CP1 - Chapter 17 Modelling

[Darragh Kelly]

Hi,

I have a few question's in relation to chapter 17 of the notes.

Section 2.5 Dynamism of the model (page 9)

For example, how life assurance bonus rates could vary with fixed-interest yields…

Just trying to connect the bonus rates to the yields. Is it because it’s at the insurance companies discretion to issue these depending on company performance or how the bonds used to back/match the life assurance bonus rates perform?

Section 3.3 Rate for discounting cashflows (page 12)

So my understanding of this is as follows. If the company selling annuities and it backs them with fixed interest bonds paying coupons, a suitable rate for pricing/valuing the future cashflows of the annuities (so a fair price in today’s terms can be derived) would be the yield of the bond? Is this what it means when it says the return required by the company

For the second bullet point, the level of statistical risk attaching… so how I get my head around this is we might not assign any probability of a future cashflow/outgo, however we can allow of the risk/probability in the discount rate. If we are reserving/valuing/pricing having a lower discount rate means a higher present value so that’s conservative as we’d allow a higher provision value. Or if we were pricing a product we’d be selling at a higher price (and margins would be built in).

Finally, isn’t using a lower risk discount rate more conservative then a higher one? If you added a discount margin to the risk-free rate isn’t this less conservative?

Section 8.4 Parameter Error (page 20)

If the product is too sensitive to be increasing withdrawal rates then a reduction in surrender values should be considered. If the product is too sensitive to mortality, then the reinsurance programme could be revised. I’m not sure why the above steps would be taken, sorry just struggling with it. Alternatively, additional margins could be included in the pricing basis to reflect the increased risk. This means including additional margins in the assumptions or price itself?

Many thanks in advance,

Darragh

 

[James Nunn]

Hi Darragh

Some answers to your questions are below.

Section 2.5 query:

Yes - that's essentially correct. So these models allow for management actions (or decisions) and these actions need to change realistically in line with other changes (ie be what management would actually do in the same situation). Changes in fixed interest yields will impact on the surplus a model comes up with (due to the change in the market value of assets and the market liabilities not being the same necessarily). The model should allow for the fact that management will distribute more surplus in bonuses if there is more available to distribute (higher surplus), and vice versa, all else being equal.

Section 3.3 query:

Regarding your first paragraph, this section is specifically about assumptions to set premiums (pricing) to achieve a required (ie specified by the company) rate of return - the 'risk discount rate' - rather than anything else (such as reserving). The task is therefore effectively to solve an equation of value for the price/premium that sets the value of income (premiums in respect of the product you're pricing) equal the value of outgo (for the same product) using a model - assets don't come into this situation.

Regarding your second paragraph, I agree. The allowance for statistical risk on top of the requirement for the product/policy to provide the required risk discount rate return and is needed to ensure that this required return is met with a satisfactorily high probability in the face of uncertainty. As you say, this statistical risk can either be allowed for by increasing the specified risk discount rate or by allowing for probabilities in the cashflows valued.

On your third paragraph, for pricing as we've covered, you’re discounting the sum of income less outgo from a product/policy. So, you'll effectively be discounting the net cashflows for each year (income less outgo) back to time zero. Hopefully, overall, these net cashflows will be more positive than negative over time (otherwise why would you want to offer the product). That means the higher your risk discount rate, the lower the value you'll place on the value of those net cashflows ... and so the more prudent your valuation (in that you’re underestimating the value of net income).

Section 8.4 query:

If profits will be impacted a lot by a small change in either mortality or surrender experience (if mortality benefits or surrender values exceed the reserve held, which would be released on death or surrender thus offsetting what would be paid out, materially), then the risk of experience being worse than expected needs to be mitigated (reduced) - at least to some degree.

Decreasing surrender values will mean that the excess of the surrender value over the reserve held against the policy will decrease, decreasing the reduction on profit due to surrender. Reinsuring death benefits will mean that income from reinsurance will cover some of the loss on death (death benefit less reserve for policy) reducing the impact on profits due to deaths. Both of these options can therefore mitigate the risk of experience beings worse than expected.

Another option is to use stronger assumptions in the pricing basis (so setting higher premiums as a result) so that experience is less likely to be worse than 'expected' (ie worse than assumed in the pricing basis) and so that the risk discount rate (required return) is more likely to be met over time.

Hopefully this helps.

 

[Darragh Kelly]

Hi Darragh

Some answers to your questions are below.

