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Hi guys

First up a brief intro - I work for Churchill Insurance company in the UK in the marketing team. I do customer insight research and a spot of analysis. I'm building a model after having been to the Vensim intensive course a few weeks ago.

I'm trying to model the insurance market in relation to policy holders in our motor business. The principle I'm going on here is start off small and make sure it works before you expand the model!

I've built the core of the model (see attachment)

The bit I'm stuck on is building in an "attrition" rate which takes out a given percentage of policy holders to represent how people cancel their policies mid term. Essentially we lose 5% give or take of our book before their 12 month policy is up.

The second bit is concerned with the "proportion of renewals" variable. It seems to work fine although the model units check doesn't seem to like it.

Any help would be much appreciated - I'm sure this is an easy problem to solve for the Vensim veterans on the forum!

Also, any general comments on the model are gratefully received

Thanks in advance (and Happy Christmas)

You first need to decide how much emphasis you want to put on detail in thinking about the problem - this is not always an easy decision. If you want to start simple and not do detail (which I would recommend) you don't actually need a policy end stock. Instead there is just a stock of policy holders. The inflows to this are new business and renewals, as you have, and the outflows are cancellations and "normal terminations" (there is probably a better term).

normal terminations = policies/policy length
renewals = normal terminations * renwal fraction
cancellations = polcies * fractional cancellation rate

if you think of things this way the whold model will be much easier to conceptualize.

The down side of this is that we are using policies/policy length as an outflow and that suggests there is an exponential distribution of policy lengths where the model constant is the average. Clearly this is not the case, so the question becomes if the approximation close enough to be suitable to your needs. For pass 1 I would say yes - then you need to decide.

Thanks Bob- I'll redesign the model with this in mind.

One thing is the "exponential distribution of policy lengths" - I'm not sure what you mean here. An insurance policy lasts for 12 months so I suppose the thinking with the current model was trying to simulate a delay or policy holder "progressing" through the 12 month cycle.

I'd like to make the model scalable so when I get the hang of this more; I can bolt on additional complexity and variables.

Thanks again

[Edited on 19-12-2006 by NeilA]

This is what I've come up with (see attached). Can't get my head around the errors on the units check though. Thanks

Hi Neil,

Fixed some of your unit errors. See if that's ok.

1. attrition - you had given it as policies/month. Since this is a fraction - it should be fraction/month or dmnl/month

2. Inputs to number of nb policies- I presume variables like online,BRTV etc are marketing inputs that generate new biz policies. All these variables also need to have policies/month as units. Think you had given units as policies.

3. Proportion of renewals - fraction as unit

Also, while I do not know enough of your model, in your current formulation a proportion of the lapsers (which is a rate), is instantaneously entering the stock of policy holders. This is because you have formulated renewals = proportion * lapsers.

Think the problem with this formulation is that in reality a proportion of lapsers instantaneously enter the stock of holders again - which means they are not lapsers at all.

Maybe, people become lapsers, and after a certain proportion of time renew their policies.

In that case, you might want to connect the lapsers rate to a stock called lapsers. And assuming an average lapser returning time, get lapsers from that stock into the renewal rate

Regards
Malli

Thanks so much malli; I'll have a look later today.

Just a couple of comments - your formulation for renewals does make sense. What you have labeled "lapsers" are simply people whose policies are expiring and some fraction of those stay insured which means they do instantly get back into the policy pool. You might want to use a term different from "lapser" such as "policies terminating normally"

Second is to reply to the concept of exponential distributions. In reality it is true that a policy lasts 12 months or some other period. However, to model explicitly when there is attrition requires extra variables that really clutter things up. For many problems doing things the simple way and the more precise way give the same answers. In that case simplicity is better. For you, even if you eventually go for more detail (using for example DELAY CONVEYOR) starting this way is probably the way to go.

Hi guys and happy new year. I'm back from the Christmas break now and have been re-familiarising myself with my model.

Having looked at it and read the replies above I can respond to comments and amendments made.

malli: I can't download the amended model you did for me. It won't open in Vensim for some reason. I'm using DSS 5.6a - Is this somehow not compatible with the version you amended the model in? In any case, as you kindly listed out all the changes you did, I did my best to replicate them in the attached "policy holders6".

Bob: I response to your first paragraph, when using the Synthesim function which I use to see if my model makes sense, the behaviour isn't what I would expect. FOr the purposes of this model, all those which reach the end of their policy either lapse (leave Churchill for a competitor) or renew. So the relationship between lapsers and renewals is inverse; if renewals go up, laspers must decrease if the model is working in proportions rather than absolute numbers. When using Synthesim, if I increase the "current retention" the renewals and lapsers increase. I guess this is because if more customers are retained, more will lapse. However, what I envisaged was something which showed the inverse relationship which I eluded to above. Could I introduuce some kind of auxillary which dictates the split between lapers and renewals?

Also, do you think this additional complexity may require building in some kind of delay function as you suggested for when things get more complex?

As always, many thanks

Hi Niel,

This is just a terminology problem. In your model model you use a rate called "lapsers" that rate should be labeled "all policies terminating" The equation for "renewals" is

renewals = all policies terminating * proportion of renewals

and the equation for policies lapsing is

policies lapsing = all policies terminating - renewals

(or you can use *(1-proportion...))

Cheers Bob. Synthesim now seems to make more sense when I flex the "current retention". I do, however, get this error on doing a model check: "-policies lapsing- is not used in the model". It still works though!

