# Beyond Expected Value | Considering Volatility

White Paper

# Beyond Expected Value | Considering Volatility

**This is the first of three white papers offered by the Brown & Brown Alternative Risk team on the fundamental tools companies use to estimate and review their corporate risk profiles.**

**White Paper 1: Beyond Expected Value – Considering Volatility****White Paper 2: Loss Dependence – A Portfolio Level View of Retained Exposure****White Paper 3: Corporate Risk Appetite and Program Structuring**

### Market Pricing

As the insurance market strives for capital efficiency, many risk managers are looking into innovative structures for financing risk. Prior to assessing the organizational value that can be added by any new program structure, Brown & Brown recommends a brief review of volatility in the context of uncertain loss outcomes to refresh one’s familiarity with the quantitative tools used to evaluate the relative merits of competing risk financing strategies.

A few simplifying assumptions made as we review volatility are as follows:

- Risk managers will look to finance losses in the most capital efficient manner available.
- Insurance purchasers, for the purposes of this review, consider risk on a line by line basis without regard for risk interconnectivity.
- A credible stochastic model has been estimated for each source of risk, and actual losses will be known and paid at the end of the year.
- Risk transfer counterparties hold capital to support each assumed risk at the 90% confidence level, and they back surplus with cash.

We understand that the assumptions are somewhat academic, but they are necessary for us to illustrate these ideas both simply and succinctly.

Volatility is defined as a quantitative measure of the potential for losses to differ from their expected value for a specific underwriting year, based on all information known about the corporation’s exposure to loss at the outset of that year.

A simplified risk transfer market pricing mechanism can be described by the following equation:

**Market premium = E(loss + LAE) + Administrative charge + Capital charge***

*computed using a market derived carrier WACC value and a risk-specific marginal economic capital requirement estimate.

In the following example, we will look at two sources of risk for Company A. Both risks have an expected annual loss pick of $1,000,000. Risk X is less volatile than Risk Y.

Volatility aversion dictates that the market premium for Risk Y be larger than for Risk X. In practice, market participants charge for volatility; this is the case whether the participant is a (re)insurance company underwriter or an institutional investor providing P&C risk capital through an alternative financing mechanism. Merely knowing the expected value of loss associated with a risk is not sufficient to assess its value in the risk transfer market.

###### Jason Flaxbeard

Alternative Risk Leader

###### Andrew Golub

Chief Innovation and Analytics Officer

###### Scott Hornyak

Chief Actuary