So, last time, we were about to run a simulation to see how we would end up if we didn’t address the fact that our customers who die before our estimation won’t die an equal distance from our estimation as those who die afterwards. Using the graph from the previous post, let’s run a simulation. Let’s imagine that 1,000 people have come to us for life insurance. They’ve been paying their premiums of £50 a year since their birth and are entitled to a pay-out of £4,200 upon their death. For our estimated age of death, we’ll use 81.

So of that 1,000, approximately…

**6 **would die under the age of 1.

**1 **would die between the ages of 1 and 4.

**1 **would die between the ages of 5 and 9.

**1** would die between the ages of 10 and 14.

**3 **would die between the ages of 15 and 19.

**3** would die between the ages of 20 and 24.

**3 **would die between the ages of 25 and 29.

**5 **would die between the ages of 30 and 34.

**6 **would die between the ages of 35 and 39.

**10 **would die between the ages of 40 and 44.

**14 **would die between the ages of 45 and 49.

**22 **would die between the ages of 50 and 54.

**29 **would die between the ages of 55 and 59.

**40** would die between the ages of 60 and 64.

**52 **would die between the ages of 65 and 69.

**67 **would die between the ages of 70 and 74.

**96 **would die between the ages of 75 and 79.

**156 **would die between the ages of 80 and 84.

**213 **would die between the ages of 85 and 89.

**179** would die between the ages of 90 and 94.

**78** would die between the ages of 95 and 100.

**16** would die from the age of 100 upwards.

To make things easier, let’s imagine that within the age group, each customer that died was in the middle of the age group (rounded up if necessary) and let’s put everything in a table to see what this means for our business.

Ages | Number of Deaths | Profit/Loss (per person, £) | Profit/Loss (total, £) |

0 | 6 | -4200 | -£25,200 |

1–4 | 1 | -4100 | -£4,100 |

5–9 | 1 | -3850 | -£3,850 |

10–14 | 1 | -3600 | -£3,600 |

15–19 | 3 | -3350 | -£10,050 |

20–24 | 3 | -3100 | -£9,300 |

25–29 | 3 | -2850 | -£8,550 |

30–34 | 5 | -2600 | -£13,000 |

35–39 | 6 | -2350 | -£14,100 |

40–44 | 10 | -2100 | -£21,000 |

45–49 | 14 | -1850 | -£25,900 |

50–54 | 22 | -1600 | -£35,200 |

55–59 | 29 | -1350 | -£39,150 |

60–64 | 40 | -1100 | -£44,000 |

65–69 | 52 | -850 | -£44,200 |

70–74 | 67 | -600 | -£40,200 |

75–79 | 96 | -350 | -£33,600 |

80–84 | 156 | -100 | -£15,600 |

85–89 | 213 | 150 | £31,950 |

90–94 | 179 | 400 | £71,600 |

95–99 | 78 | 650 | £50,700 |

100+ | 16 | 900 | £14,400 |

When we final add up all our losses and profits, we get…

**A loss of £221,950.00**

This is, of course, only simulation and so there are many flaws in its design. For example, people don’t take out life insurance policies from the moment they are born and so we can discount most individuals up to the age of around 30. In addition, the value of sterling is likely to change over the 100+ years our policy would eventually last for, meaning that what a customer pays us at the start of the policy may have a very different value to what he or she pays us at the end, or what we pay him or her. As well as this, people tend to drop out of life insurance policies for a huge host of reasons, and similarly, certain types of death such as suicide, do not result in a pay-out settlement. Overall then, our estimation isn’t perfect, but it does demonstrate a hole in our logic and accompanying business plan.

So how do we fix it? How do we improve our profits and make sure we stay in business? Well, there are a few ways…

__1: Change the split__

Perhaps most obviously, we could change our estimation, so that more than 50% of people pay off their premium before they receive their pay-out. Going back to our equation,

… by decreasing the age of our customers’ estimated deaths, we would increase the likelihood that they would pay off their policy before their death (meaning a profit for us), but at the cost of a higher annual payment or a lower pay-out sum. Given the deficit generated with our current estimate, I would say that this method is a good place to start.

