|
Using DFA in Asset Allocation
 |
| Risk Measure |
Portfolio Superior to Current Portfolio |
Portfolio Interior to
Current Portfolio |
|
| Standard Deviation |
C5, B6 |
- |
| Short Term Downside Risk |
C5, B6, C6 |
- |
| Long Term Downside Risk |
C5, B6, C6, D6 |
B5 |
| Competitor Risk |
C5, B6, C6, D6 |
B4, A5, B5, A6 |
|
Optimization
DFA at Holborn
 DFA is a study of alternative strategies comparing the overall
performance of an insurer under a wide range of possible results.
Brokers have done “as if” studies of different reinsurance structures
for many, many years, looking at actual loss histories or simple
“what if’ scenarios.
Holborn presented a first-of-its-kind DFA analysis in 1994 that individually
modeled potential losses -- and reinsurance recoveries -- by line. This
client used our DFA results to see what reinsurance strategies performed
best, most frequently, against which loss scenarios, and why.
Innovations in computers and financial theory have allowed us to use
these tools in new ways to help insurers manage their catastrophe
exposure.
Two Case Studies
- Short-term perspective: Where to add business to get the
“best” spread of risk.
- Long-term perspective: Which types of loss exposures add
disproportionately to an insurer’s total volatility, and merit
the most management attention.
Descriptions changed for client confidentiality.
Case Study One –
“A Tale of Two Markets”
A Holborn client has a large, profitable book of business
in the Carolinas. They are offered an opportunity to
write profitable business in Baltimore. How much new
business should they take on?
Issues
The Baltimore market is more concentrated than the Carolinas.
There is less natural spread within this area than across the
current book.
A single loss could effect both markets, defeating the purpose of
diversifying into Baltimore.
Rates appear adequate in both markets.
Baltimore agent has Ravens tickets.
Consideration
A piece of new business is attractive to a company and should be
written when:
Premiums are greater than expected loses,
The company can tolerate the size of loss that may result,
The increase in the company’s PML caused by correlation
between the new business and the current book is reasonable in
comparison to the expected increase in profit.
Catastrophe Model Results
1,000+ simulated storms hit the Carolinas.
95 simulated storms hit Baltimore.
7 simulated storms hit both markets
Results are presented gross, since this client wants to manage the
total cost of risk: net or ceded.
Possible frameworks for optimization
Choose the mix of Baltimore business that minimizes the measured
level of risk relative to gross earned Property premiums as measured by:
- The standard deviation of gross losses.
- The probability of a loss over a year’s premiums.
- The estimated 1-in-250 year loss.
Results
|
| Optimization Framework |
Optimal Mix of Business |
Current Measure |
Optimal Measure |
Improvement |
|
| 1. SD of Losse /Premiums |
6% : 94% |
162% |
149% |
8.3 percent |
| 2. Prob of Loss > Premiums |
12% : 88% |
5.66% |
5.33% |
6.0 percent |
| 3. 1 in 250 Loss / Premiums |
8% : 92% |
685% |
625% |
9.8 percent |
|
|
Previous