Risk Discount Rates

[td290]

On several occasions, the core reading mentions the practice of using a higher discount rate to value risky liabilities. I understand why this approach is sometimes applied to assets and I also understand the concept of asset/liability matching. But in situations where there is no portfolio of assets that will replicate the payments to the liabilities under all scenarios, as is frequently the case with insurance liabilities, surely the approach is inappropriate? Indeed it seems to yield various absurd consequences, e.g. an insurance company would price a policy at below the expected NPV (based on risk free interest rates) of its associated liabilities on the basis that the liabilities are risky and therefore a higher discount rate should be used.

Another obvious instance would be the core reading example in chapter 36 (Valuing Liabilities 2). The model solution to part i) states that “It may be appropriate to use a discount rate that is higher than the real yield on the bond index. This is to reflect the uncertainties associated with the liabilities, e.g. uncertainty over the duration of future employment.” But this would lead to the lump sum award being lower, whereas surely the claimant should be paid a premium for bearing this risk?

 

[Katherine Young]

Hi td290,

a) A company could calculate the total value of its future liability cashflows, and hold an amount equal to this, as its provisions.
b) But this would be unnecessarily penal, since the company will be earning investment returns on these provisions.
c) So it is allowed to discount the value of its liabilities. The question then reduces to which discount rate to choose.

1) It could use the market rate on matching bonds (matching nature, term, etc). This would generally be a prudent approach, since the yield on bonds would often be lower than the returns on other investments. On the other hand it might not be very realistic, ie if the company holds assets other than bonds.

2) So it could use a discount rate that allows for returns on other assets; equities say. This might be more realistic, if it is indeed holding these assets, but wouldn't be so prudent.

If we apply this to your queries below:

an insurance company would price a policy at below the expected NPV

Not necessarily. If it uses a discount rate that exactly matches the return it would achieve on the assets used to match its liabilities, then the price of a policy would exactly equal the PV of the liability outgo.

surely the claimant should be paid a premium for bearing [unemployment] risk

No. The claimant would have borne his employment risk (eg risk of redundancy) whether or not he had been injured at work. Therefore it is not up to the insurer to compensate for that. Indeed, the lump sum benefit should actually be lower, since the insurer's calculations would be based on 15 years' lost earnings, when in reality the individual may have lost his job only 1 year later.

(Note that an allowance for the uncertainty in liabilities can be made either by adjusting the discount rate, or by using expected future cashflows.)

Kind regards,

Katherine.

 

[td290]

Hi Katherine,

Thanks for your response. I’ve been giving this some thought. I hadn’t realised that it was a case of using expected cashflows or adjusting the discount rate. None of this seems to allow for what is often referred to under Solvency II as a “risk margin”, i.e. a margin above the expected NPV of the liabilities (at risk-free rates); this is what I was referring to when I suggested the claimant who was injured at work should be paid a risk premium, i.e. a premium above the expected NPV. (In this case the risk in question is not the risk of the claimant being made redundant, but rather the risk that the lump sum awarded to him falls short of the lost earnings in the case that he isn't made redundant. Ultimately, he isn't being given a choice about whether to accept a lump sum in lieu of his future earnings; assuming he was happy with the status quo, i.e. he got what he earned, he is now being forced to bear a risk that he wasn't previously.) The incorporation of the risk premium might be achieved by lowering the discount rate (from the risk-free rates) or by adjusting the expected cashflows upwards.

The general risk margin/risk premium concept turns up frequently when talking about assets, e.g. an equity risk premium, credit risk premium, etc. Why not when talking about the fair value of liabilities? Moreover the “two wrongs make a right” philosophy behind assuming the claimant carries on working for 15 years and then increasing the discount rate to compensate seems rather old school (not to mention being of dubious compliance with TASs). The question doesn’t specify that this is how the calculation is being done so I’m surprised we’re expected to make that assumption automatically.

Thanks for your help.

 

[mugono]

Hi

I think it's really good that you're trying to link things the way you are doing

Four comments I would make:

1. The ca1 exam is not country specific so mention of the TAS wouldn't score.

2. CA1 is a 'generalist' subject so be careful of the level of detail you go into

3. Regarding your point about the risk margin ( in a solvency 2 world!), the margin is needed to ensure non-hedge able risks are market consistent. It's not a margin intended to compensate the policyholder but more to compensate a third party who might take on the risk of meeting policyholder benefits. Recall that with best estimate liabilities there's a 50-50 chance of the reserves held being too big or too small.

Solvency 2 is only mentioned in a chapter or two, much of the course isn't!

4. In determining the lump sum to pay it may be worth thinking more widely and not just technically about the choice of discount rate (which is a guess anyway ) For e.g. What has the company historically paid, what benefits are paid by competitors, what did the market literature say, what about any key features documents etc.

These would be considered when the product would have been PRICED, how it is then subsequently reserved for is not the policyholder's problem (it's between the company and their regulator)

At the end of the day, if the benefits are 'too low' (e.g. Because the discount rate is too high) then the policy simply wouldn't sell!

Any comments, queries welcome

 

[td290]

Thanks mugono. I wasn't sure whether I was allowed to reproduce the question from the core reading here but I see others doing similar things so I'm going to risk it!

"An expert witness is advising on a suitable discount rate to calculate the value of a lump sum award to a 50-year old individual in compensation for his claim for loss of earnings following an injury at work.

The amount of the award is based on the annual earnings lost and the number of years out of work and makes use of a discount rate in order to create a present value.

In previous cases the discount rate has been the real yield available on an index of long-dated index-linked government securities.

i) Give reasons why the real yield on a long-dated index-linked government securities index could be an inappropriate discount rate at this time.

ii) It has been suggested that a more reasonable discount rate would be the expected return above inflation on a portfolio of mixed assets. List the type of assets that a typical individual investor would hold in such a portfolio and the factors that would be considered in determining an appropriate discount rate."

So we're not actually talking about policyholder benefits, we're talking about a negligent party having to commute a risky liability, equal to the lost earnings. My argument is that since the value of the liability is unknown and contingent on whether the claimant is able to stay in work until normal retirement age, this is a non-hedgeable risk and so should be commuted at a value above the expected NPV.

Thanks for your help.

(By the way, I appreciate S2 and TAS I are not universal, but they say what they say for a reason. Surely those reasons are universal?! Risk margins are not unique to S2. Versions of them exist in SST and IFRS proposals.)

 

[mugono]

Hi

My gut instinct is that it may no longer be appropriate if it was felt to represent inequity between the insurer and/or those remaining (for e.g. It created a liquidity risk for the insurer or reduced benefit security for remaining policyholders...).

The higher the lump sum paid out the larger the amount of assets will need to be sold to meet it.

Historically, maybe salaries were linked to price inflation, which may no longer be the case, maybe the company in question doesn't increase salaries for those who become injured or maybe the company has the intention to link salaries to an earnings or other investment in the future??

If we take a replicating portfolio approach to valuing liabilities then as the earnings/investment index may be expected to earn above IL government securities then this could justify increasing the discount rate.

It may also be worth drawing on the "long-dated" nature of the IL bond. Given the life is aged 50, 15 years would be the longest term to retirement (assuming a NRA of 65) On average it could be argued that the most likely duration may be less than 15 years, maybe a shorter dated IL bond would be more suitable?

These are just ideas - the examiners may have had some other wonderful ideas in mind

Depending on the marks available the question is admittedly quite narrow and hence tricky.

Any comments/queries welcome