Market Consistent Valuation

[claire3000006]

For MCEV and SII market consistent valuation of liabilities involves discounting the cashflows at a risk free rate.

On p23 of Chapter 22 it says 'To calculate a market consistent EV: Cashflows for products that do not contain options and guarantees are discounted at a rate that reflects the riskiness of each cashflow.'

Why the difference?

 

[scarlets]

I find this confusing too.

 

[Mark Willder]

For MCEV and SII market consistent valuation of liabilities involves discounting the cashflows at a risk free rate.

On p23 of Chapter 22 it says 'To calculate a market consistent EV: Cashflows for products that do not contain options and guarantees are discounted at a rate that reflects the riskiness of each cashflow.'

Why the difference?

Page 23 of chapter 22 is correct - to be market consistent we should discount cashflows at a rate that reflects their riskiness. However, there are a number of different ways to do this (which is where it gets confusing).

To illustrate the basic idea, consider two assets: a bond and a share. Both assets have market value of 100 - so any market consistent valuation should place a value of 100 on these assets.

The bond has expected payoff of 104 in one year's time. So if we discount at 4% we get the market consistent value of 100.

The share has expected payoff of 108 in one year's time. So if we discount at 8% we get the market consistent value of 100.

So, we have discounted the more risky asset at a higher rate. This can be applied to any asset, eg unquoted assets. The future profits from in force business is an asset too - so again we should discount the profits at a higher rate if they are more risky.

The question now is - how to derive the market consistent risk discount rate for unquoted assets (including future profits on in force business)? Solvency II and MCEV Principles both use a similar approach (but there are other market consistent techniques that do not follow this approach).

Both SII and MCEV Principles discount the unhedgeable liability cashflows at the risk free discount rate. However, this gives the wrong answer (as the cashflows are risky). So, SII adds a risk margin to the liabilities using the cost of capital method. Similarly the MCEV Principles deduct the cost of residual non-hedgeable risks from the VIF.

A simple numerical example may help. Consider an insurance policy that will release a profit of 110 in one year's time. If a suitable risk discount rate is 10% then the market consistent VIF is 100.

An alternative way to value the policy is to follow the MCEV principles. Here we discount the profit at the risk free rate of 4% to give 110 / 1.04 = 105.76. We must then deduct the cost of residual non-hedgeable risks. If this cost is 5.76, then again we have the same market consistent value of 100. So we could say that the MCEV Principles have implicitly discounted the cashflows at 10% in this case.

I hope this example helps.

Best wishes

Mark

 

[echo20]

Hi Mark,

I'm a bit confused over your reply below. I think it stems from the difference between how asset and liability cashflows should account for risk. i.e. isn't VIF an asset, which should be attributed a lower value to account for risk (i.e with a risk premium added to the discount rate), whereas liability cashflows should be attributed a relatively higher value (i.e. no addition to risk free discount rate)? I've got a few further specific queries:

1. You say that both SII and MCEV Principles discount the unhedgeable liability cashflows at the risk free rate. I can see how this is appropriate for SII liabilities, but do we ever actually discount liability cashflows for MCEV - I thought it was the shareholder profits (i.e. generally an asset, if not loss-making) that we discounted?

2. What about hedgeable liabilities? What's meant by hedgeable anyway? Does this mean we can find a (risk free) asset that exactly replicates the liability cashflow? E.g. an annuity payment matched by a zero coupon bond? Would the longevity risk also be deemed hedgeable, by valuing at the cost of a longevity swap?

3. MCEV Principle 13 says "VIF should be discounted using discount rates consistent with those that would be used to value such cash flows in the capital markets". This doesn't sound like a risk-free rate to me! Although it goes on to say that an alternative is to assume assets earn, and discount all cashflows at, the risk free rate. Does the latter method mean that it's only legitimate to discount VIF at the risk free rate if the assets are assumed to grow at this rate too?

Sorry for the long rant, but it's a topic that continues to confuse me!

 

[Mark Willder]

I'm a bit confused over your reply below. I think it stems from the difference between how asset and liability cashflows should account for risk. i.e. isn't VIF an asset, which should be attributed a lower value to account for risk (i.e with a risk premium added to the discount rate), whereas liability cashflows should be attributed a relatively higher value (i.e. no addition to risk free discount rate)?

Yes, VIF is an asset. So in MCEV we deduct the cost of residual non-hedgeable risks from the VIF, which gives a lower VIF as required.

In Solvency II we are looking at liabilities, so we add a risk margin to the liabilities using the cost of capital method, which gives a higher liability as required.

I've got a few further specific queries:

1. You say that both SII and MCEV Principles discount the unhedgeable liability cashflows at the risk free rate. I can see how this is appropriate for SII liabilities, but do we ever actually discount liability cashflows for MCEV - I thought it was the shareholder profits (i.e. generally an asset, if not loss-making) that we discounted?

Yes, we discount profits in MCEV. But profits are just liability cashflows less the increase in reserves. So effectively we are discounting cashflows in MCEV (but we're discounting the flows to and from reserves too).

2. What about hedgeable liabilities? What's meant by hedgeable anyway? Does this mean we can find a (risk free) asset that exactly replicates the liability cashflow? E.g. an annuity payment matched by a zero coupon bond? Would the longevity risk also be deemed hedgeable, by valuing at the cost of a longevity swap?