Section 2.5 query:

Yes - that's essentially correct. So these models allow for management actions (or decisions) and these actions need to change realistically in line with other changes (ie be what management would actually do in the same situation). Changes in fixed interest yields will impact on the surplus a model comes up with (due to the change in the market value of assets and the market liabilities not being the same necessarily). The model should allow for the fact that management will distribute more surplus in bonuses if there is more available to distribute (higher surplus), and vice versa, all else being equal.

Section 3.3 query:

Regarding your first paragraph, this section is specifically about assumptions to set premiums (pricing) to achieve a required (ie specified by the company) rate of return - the 'risk discount rate' - rather than anything else (such as reserving). The task is therefore effectively to solve an equation of value for the price/premium that sets the value of income (premiums in respect of the product you're pricing) equal the value of outgo (for the same product) using a model - assets don't come into this situation.

Regarding your second paragraph, I agree. The allowance for statistical risk on top of the requirement for the product/policy to provide the required risk discount rate return and is needed to ensure that this required return is met with a satisfactorily high probability in the face of uncertainty. As you say, this statistical risk can either be allowed for by increasing the specified risk discount rate or by allowing for probabilities in the cashflows valued.

On your third paragraph, for pricing as we've covered, you’re discounting the sum of income less outgo from a product/policy. So, you'll effectively be discounting the net cashflows for each year (income less outgo) back to time zero. Hopefully, overall, these net cashflows will be more positive than negative over time (otherwise why would you want to offer the product). That means the higher your risk discount rate, the lower the value you'll place on the value of those net cashflows ... and so the more prudent your valuation (in that you’re underestimating the value of net income).

Section 8.4 query:

If profits will be impacted a lot by a small change in either mortality or surrender experience (if mortality benefits or surrender values exceed the reserve held, which would be released on death or surrender thus offsetting what would be paid out, materially), then the risk of experience being worse than expected needs to be mitigated (reduced) - at least to some degree.

Decreasing surrender values will mean that the excess of the surrender value over the reserve held against the policy will decrease, decreasing the reduction on profit due to surrender. Reinsuring death benefits will mean that income from reinsurance will cover some of the loss on death (death benefit less reserve for policy) reducing the impact on profits due to deaths. Both of these options can therefore mitigate the risk of experience beings worse than expected.

Another option is to use stronger assumptions in the pricing basis (so setting higher premiums as a result) so that experience is less likely to be worse than 'expected' (ie worse than assumed in the pricing basis) and so that the risk discount rate (required return) is more likely to be met over time.

Hopefully this helps.

Hi James,

Section 3.3 query:
First Paragraph - So basically as you said in this context the risk discount rate, is used for pricing here to solve for the equation of value setting income to outgo? It can be used for valuations / reserving also the same rate?

Third paragraph - I think get what you mean now from a pricing point of view - a higher risk discount rate means a lower net value of income. But what about if you were calculating the present value of benefit payouts. A higher risk discount rate would mean lower value of benefits so would it not be more conservative in this scenario to use a higher rate? So higher rate more conservative for net income, lower rate more conservative for liabilities?

The rest is very clear and understand now thank you for the clear explanations.

Thanks,

Darragh

 

[James Nunn]

Hi Darragh

Regarding the first paragraph, a risk discount rate ('RDR') is set by the insurer to ensure a certain level of return, and this is used in an equation of value to set premiums that will then provide that return (all else being equal).

The discount rates used in reserving are different to the RDR and can be derived using a few different methods - these will be covered in your Day 5 tutorial. Sometimes the reserving discount rates are based on the assets held and sometimes not. Please see section 1 of Chapter 32 for the different methods of setting discount rates if you'd prefer not to wait until your Day 5 tutorial.

Regarding the third paragraph, for pricing, you're valuing income less outgo. Both income and outgo are decreased by an increase in the RDR. However, for projects, the average duration of income is usually longer than that of the assets and you'd hope the value of income was greater than that of outgo too. This means a higher RDR would be expected to decrease the value of income by more than the reduction in the value of outgo, and so reduce the estimate of profit, providing a more conservative estimate of this. (If there is no profit at the required RDR, income needs to be increased - eg by increase premium - or the required rate of return (RDR) will not be met.)

If you are valuing liabilities in isolation for reserving purposes (ie assuming assets are unaffected by changes in the discount rate used) then, again, the value of outgo required in respect of the liabilities falls, but the value of the assets is unchanged so, yes, the valuation becomes less conservative - the liability value falls relative to the asset value and surplus is then more likely to be overstated.

Hopefully this helps.

 

[Darragh Kelly]

Hi James,

Apololgies on delayed response. That's all clear now thanks for explaining that in detail - very clear on difference between the rates and their purpose.

Thanks,

Darragh