__2: Invest__

I’m not an economics student or a business student, and so my knowledge on the various ways businesses make more money from some money is fairly limited. Nonetheless, I’ll try and very briefly cover a couple of “business” ways our life insurance company could stay afloat.

One way is to invest the money we receive in payments, in the hope that those investments will mature and eventually be worth more than we’ll ever need to pay back to the customer. That way, even if the customer dies before our estimation, we still make money. How exactly this works is something I am unsure about, but I have been told on good authority that such a method is employed by almost all life insurance companies, so it’s probably a good one.

__3: Delayed Cover__

One way of decreasing the number of exceedingly large pay-outs our life insurance company would have to make if any of our customers died prematurely, is to delay when the policy begins until a certain number of years have passed. This way, if a customer passes away at the very start of their policy, and would therefore cost us a lot of money, we wouldn’t be forced to pay-out. For example, let’s imagine a 30-year-old customer took out a life insurance policy with us, but we stipulated that the cover would only begin after 5 years of annual payments. Then, if the customer passed away in the first 5 years, where our losses would be the greatest, we aren’t forced to pay-out. This would also cover us in the event that a customer takes out a life insurance policy towards the end of his or her life, where his or her chances of dying in the next few years are higher. We can remove the biggest losses from premature death by limiting how premature a death can be, and therefore how much we can lose, before the cover starts.

__4: Estimate Better__

The final, stats-based method for improving our life insurance business is to better estimate when any customer is going to die, thus decreasing the number of individuals who die before their premium is paid off. If a customer has a family history of passing away at a young age, then it wouldn’t be appropriate to assume that he or she has the same chance as everyone else of making it to life expectancy age. So, we would lower our estimation, and decrease the likelihood that he or she would die before the equivalent to the pay-out sum had already been paid in annual payments.

This method is largely an extension of the logic we’ve employed during our start-up. The graph we previously looked at is the result of an amalgamation of lots of different women’s ages of death from all over Australia. It includes women with hereditary heart disease, smokers, women with a family history of breast cancer, avid joggers, fitness enthusiasts, and every type of person under the sun. In reality, these different groups of people all have very different chances of passing away at any given age.

By measuring these influences, we can better estimate any given individual’s life expectancy. For example, if we know that they are a smoker, then we can take some years off. If we know that they have no history of heart disease, mental illness, or any life-threatening illnesses, don’t smoke and go running every day, then chances are they’ll probably live past the population’s life expectancy. Using this information therefore, we can decrease the likelihood of an individual not living to their expected age by better estimating their age of death. In doing so, we decrease the chance that a customer will die before their estimated death, and therefore decrease the chance we will lose money. The better we can estimate a customer’s time of death, the less likely we are to lose money.

For example, let’s take Mrs Smith. Mrs Smith is aged 40, is a smoker, and has a family history of breast cancer. Now, according to the above graph, a woman in Australia has the life expectancy of around 81. Would it therefore be appropriate to say that Mrs Smith’s life expectancy is 81? Not really. Because, within the class of “all the women in the U.K.”, there are also smaller classes that better define the life expectancy of Mrs Smith. For example, the graph of women in the U.K. who smoke may be shifted more to the left, and the life expectancy according to that graph may be 65. So, is it appropriate to say that Mrs Smith’s life expectancy is 65? Well, it’s more appropriate, but we can still refine our guess further. We can use the information that Mrs Smith also has a family history of breast cancer, and so her life estimate is likely to be lower still. Using this method of taking lifestyle and health variables into consideration, we can better estimate when Mrs Smith (or any individual for that matter) is going to die.

Mrs Smith was, of course, just an example, but the logic can be applied to any individual to

best estimate their life expectancy. By better estimating their time of death, we can tailor their policy to increase the chance that he or she will pay off her premium before his or her time comes. And this is what many life insurance companies do. Among the questions you will be forced to fill in when applying for health insurance will be a myriad of health and lifestyle questions designed to reduce the breadth of your class to as small as possible. But can they estimate your life expectancy too well? We’ll examine this next time.