We would normally only consider the market risks to be hedgeable. So yes, a hedgeable liability is one for which we can find an asset that exactly replicates the liability cashflows (the asset itself can be risky as long as it responds to risk in exactly the same way as the liability cashflows). So we could match the expected annuity payments by matching with zero coupon bonds as you suggest (we'd then have hedged the interest rate risk).

We probably wouldn't consider longevity risk to be hedgeable at present. The swap market is probably insufficiently deep and liquid to give fair values. The transactions are also not performed at arms length.

Perhaps as the longevity swap/bonds markets develop we may consider these risks to be hedgeable too.

3. MCEV Principle 13 says "VIF should be discounted using discount rates consistent with those that would be used to value such cash flows in the capital markets". This doesn't sound like a risk-free rate to me! Although it goes on to say that an alternative is to assume assets earn, and discount all cashflows at, the risk free rate. Does the latter method mean that it's only legitimate to discount VIF at the risk free rate if the assets are assumed to grow at this rate too?

A key idea from financial economics is that the value of liabilities is unaffected by the assets actually held. So we should discount at a risk-free rate regardless of the actual return on assets.

Note that the correct discount rate is not necessarily the same as the yield on (risk free) government bonds. If we have a liability to pay the value of one share in ABC Co, then the asset that perfectly matches the liability is one ABC share - so we should discount at a rate consistent with the rate used to value this share in the capital markets (which will be higher than the yield on a bond).

Best wishes

Mark

 

[echo20]

Thanks again, Mark!

 

[gruhaa]

Hi Mark
As you mentioned, liability hedging is using an asset whose cash flows replicate the liability cash flows. Then what is the difference between liability matching(which is rare for many liability cashfflow) and liability hedging?

 

[Lindsay Smitherman]

Hi: this CA1 thread might be helpful

https://www.acted.co.uk/forums/index.php?threads/liability-hedging-vs-perfect-matching.4406/

 

[marilize]

Page 23 of chapter 22 is correct - to be market consistent we should discount cashflows at a rate that reflects their riskiness. However, there are a number of different ways to do this (which is where it gets confusing).

To illustrate the basic idea, consider two assets: a bond and a share. Both assets have market value of 100 - so any market consistent valuation should place a value of 100 on these assets.

The bond has expected payoff of 104 in one year's time. So if we discount at 4% we get the market consistent value of 100.

The share has expected payoff of 108 in one year's time. So if we discount at 8% we get the market consistent value of 100.

So, we have discounted the more risky asset at a higher rate. This can be applied to any asset, eg unquoted assets. The future profits from in force business is an asset too - so again we should discount the profits at a higher rate if they are more risky.

The question now is - how to derive the market consistent risk discount rate for unquoted assets (including future profits on in force business)? Solvency II and MCEV Principles both use a similar approach (but there are other market consistent techniques that do not follow this approach).

Both SII and MCEV Principles discount the unhedgeable liability cashflows at the risk free discount rate. However, this gives the wrong answer (as the cashflows are risky). So, SII adds a risk margin to the liabilities using the cost of capital method. Similarly the MCEV Principles deduct the cost of residual non-hedgeable risks from the VIF.

A simple numerical example may help. Consider an insurance policy that will release a profit of 110 in one year's time. If a suitable risk discount rate is 10% then the market consistent VIF is 100.

An alternative way to value the policy is to follow the MCEV principles. Here we discount the profit at the risk free rate of 4% to give 110 / 1.04 = 105.76. We must then deduct the cost of residual non-hedgeable risks. If this cost is 5.76, then again we have the same market consistent value of 100. So we could say that the MCEV Principles have implicitly discounted the cashflows at 10% in this case.

I hope this example helps.

Best wishes

Mark

Hi Mark

The above post is so insightful, thank you!

I have a question on how you would treat investment returns on assets valued at market consistent values. For Solvency II, would we assume these will be the risk-free rates, regardless of the type of asset (e.g. equities, property, bonds)? But then in your example above, we would not arrive at different cash flows for the bond and the share?

I want to understand how I would project charges dependent on future unit fund values.

Thanks in advance for your help.

 

[mugono]

Hi Mark

The above post is so insightful, thank you!

I have a question on how you would treat investment returns on assets valued at market consistent values. For Solvency II, would we assume these will be the risk-free rates, regardless of the type of asset (e.g. equities, property, bonds)? But then in your example above, we would not arrive at different cash flows for the bond and the share?

I want to understand how I would project charges dependent on future unit fund values.

Thanks in advance for your help.

In a solvency 2 context, the unit fund would be projected at the risk free rate (or at risk free plus a volatility adjustment / matching adjustment were this to apply).

The type of assets held would be relevant where financial guarantees exists as this would affect the implied volatilities used to simulate the unit funds used to calculate the guarantee cost.

The addition of a risk margin on the non hedgeable risk elements of the non unit reserves (eg expenses) would get you to the market consistent liability valuation.

The market consistent value of a bond or share implicitly includes an allowance for risk (investors are risk averse) in the price.

Hope that helps.