Price Optimisation : Myth vs Fact (part 2)

Thanks for clicking through to read part 2 of my attempt to de-myth-tify price optimisation in insurance. The first part dealt with 5 common statements, my view on whether it was a myth or a fact, and an explanation of why. And hopefully something interesting about price optimisation was explained along the way! More of the same today, focusing on the next 5 statements.

If you haven't seen part 1 yet then please visit here first:

Part 2

1. I can't optimise if I send my prices to a broker who can change them.
2. Optimisation can work well even in a rapidly changing marketplace.
3. If I have larger overheads then I need to set a different optimal price.
4. Optimisation can improve your prices across your portfolio.
5. It is not possible to optimise in a post GIPP world.

Remember to have a quick think and a guess yourself first!

Let's go!

1 - I can't optimise if I send my prices to a broker who can change them.

MYTH!

Optimisation works just as well whether you are an insurer selling directly to your customers, or one that is providing a net rate to a broker who is allowed to adjust their prices as well. There are some areas where you are constrained a little, but other areas where you are freed up.

Let's look at what optimisation is again:

1. Optimisation is about adjusting prices where you are already competitive to maximise profit (contribution) over your sales.
2. This is the same as old school customer segmented pricing, except on a more granular level where we use models rather than just observed KPIs.
3. Both of these fall under the remit of Retail Pricing, which is about working out how much profit you can add on top of your technical price.
4. Your Risk Premium calculation should be trying to estimate Loss Ratio at 100%, so you need to add premium on top to make a profit.

If you are an insurer writing business through a broker all of those same 4 steps apply. First you calculate your expected risk, and then you add your costs and profit on top. And you can still optimise your profit by asking for more in some places and less in others.

Where the difficulties lie is in that you don't have full control over your profile of sales. Brokers can identify areas where they can make profitable sales and then seek to adjust prices above and beyond yours. And these customers are not necessarily the ones you wanted - often they are the opposite!

But with every threat comes an opportunity. If the brokers are able to make a lot of money from these customers then they are willing to pay more for them. That's where optimisation comes in, because you will be able to carry a higher net rate to cover the risk, but still make sales when the broker sub-nets the commission.

And the benefit works both ways. Brokers have a big advantage that their cost base is a fixed amount (mostly) because they are buying in the risk at a set cost (the net premium) without having to worry about building their own risk models and then waiting 18 months in the hope they predicted inflation correctly (a difficult job these days!). So optimisation allows them to compete in a price-driven market against other brokers who likely have the same net premium winning their panel.

2 - Optimisation can work well even in a rapidly changing marketplace.

FACT!

In Part 1 I spoke about the need to change how you might be optimising by moving away from large price changes that sat on top of your technical price to smaller but faster changes that built upon your previous round of optimisation. This means that you can react to changes in the market much faster because you are taking lots of smaller steps rather than the occasional big one.

The benefit of more frequent but smaller steps that are building on the previous set of rates is that it is very adaptable to change. We often talk about the optimal price as being a constant fixed amount, but in reality it is going to move around because everyone else is also going to be changing their prices.

This is one of the biggest mindset differences between Risk and Retail pricing. Anyone who has built a Risk model knows how important time consistency tests are to ensure forward predictive power. But these tests can't work for Retail Pricing because the market is constantly changing. The only thing that is constant is change! So we adapt. We take the first philosophical point I made in Part 1 that optimisation is an engineering problem not a mathematical one.

The speed at which you can do this is constrained by the volume of sales that you make. Every time you deploy a new set of rates you effectively invalidate (at least partially) your previous models. There are mechanisms to measure this, but the important thing is that to run the next round of optimisation you will need to refresh your models with the new data, and to do that requires enough data to build the models.

But you don't need to just wait in the interim. This is where a strong Trading Team comes into play. They are able to look at the results and make less granular changes between optimisation runs. That keeps your performance strong, and then when you run your next round of optimisation all of those price changes can be subsumed into the next round. And simple tools like Chi-Squared* tests can help decide not only if a change has worked, but how long you will need to wait to get enough data to make that judgement call.

* see our Chi-squared template for a simple tool to judge whether your A/B deployment has worked correctly.

3 - If I have larger overheads then I need to set a different optimal price.

MYTH!

This one takes a bit of getting your head around. I'm going to prove it in two ways, so hold your hats fellow maths enthusiasts because I'm going to take you back to your A-levels.

So here's the scenario. You have 2 companies, otherwise identical. Same team, same models, same customers, same pricing, everything. Both have around half a million customers per year, at an average profit of £40 per customer, and are embarking on optimisation. The only difference is that one is in a small inexpensive office, and the other has rented 4 floors of the Gherkin. Company 1 has an expense base that is £3m per year less than Company 2.

If the optimal price for Company 1 is £400 for a customer, what is the optimal price for that same customer for Company 2?

It's exactly the same.

Bit weird, right? Intuitively you'd think that if Company 2 has to cover £3m more of costs then the price needs to reflect that. And at 0.5m customers that's an extra £6 per customer that needs to be covered. But it doesn't work like that. Here's why.

When you are optimising you want to know your total profit for the year. So although it's not often expressed like this (we often use conversion rates when really we should be looking at number of customers) our conversion models are doing exactly that. It is saying you can get 0.5m sales for a total of £20m "profit". Except it's not quite profit, it's actually the sum of the margins of all of those customers. And margin is the Premium charged + other income - all costs.

