Chapter 36: Capital requirements

[JL24]

Hello there, on page 4 of the course notes, the second paragraph below the diagram states:
"The additional risk margin is intended to represent an estimate of the 'fair value' of the non-market risk within the best estimate liabilities, and so could be considered to be part of the 'best estimate' (or, in the case of Solvency II, 'market-consistent') provisions rather than as an additional capital requirement or prudential margin."

1. Why do the non-market risks within the best estimate liabilities need to be adjusted with an additional risk margin to make it the 'fair value', and why do the market risks not require this additional margin?

2. From what I understand from the above,
Technical provisions = Best estimate liabilities (i.e. present value of expected future liabilities) + an additional risk margin

Is the best estimate of liabilities found by discounting at either the yield of a portfolio of assets replicating the liabilities or the actual assets held, just like the methods stated in Chapter 32, Section 2 (the Fair Value section)?

3. Are 'technical provisions' and 'provisions' the same?

Thank you!

 

[Lindsay Smitherman]

Hi - I'm going to answer your questions slightly out of order, if that's OK.

There are various terms used in different jurisdictions for what is basically 'the value of liabilities' in an insurance company, including 'provisions' and 'reserves'. The phrase specifically used under Solvency II is 'technical provisions'.

These are calculated on a market-consistent basis, which is equivalent to a 'fair value' assessment - as described in the course. In order to determine the market-consistent / fair value of liabilities, we would need to determine what a deep and liquid market would be prepared to trade those liabilities (and their inherent risks) at.

Under Solvency II, the market risks are dealt with either:

• by finding a (perfect) replicating portfolio of assets (eg value of unit fund as the unit reserve for unit-linked business, derivatives for some embedded guarantees/options) - then, where this is possible, value of liabilities = value of replicating assets
• by using a risk-neutral market-consistent basis - ie all assets are expected to earn the risk-free rate and so discounting is done at risk-free rates.

However, there isn't a sufficiently deep and liquid market in the non-market risks (eg expenses, persistency, mortality) to be able to observe the rates at which the market would trade those risks. So we start from best estimate assumptions for those risks (in the basic 'best estimate liability'). However, we can reasonably assume that the market would not trade these liability risks at best estimate (50% of the time, this would not be enough): it would want some compensation for the risk that best estimate is insufficient. The risk margin is added to reflect that. This only has to relate to the non-market risks, since the market risk is already taken into account through using the market-consistent approaches bullet pointed above. [As mentioned in the course, alternatively a risk margin could be loaded into each of the best estimate non-market assumptions, to give fair value / market-consistent value of liabilities - but this isn't how it is prescribed for Solvency II.]

Hence:
Solvency II technical provisions = Market-consistent value of liabilities = 'Best estimate liabilities' (using risk-free rates for discounting and best estimate assumptions for non-market assumptions) + Risk margin (for non-market assumptions only)

What the paragraph that you refer to is basically saying is that the 'additional risk margin' is not part of 'required capital', it is part of 'provisions' - and it is one component of what is needed to make those provisions 'fair value'.

Don't worry if this all feels a bit technical. We are definitely encroaching into Specialist area here, and you will discover more about this in those later subjects if you work in one of the insurance practice areas.

Hope that helps clear this up for now though.

 

[JL24]

Hi Lindsay, thank you for your explanation! If you don't mind, I have some follow-up questions:

1. Does the treatment for market / non-market risks here directly relate to the allowance for financial / non-financial risk as mentioned in Chapter 32, Section 5.2? However, I am slightly confused as the section in Chapter 32 distinguishes between financial / non-financial risk, rather than market / non-market risks. From what I understand, market risks are financial risks, but there are also non-market risks that are considered financial risks (such as persistency, which is a business risk and hence a financial risk); hence the two sections of the notes don't seem to be entirely comparable.

