heavily on the insureds with the riskiest exposures, because they will have the largest losses in insolvent states.

Figure 1: Players and their roles. The regulator applies a capital risk measure to determine required insurer assets. The pricing risk measure gives the cost of investors’ capital. Assets in excess of losses are paid to investors as the residual value of the business.

What risks?

Why is risk capital expensive?

  1. Principal-agent problem: investors and management do not have perfectly aligned incentives. Insurance is opaque and investors find it very difficult to monitor management. This is especially true for non-standard lines of business.
  2. No independent validation of insurance pricing: insurance is not expertizable. Catastrophe risk, where pricing can be evaluated using independent third-party models, is an exception.
  3. Equity requires a long-term commitment to a cyclical business. Public securities markets provide an exit, but valuations may follow the underwriting cycle.
  4. Returns are left-skewed. Investors prefer right-skewed returns with a big upside, such as technology stocks, Froot (2007).
  5. Regulatory minimum capital standards can force an insurer into supervision before it is technically insolvent. Regulation restricts dividend payments and other capital withdrawals from regulated entities.
  6. Returns to investors may be subject to double taxation, because the insurer pays corporate taxes and dividend distributions are also taxed. As a result, investors incur an extra tax expense by holding income producing assets in an insurer legal entity.

How do these risks affect market participants?

Figure 2: There are information asymmetries between insureds and insurers, and insurer management and investors.

Here is fig 1. How does that work?

Insurers can be impaired by a shock-loss—a catastrophe—or by the cumulative impact of past pricing and underwriting decisions, generally manifest in reserve development that can also be mistaken for a catastrophe. (Other mechanisms: fraud and accounting shenanigans, asset impairments.) The regulator is on-guard against both of these catastrophes in setting regulatory capital requirements.


Bodoff (2021) implications of PAT (principal agent theory)

  1. Cost of monitoring
  2. Cost of imperfectly measuring outcomes (measure performance by outcome); pay on commission, can’t monitor sales effort.
  3. Cost of excessive risk taking (p benefits from upside not downside).
  4. Cost of excessive risk aversion (worried about assessment of skill level).

Winner’s curse. Jensen.

Cat bond investors:equity vs. debt; lower agency costs; forfeit flexibility of equity capital “commitment device”.

Risk aversion and cost of risk for casualty vs. property “numerically equivalent” amount of risk

If adverse outcomes are more easily “explained away” in one arena versus another, then that business will have lower agency costs.

Hence prop cat has lower agency costs (vs. casualty). Story line matters.

Are reserve misses harder to explain away (more directly controlled)? YES

Corporate structure.

Risk disclosure as CYA.

Focus = lower PAT (easier to monitor) but less diversification benefit, less capital efficient.

Large, broadly diversified: higher PAT but more capital efficient.

Portfolio theory Principal-Agent theory
ROE Info asymmetry
Performance relative to capital relative to peers
Prob corporate ruin Executive ruin
Earnings vol Loss relative to peers or plan
Loss of franchise value Exec reputation

Margin = risk load + (PA cost + other frictions)

How to quantify.

Portfolio view good because it is generally accepted (not necessarily because it is true). Intersubjectivity, Harari and Sapiens book.

Information and the Cost of Capital Easley and O’hara (2004)

3839 Google Scholar citations

We have developed an asset-pricing model in which both public and private information affect asset returns. Because the return investors demand deter- mines a firm’s cost of equity capital, our analysis provides the linkage between a firm’s information structure and its cost of capital. We have demonstrated that investors demand a higher return to hold stocks with greater private information. This higher return reflects the fact that private information increases the risk to uninformed investors of holding the stock, because informed investors are better able to shift their portfolio weights to incorporate new information. Private information thus induces a form of systematic risk, and in equilibrium investors require compensation for bearing this risk.

An important implication of our research is that firms can influence their cost of capital by affecting the precision and quantity of information available to investors.

Information production and capital allocation: Decentralized versus hierarchical firms, Stein (2002)

This paper asks how well different organizational structures perform in terms of generating information about investment projects and allocating capital to these projects. A decentralized approach—with small, single-manager firms—is most likely to be attractive when information about projects is “soft” and cannot be credibly transmitted. In contrast, large hierarchies perform better when information can be costlessly “hardened” and passed along inside the firm. The model can be used to think about the consequences of consolidation in the banking industry, particularly the documented tendency for mergers to lead to declines in small-business lending.

information that is “soft”—that is, information that cannot be directly verified by anyone other than the agent who produces it. For example, a loan officer who has worked with a small-company president may come to believe that the president is honest and hardworking—in other words, the classic candidate for an unsecured “character loan.” Unfortunately, these attributes cannot be unambiguously documented in a report that the loan officer can pass on to his superiors. This situation contrasts sharply with, for example, an application for a home mortgage loan. Here the decision of whether or not to extend credit is likely to be made primarily based on “hard,” verifiable information, such as the income shown on the borrower’s last several tax returns.

Thus, with soft information, the advantage of decentralization relative to hierarchy is higher-powered research incentives and better capital allocation within operating units. However, there is also a countervailing cost: Under decentralization, reallocations across operating units have to be mediated by the external capital market, while under a hierarchical design, they are implemented by the integrated firm’s CEO.

Things work very differently when the information produced by line managers can be hardened and passed on to their superiors. Now, not only does a hierarchy do better than the external capital market in terms of moving money across operating units, it can also generate more research on the part of line managers, and, hence, better within-unit allocations. This is because with hard information, line managers become advocates for their units; if they can produce verifiable positive information and pass it on to their superiors, they can increase their capital budgets. Here, paradoxically, separating authority from expertise actually improves research incentives, as line managers struggle to produce enough information to convince their bosses that they should get more of the firm’s resources.

Notes and References

Aon Benfield. 2015. Insurance Risk Study. 10th ed.
Bodoff, Neil M. 2021. The Roulette Wheel and the Drunken Sailor: Principal-Agent Theory and its Ramifications for Insurance and Reinsurance Risk Management.” CAS E-Forum Fall: 1–33.
Cummins, David J. 1988. Risk-Based Premiums for Insurance Guaranty Funds.” Journal of Finance 43 (4): 823–39.
Easley, David, and M O’hara. 2004. Information and the cost of capital.” The Journal of Finance LIX (4). http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.2004.00672.x/full.
Froot, Kenneth A. 2007. Risk management, capital budgeting, and capital structure policy for insurers and reinsurers.” Journal of Risk and Insurance 74 (2): 273–99. http://onlinelibrary.wiley.com/doi/10.1111/j.1539-6975.2007.00213.x/full.
Stein, Jeremy C. 2002. Information production and capital allocation: Decentralized versus hierarchical firms.” Journal of Finance 57 (5): 1891–921. https://doi.org/10.1111/0022-1082.00483.

posted 2022-02-20 | tags: insurance, risk, return, principal agent problem, non, additive probability

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