Originally posted by NeilA
Cheers Bob. Synthesim now seems to make more sense when I flex the "current retention". I do, however, get this error on doing a model check: "-policies lapsing- is not used in the model". It still works though!

It's not an error but a warning that "policies lapsing" is not used in any other equations. It's a useful tool for identifying loose ends in a model. If policies lapsing is really not to influence anything else and you wish to remove the warning, check the "supplemental" box in the equation editor for the variable.

Splendid, every day's a school day! Thanks Lee.

OK, I've added another bit onto the model introducing the various means by which new business policies are generated. The basic theory behind this part is that things like BRTV (brand TV), DRTV (direct response TV), doordrops, DM etc are all channels through which new business can be generated. Any given media can either generate new business (NB), increase our brand awareness or do both. For instance, putting our name in yellow pages may generate policies but won't enhance our brand's standing. Likewise, advertising on the TV will enhance our brand (hopefully) and drive business.

TV affects our brand measures. The measures included on this model are "TV Cut Through" (proven recall of specific TV executions) and what I've called "brand equity" which for the purposes of this model is a measure of how the general publics "considers" us when they are shopping for insurance. TV cut-through on the model is affected by firstly how good the ads are (creativeness) and the weight of advertising (weight).

The next thing I'd like to introduce is some kind of delay function. For instance, going on the TV with a lot of weight will result in new policies within a short space of time. However, in order to build and increase our fundamental brand equity as a credible and worthy insurer takes a lot more time. This is something which I currently do not know how to build into the model (or even know if the current model as it is compatible with using delay functions)

[Edited on 5-1-2007 by NeilA]

Hi

The utility of modelling is generally not to give precise results but to help better understand the problem at hand.
This understanding comes gradually and it is to my opinion better to build very simple models first and use them
extensively to get a feel of the problem.
I think it is much more difficult to analyse properly a model and the results it can give than to build it.
It is then easier to analyze a simple model and it is very easy to fall into the trap of developing the model without analyzing fully the intermediate models and finish with a model that is very difficult to analyze and then to get some insights from it.
So before going further I think you might try to study first what your present model can give you even if it is very far from reality and what you feel it would ultimately look like.
Further on, this first analyze will help you choose a better next step.
Regards.
JJ

Hi Neil,

You can probably find a few things written up on advertising effectiveness and brand awareness. It is worth pointing out though, that is someone actually has gotten this right they are unlikely to talk about it.

In general, however, the idea is simple. One of the most common formualtions is

brand awareness = INTEG(bulding awareness - awareness decay) ~ Thought/Day
awareness decay = brand awareness/decay time ~ Thought/Day/Year
building awareness = advertising spending * advertising effectiveness ~ Though/Day/Year

note that the units for advertising effectivness wil be Thought/Day/$ (or pound) - that is if you spend 1$ on advertising how many thoughts per day are generated (over all people seeing the ad).

Note the units of measure Thought/Day, while somewhat abstract, convey that is going on with brand awareness.

I hope that is helpful - you are actually getting into interesting and difficult territory.

Thanks again guys. I'll mull it over and see if I can incorporate it into the model. The idea of decay appeals as it makes the model a lot more realistic as you have to continually be advertising to compete for people's mental "consideration space"; especially in such a competitive and crowded market as car insurance.

Bob: The problem I'm struggling to get my head around is that of transforming "consideration" or a mental intention to buy into sales per month of whatever. The two seem incompatible. I'm also struggling with my complete lack of formal training in systems dynamics! Still, as you say it is interesting. Thanks for your formulation too.

Would it be possible to use the model on page 58 of this document? :

http://www.agsm.edu.au/~bobm/teaching/SSS/VENPLE.PDF

I've put the following into a mini model:

"brand awareness = INTEG(bulding awareness - awareness decay) ~ Thought/Day
awareness decay = brand awareness/decay time ~ Thought/Day/Year
building awareness = advertising spending * advertising effectiveness ~ Though/Day/Year"

I've attached the model but it keep throwing up an error which I don't fully understand. It also didn't like the INTEG.

Forum froze on me, let's try again....

the forumlation I gave you is the same as the one in the old PLE User's Guide. Note that Brand Awareness is a level - I left the initial condition off of the brand awareness function

brand awareness = INTEG(bulding awareness - awareness decay,initial brand awareness)

Hope that helps.

Cheers Bob,

I've added the little "brand bolt on" bit onto my main model and applied it to one of the many media's which contributes to the brand effectiveness. The model "IS OK" according to Vensim which was frankly a surprise to me! There are loads of unit errors which I haven't even attempted to look at yet- most of them probably apply to the misuse of days and months etc.

What do you make of all the stuff in red? It's fried my brain a little.

Thanks again

I've rejigged version 9 and created version 11...

Hi Neil,

Without a clear understanding of your purpose in building this model it is hard to really comment on it. For a model with only 2 level variables it has an incredible amount of detail. If you are using this as a thinking tool to just map out the different ways you might approach marketing that may be fairly effective, but it is not really taking a feedback perspective. For example things like happy customers bringing in new customers, or poor sales causing pressure on underwriters causing poor financial performance are just not there.

Also, there is structure to build brand awareness in your model, but that does seem to impact anything else.

If you look at the system dynamics bibliography at http://www.systemdynamics.org you will find a fair bit written up on Hanover insurance that might be useful. It might also be worth studying the molecules available from http://www.vensim.com as these do tough on a number of issues you are concerned with.

Thanks very much Bob. There are laods of other things I want to build into it, because as you say there aren't any feedback loops at the moment. I'll check out those links.