2. In your second bullet point on dealing with market risks, is this referring to Chapter 32, Section 2.6?
- How does using risk-free rates account for market risks? Is it because we are not recognising the risk premium in our discount rate since this risk premium relates to the market risk and is therefore not guaranteed; and hence discounting at the (lower) risk-free rate?
- Do the other approaches in Chapter 32 (i.e. Sections 2.3-2.5) not reflect market risk? How do the approaches in Chapter 32, 2.3-2.5 compare to Section 2.6, and how are they related?

Sorry for asking so many questions, including some from another chapter - I feel like they relate to each other, and clarifying concepts from that chapter might help with understanding the current one. Thank you so much!

 

[Lindsay Smitherman]

No problem at all - this is tricky stuff! Taking each in turn ...

1. Does the treatment for market / non-market risks here directly relate to the allowance for financial / non-financial risk as mentioned in Chapter 32, Section 5.2? However, I am slightly confused as the section in Chapter 32 distinguishes between financial / non-financial risk, rather than market / non-market risks. From what I understand, market risks are financial risks, but there are also non-market risks that are considered financial risks (such as persistency, which is a business risk and hence a financial risk); hence the two sections of the notes don't seem to be entirely comparable.

Yes, that Chapter 32 reference is spot on. I wouldn't worry too much about the terminology being used: there isn't any definitive split between what would be considered to be a 'financial' or 'non-financial' risk so there can be some wooliness in how these terms are used. But yes, in this case (ie what is described in Section 5.2 of Chapter 32) I agree that it is probably better to think of them as market vs non-market.

 

[Lindsay Smitherman]

2. In your second bullet point on dealing with market risks, is this referring to Chapter 32, Section 2.6?

Yes, that's right

- How does using risk-free rates account for market risks? Is it because we are not recognising the risk premium in our discount rate since this risk premium relates to the market risk and is therefore not guaranteed; and hence discounting at the (lower) risk-free rate?

Yes, that's also correct.

- Do the other approaches in Chapter 32 (i.e. Sections 2.3-2.5) not reflect market risk? How do the approaches in Chapter 32, 2.3-2.5 compare to Section 2.6, and how are they related?

The approach in Section 2.3 is actually the same as that in Section 2.6 if the replicating portfolio chosen comprises a series of risk-free zero-coupon bonds with redemption amounts equal to the expected liability cashflows. So it is a market-consistent approach.

However, the approach in Section 2.4 allows credit to be taken in the discount rate for the equity (or whatever) risk premium. Liabilities are discounted at a higher rate, reflecting the higher expected return from risky assets, without allowance being made for the higher risks from investing in such assets. Hence the paragraph 'There is a school of ...'.

The approach in Section 2.5 would also allow a higher discount rate to be used for equities, say, as the return implied by the current market price and expected income / sales proceeds will be higher to reflect the higher risk. [This ties up with the ideas in Chapter 13 about required returns and risk premia.] So, again, liabilities backed by equities would be discounted at a higher rate (and so given a lower value) without any allowance being made for the higher risks involved in investing in such assets.

Hope that helps a bit more. Good challenges!

 

[JL24]

Yes, that's right



Yes, that's also correct.



The approach in Section 2.3 is actually the same as that in Section 2.6 if the replicating portfolio chosen comprises a series of risk-free zero-coupon bonds with redemption amounts equal to the expected liability cashflows. So it is a market-consistent approach.

However, the approach in Section 2.4 allows credit to be taken in the discount rate for the equity (or whatever) risk premium. Liabilities are discounted at a higher rate, reflecting the higher expected return from risky assets, without allowance being made for the higher risks from investing in such assets. Hence the paragraph 'There is a school of ...'.

The approach in Section 2.5 would also allow a higher discount rate to be used for equities, say, as the return implied by the current market price and expected income / sales proceeds will be higher to reflect the higher risk. [This ties up with the ideas in Chapter 13 about required returns and risk premia.] So, again, liabilities backed by equities would be discounted at a higher rate (and so given a lower value) without any allowance being made for the higher risks involved in investing in such assets.

Hope that helps a bit more. Good challenges!

Yes, I definitely understand these concepts better now. Thank you so much for your help, Lindsay!