# Best Estimate basis - Mean or median

Discussion in 'CP1' started by Logarithm n Blues, Jan 19, 2020.

1. ### Logarithm n BluesActive Member

Hi,

In some materials I have seen the best estimate basis described as having an equal probability of over or under-estimating the value of the liabilities. This suggests that given a distribution of liability values, we would take the median value.
In work context I feel like I have used a mean value for the best estimate (I could be wrong!) I also feel like I remember reading that the expectation (ie. mean) of the distribution is appropriate for best estimate.

In most circumstances these will be essentially the same as we usually assume a normal distribution or at least a not-particularly-skew distribution. But is one technically correct? or do we not recognise the distinction?

2. There is a distinction to be made. The best estimate represents an expectation (ie mean). The distribution that may be used to model a risk will vary.

It may not be unreasonable to assume that the residuals (difference between the model and actual observations) exhibit normality; but I’d question the appropriateness of assuming normality as a default.

For example, is it appropriate to model mortality or stock prices using a normal distribution...

3. ### Lindsay SmithermanActEd TutorStaff Member

Hi - yes I agree there is a distinction.

Simplistically, if we are trying to set an assumption for something which broadly has a symmetric outcome range, then thinking about it in the way you mentioned can be helpful: we need to set the assumption at the level where we believe we have about the same chance of having over-stated it as of having under-stated it. So effectively we are thinking about the median - which should also (for a symmetric-ish outcome) be pretty much the same as the mean.

But of course if the outcome isn't symmetric, they aren't going to be the same thing. A good example would be setting a best estimate liability for the cost of a financial guarantee, such as a minimum guaranteed amount on a unit-linked life insurance policy. If this were modelled stochastically, we would determine the cost under each simulation by taking the higher of {the guaranteed amount minus the unit fund} and zero. Unless the guarantee is looking rather generous, over a large number of simulations the median outcome would likely be zero. However, in order to capture the time value (allowing for the probability that it could bite, even if it currently isn't expected to), we would need to take the mean value across all simulations. So in this case the best estimate liability would have to be based on a mean rather than median outcome.

So yes, the best estimate should be based on a mean - but in many cases setting an assumption by thinking about the median will be close enough the same thing.

4. ### Logarithm n BluesActive Member

Thanks both.
I really appreciate the guarantee example especially.

To confirm, for example the online classroom video for CP1 'Setting the basis' defines the best estimate basis as having 'Equal probability of overstating or understating the value of the assets and liabilities'.
It seems like we're all agreed that this isn't technically correct (But will of course be close to correct in a lot of situations and can be considered broadly correct)

(To be clear, I'm absolutely not trying to criticise the material - just make sure my personal understanding is on firm footing)

5. ### Lindsay SmithermanActEd TutorStaff Member

Yes - this sounds like a fair summary to me The Core Reading quoted here has simplified the situation - as it has in a few other places; you will tend to find the added (unstated) complexities being brought out more in the specialist level subjects.