If I put my prices up then I will make fewer sales, but at a higher premium. So my margin will be higher. Now my total income may fall but that's ok because my costs have also fallen. I no longer need to pay the claims these customers have, or service their calls, or pay for that 4th floor of the Gherkin... oh wait. No actually that cost hasn't fallen. Regardless of making 1 sale or 500,000 sales that cost is fixed. And that means that the cost is spread over all the sales that I make. But if I get my customer prediction wrong then I also get this expense ratio wrong, which means I am not pricing optimally. How do I fix that?

Simple - ignore it.

The margin that you make per customer is not affected by your fixed expenses. Selling 0.5m policies at £40 margin each is the optimal price point whether your fixed costs are £10m or £1. Any deviation will result in a lower sum of those margins. Your fixed costs have nothing to do with the policies that you sell. That's why we don't call it profit, but we give it a special name - contribution. And even that is a contraction, the full name is:

Contribution to Fixed Expenses.

In reality there's no such thing as a fully fixed expense. All expenses can change. But as a rule of thumb if your expense isn't going to change over the course of 1 year based on an expected maximum deviation in customer numbers (up or down) then it is a Fixed Expense.

The maths bit:

So I promised my fellow maths nerds some calculus, and here it is. How do you calculate maximum contribution? Well it's just the maximum of our contribution curve. Here's that graphic again that we are trying to find the maximum point of:

To describe the exact shape of this parabola we need to work out how Volume and Margin are multiplied together. We can describe both of these as "x", based on the value of the x-axis, as both are a function of the price charged. We need a term for exactly how they interact (calculated from our conversion and elasticity models) and we'll call that "a". We also need to account for our Variable Expenses. These will also scale with the Volume, and therefore "x", and the relationship we'll call "b". Finally we need our Fixed Expenses, which are a set amount not dependent on Volume, and we'll call that "c".

So "a" will interact with Volume and Margin, which are both "x", to give ax2

And "b" will interact with just Volume to give us bx

And "c" sits by itself to give us just c        

And there you have it - your Fixed Expenses are 'c' and that drops off when you differentiate. Or integrate. Wait, no differentiate. I think. Why can I never remember which way around they are these days?

4 - Optimisation can improve your prices across your portfolio.

MYTH!

So you should have got this one based on previous comments. Optimisation is only good for quotes that are competitive - where a change in the premium can make a credible difference to the chance of making a sale. Premiums outside of this window can go through an optimisation process, but you are not going to get any improvement in the results.

Why is this?

To illustrate let's say we look at an insurance company, or broker, that is moderately competitive on price comparison websites (PCWs) and see that they have a conversion rate of around 1% of customers. So when price, cover level ticks, excess, and brand strength have all been weighed up, about 1 in 100 customers will decide to purchase with them. But we also know that this distribution channel tends to be highly commoditised (products are mostly the same), and most customers purchase on price over brand. This would probably give us the below scenario:

If you are in that middle band then your price is close enough to the market rate that small price changes can have a big impact on your chance to sell. You could expect around 5% of your quotes to be in this band, of which 1 in 5 of them would result in a sale. This is the area that optimisation can have a big impact on, as a change in price results in a change in conversion rate so you can trade some customers for others.

The band to the left is where you are much cheaper than the market rate. Elasticity will be low because even a decent price increase would still leave you cheapest. Optimisation can have an effect here because it will try to push prices up, but the volume of quotes in this band is often small so the effect is negligible.

The band to the right is where you are not close to the market rate. Optimisation will have no affect here for 2 reasons. Firstly you are not selling no matter what price change happens, so the real world impact is zero. Secondly, from a modelling perspective, elasticities are so low that optimisation will generally want to increase prices further because 0.00001% conversion rate can't get any lower.

And it's this final band that is often overlooked. Companies fear selling too much because what they are thinking about is the quotes in that middle band moving into the left band and being under-priced. But the majority of your quotes are going to be nowhere near cheap enough to sell; and they can't all be bad because these are the sales other companies are making, and not all of them are bad. It's not like all the biggest insurers are performing worse than the more selective ones; book size and performance are not correlated.

This is the area that optimisation cannot help with. And as powerful as optimisation is, and as beneficial as it can be to getting the most out of where your Risk Premium is competitive, it is not a silver bullet. Most of your prices optimisation will do absolutely nothing for.

5 - It is not possible to optimise in a post GIPP world.

MYTH!

So this statement is really just the summary of all the points we have talked about so far. Hopefully you'll have a strong enough understanding of optimisation to realise it's capabilities. It is a powerful tool, but not a silver bullet and not one that can (or is looking to) replace good strong Risk Pricing. It also has very little to do with why GIPP was brought in, because it wasn't the problem that was causing the heavy subsidisation followed by loyalty-punishing increases.

I see a lot of companies doing optimisation really well, and seeing the benefits coming through from their investment in it. But I also see a lot of companies thinking that it is not the right thing for them, and whilst I respect and understand this position if it is a considered reaction to a mechanism that does require time and effort, I also think it is a shame when the same decision comes from a misunderstanding.

It is just as possible to optimise now as it ever was, because optimisation is just old school customer segmented trading, but at a deep granular level.

If you want to have a conversation with us about optimisation, or any aspect of insurance pricing, then please contact myself or Sherdin Omar - even if it is just to say hello and share some experiences.