 | Vol 1., No. 7 June 21, 2023 Scott Clearwater, Gridmetrics, Inc.® s.clearwater-c@gridmetrics.io |
One of the most difficult challenges in any data analysis is what happens at the extreme values, the tails of the distribution of whatever is being measured. These situations are by definition rare occurrences so modeling them analytically or with a data-driven approach has significant implications for any conclusions drawn from that data. For the insurance or re-insurance (insurance providers for insurance companies) industry understanding the risk involved with tail events is tantamount to being able to profitably underwrite policies.
With increasing property losses due to extreme weather events it is therefore critical that any (re)-insurance company understand the business disruption that occurs. Power outages are a direct consequence of extreme weather and the tail of the power outage probability distribution contains the cases where widespread outages occur that last for a significant period of time. To see how Gridmetrics provides unprecedented insights into power outage tail risk we look at power outages with a duration of at least 660 seconds (to take into account missed or delayed readings) and then look at the adjusted gross income (AGI from the IRS 2019) by zip code for these events. The financial risk of power outage events is assumed to be the population-weighted sum of the AGIs by income range times the fraction of a year that the outage took place. The AGI is meant here to be a proxy for the GDP for a region. In this way Gridmetrics could be used as part of a more comprehensive reinsurance technology suite.
As a specific example, the calculation of GDP loss defined above is done on a daily basis for 2021 and 2022 for twenty metropolitan areas in the US for which Gridmetrics has high sensor coverage. The results are shown in the figures below and give the fraction of GDP lost per day for that metro area. In each case one can see the exponentially large losses that occur for the least frequent and most damaging outage events. The vertical axes are the losses in the fraction of GDP (AGI) lost per day according to our methodology. The horizontal axis is the probability of an event occurring with increasingly rare events found to the right side.
The interpretation of these curves is that when they start their exponential rise “earlier,” meaning closer to the left edge of the plot, these are the areas most prone to more extreme outage events. Also, cities with a very sharp rise at the extreme right of the plot show rare catastrophic events such as in the Houston freeze in 2021. Curves that are very similar from one year to the next (e.g., San Francisco) are easier to model for insurance purposes. Most areas are fairly consistent in the two years covered but diverge at the most extreme tail events—exactly those that need to be best understand for insurance purposes.
Fig. 1 Distribution of daily AGI (“GDP”) losses by MSA for 2021 and 2022.
Rather than using a qualitative “early riser” criteria we can try to characterize these curves as a means to rank the different areas. Neither exponential nor hyperbolic fits gave consistently good results. One straightforward way is to look at the fraction of average daily GDP lost beyond the 1% percentile of outage events. This value could then be used as the basis for a parametric insurance policy for businesses located in these areas. That is, payouts could be scaled to different thresholds of the fraction of GDP lost beyond the 1% level event. A hypothetical parametric term sheet is shown below.
Table 1. Avg. Daily GDP Lost Term Sheet
| GDP Lost Thresholds At 1% | Payout |
| GDP lost < 0.250 | 0% |
| 0.250 ≤ GDP lost < 0.350 | 25% |
| 0.350 ≤ GDP lost < 0.500 | 50% |
| 0.500 ≤ GDP lost < 0.650 | 75% |
| 0.650 ≤ GDP lost | 100% |
Now assume one year contracts for all the metro areas and an interest rate of 5% and a probability of GDP lost > 0.250 = 7.5% (calculated from the 2021 and 2022 data). Then the expected actuarial net present value per premium amount equals 7.5% / 1.05 = 7.14%, which the insurance firm will use in its premium calculation. Any losses amounting to less than 7.14% of the premium will result in a profit for the firm.
We now explore twenty metropolitan areas to see what their payouts would have looked like given the actual calculated GDP lost values for each metro area. Given the contrived data from Table 1 and actual outage data from 2021 and 2022 we can construct the hypothetical business scenario as shown in Table 2. The results for this example show that 2021 is slightly unprofitable but 2022 looks like a year with more reasonable returns. Note that the average loss at the 1%-level are not that different between 2021 and 2022, but the extreme events in 2021 drove the unprofitability in 2021.
Table 2. Average MSA Daily GDP lost for 1% tail and 2021/2022 Hypothetical Payouts
| MSA | GDP Lost 2021 | 2021 Payout | GDP Lost 2022 | 2022 Payout |
| Atlanta | .073 | 0% | .156 | 0% |
| Baltimore | .072 | 0% | .216 | 0% |
| Boston | .149 | 0% | .098 | 0% |
| Chicago | .125 | 0% | .088 | 0% |
| Denver | .049 | 0% | .115 | 0% |
| Detroit | .392 | 50% | .366 | 50% |
| Houston | .765 | 100% | .165 | 0% |
| Indianapolis | .086 | 0% | .070 | 0% |
| Las Vegas | .047 | 0% | .058 | 0% |
| Miami | .046 | 0% | .125 | 0% |
| Minneapolis | .056 | 0% | .111 | 0% |
| Philadelphia | .090 | 0% | .068 | 0% |
| Phoenix | .056 | 0% | .079 | 0% |
| Pittsburgh | .155 | 0% | .137 | 0% |
| Portland | .244 | 0% | .172 | 0% |
| Sacramento | .151 | 0% | .037 | 0% |
| San Francisco | .098 | 0% | .056 | 0% |
| San Jose | .119 | 0% | .168 | 0% |
| Seattle | .240 | 0% | .174 | 0% |
| Washington, DC | .069 | 0% | .129 | 0% |
| Average | .154 | 150% / 20 = 7.50% | .129 | 50% / 20 = 2.50% |
| Average Overall Premium | 7.14% | 7.14% | ||
| Expense Ratio | 1.003 | 0.957 |
A plot of the average daily 1% GDP losses is shown in Fig. 2. Note the outlier for Houston in 2021. Without the Houston 2021 data the average daily loss for 2021 would have been .121 which is lower than 2022’s average. In fact, the median for 2021 was 0.094 which is lower than 2022’s 0.120. Once again we see the effects of outliers on average results.
Fig. 2 Distribution of average 1% daily GDP lost for 2021 and 2022.
The results shown here represent currently available capabilities that could be used by the insurance and reinsurance industries. In addition to power outages, Gridmetrics has a number of proprietary power resilience indexes that could also be folded into a uniquely comprehensive power resilience reinsurance technology suite.
Learn more about Gridmetrics actionable power intelligence solutions.
