Why the Math Matters
- theangryactuary
- Sep 11, 2023
- 4 min read
“It’s all about relationships” a sales person once told me. When it comes to selling goods with a fixed cost of production, I’d agree. When it comes to an industry like finance and/or insurance, it’s a very different proposition. General insurance products are sold with an unknown cost for any given policy. It’s only when there are many similar policies that the law of large numbers takes over and we generate a more predictable loss outcome (cost of goods). You tend to want to get a math specialist (ahem, a.k.a. Actuary) for this sort of thing.
Like in any business, it’s about the bottom line that truly matters. It does’t matter how good a relationship there is with any business partner or customer. If the relationship doesn’t yield profit generating business, it’s not a fruitful relationship. It’s like saying that being taken advantage of is enough as long as you’re keeping the customer happy. When the math geek is telling you that the deal you’re about to agree to is expected to lose money in the long run, you should pay attention.
This basic premise reminded me of a couple of examples involving risk related scenarios where ignoring the math gets you into trouble:
Black Jack:
Don Johnson, a professional Black Jack player, became famous in 2010 after the financial crisis. He was able to win nearly $6M from Tropicana, $5M from Borgata and $4M from Caesars. The casinos were in a dip after the financial crisis of 2008 and relationship managers attempted to attract “whales”, clients who were able to bet big, by offering incentives. Unfortunately, on top of nice free hotel rooms, dinners, drinks and shows, some of these incentives included changes to the rules of the game that ended up favoring the player against the house.
Black Jack is a simple game, but like the English language, it’s easy to learn but difficult to master. The aim is to take cards from the deck until you are at 21 (or as close as possible). But once the hand is over 21, it’s automatic game over for either the dealer or player. Cards are assigned their face value, with face cards all being valued at 10 while the Aces are special, having a value of either 1 or 11, whichever is more favorable for the hand. The dealer always plays out their hand last. If the dealer busts (goes over 21), every player still in the game wins.
Math geeks have been able to run simulations for decks with multiple sets of standard 52 playing cards to calculate the odds of winning against the dealer in every situation. Based on these simulations, they have been able to generate “basic strategy” tables, where the best course of action for a player has been informed by the probability of winning. Basic strategy also suggests when a player has an advantage and should increase their bet size in the few situations where this is allowed (double down and split scenarios).
Don Johnson was able to learn how to play basic strategy perfectly. In most situations, Black Jack has a payback rate above 90% and is closer to 100% than any other casino game. But because Don was a whale, the relationship manager had agreed to make several small but significant changes that had the cumulative effect of changing the odds in Don’s favour. If they’d actually sat down to analyze the numbers, they would have realized that the odds were no longer acceptable for the casino.
The resulting winnings for Don sent the monthly earnings of one of the casinos to zero. So much for relationships. When both sides of a business transaction are trying to make some sort of gain that results in a loss to the other side, there is an adversarial element that cannot be ignored.
The Insurance Market Cycle:
Much more relevant for my line of work. This cycle is very well known, but insurance companies still manage to get it wrong despite the fact that this is common knowledge. This is where traditional underwriters will harp on about relationship management and forget when an angry actuary is yelling at them to remember the fundamentals of the business and to make sure to charge enough premium to cover expected losses.
The cycle starts with low numbers of insurance providers as there was likely a large loss in the market that resulted in several competitors having to exit the market. When this happens, the survivors increase premiums to make up for losses just paid and to make sure that future claims will be paid. However, as time wears on and profitability returns, new market participants enter (or re-enter) the market, increasing competition and driving down rates. When this happens, a large loss event or several years of poor performance follow and the cycle starts again.
This is where actuaries get angry. They will be making it clear that the rates being offered in the market are no longer expected to be profitable but the underwriters will use the old chestnut of “it’s about relationships” with their brokers to justify their actions. Honest underwriters will be the ones to notify management that original top line business plan premiums may no longer be achievable given market conditions.
Takeaways:
Sales people, as skillful as they can be, need to be restricted when it comes to the leeway they are given to make the sale. When the deal structure is complicated, it makes sense that just being able to manage a relationship and make a client feel warm and fuzzy is not going to lead to profitable business. If the deal is complicated, the authority to make the deal needs to be shifted in some part to the math specialist. For balance, the math specialist also needs to have a degree of commerciality and would benefit from having a reporting line separate to the sales function. Finally, sales should be compensated not on top line performance, but should have a portion of bonuses paid out over the longer term, tied to profitability.
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