Risk Discount Rate

[Myself]

Good day

I have 2 questions surrounding the risk discount rate (RDR). I understand the RDR to be the rate being used to discount cashflows and determine the premium for a policy. The RDR effectively represents the required return of the shareholders for their investment into the company.

1) CAPM does not provide a good RDR since it does not account for the specific risks. So then how does CAPM relate to the RDR? In particular, how do we use the rate determined by CAPM in the statistical method of determining the RDR?

2) How does RDR differ from return on capital (if any)? I also understand that in the beginning of a policy, we experience strain. To cope with the strain, we require capital. I assume this is the capital that our shareholders have provided and so they require a return on. Wouldn't this just be the RDR?

Thank you in advance.

 

[Mark Willder]

Good day

I have 2 questions surrounding the risk discount rate (RDR). I understand the RDR to be the rate being used to discount cashflows and determine the premium for a policy. The RDR effectively represents the required return of the shareholders for their investment into the company.

1) CAPM does not provide a good RDR since it does not account for the specific risks. So then how does CAPM relate to the RDR? In particular, how do we use the rate determined by CAPM in the statistical method of determining the RDR?

2) How does RDR differ from return on capital (if any)? I also understand that in the beginning of a policy, we experience strain. To cope with the strain, we require capital. I assume this is the capital that our shareholders have provided and so they require a return on. Wouldn't this just be the RDR?

Thank you in advance.

Hi

1) If we want to use CAPM then we can set RDR = r + (E_M - r) Beta_i by estimating the historical beta of the insurer's shares. If we think the particular product we are pricing is more risky than our usual business then we would adjust the RDR upwards. We don't develop the statistics of this further for SP2.

2) When we profit test a policy we can allow for the reserves and solvency capital that need to be set up. Often the reserving/solvency requirements plus initial expenses are more than the first premium and so we have new business strain. By using an RDR equal to the cost of capital we can price the contract to make sure that the future profits are enough to provide the shareholders with their required return on their initial investment (the initial investment being the capital injection to cover the new business strain).

Best wishes

Mark

 

[Myself]

Hi

1) If we want to use CAPM then we can set RDR = r + (E_M - r) Beta_i by estimating the historical beta of the insurer's shares. If we think the particular product we are pricing is more risky than our usual business then we would adjust the RDR upwards. We don't develop the statistics of this further for SP2.

2) When we profit test a policy we can allow for the reserves and solvency capital that need to be set up. Often the reserving/solvency requirements plus initial expenses are more than the first premium and so we have new business strain. By using an RDR equal to the cost of capital we can price the contract to make sure that the future profits are enough to provide the shareholders with their required return on their initial investment (the initial investment being the capital injection to cover the new business strain).

Best wishes

Mark

Thanks for the reply.

Just to clear up some stuff.
I understand that to calculate premiums we apply formula: PV(Premiums) = PV(Benefits) + PV(Expenses) [As a basic form]. Now we are required to discount the cashflows in this formula. Now there are 3 ways to do that: (1) We use the risk free rate and include margins in the assumptions, (2) Risk free rate and best estimate assumptions with distribution for the assumptions, and (3) High risk discount rate and best estimate assumptions.
Does that imply that for approach (3) we use the required rate of return of shareholders as the RDR?

Additionally, say we calculated the premium as using the formula above and also applied approach (3) with the required rate of return. If we know want to profit test, we will use the premium and look at: Profit = Premium + Interest - Expenses - Increase in reserve.
It follows then that this profit must be discounted backwards. What rate should be used then? - I assume that our net present value of profits will be lower (if not below zero) if we continue to use the required rate of return as the RDR since we now have the cost of reserves.
[Please address the profit testing with regard to new policies and existing ones]

 

[Mark Willder]

Thanks for the reply.

Just to clear up some stuff.
I understand that to calculate premiums we apply formula: PV(Premiums) = PV(Benefits) + PV(Expenses) [As a basic form]. Now we are required to discount the cashflows in this formula. Now there are 3 ways to do that: (1) We use the risk free rate and include margins in the assumptions, (2) Risk free rate and best estimate assumptions with distribution for the assumptions, and (3) High risk discount rate and best estimate assumptions.
Does that imply that for approach (3) we use the required rate of return of shareholders as the RDR?

Additionally, say we calculated the premium as using the formula above and also applied approach (3) with the required rate of return. If we know want to profit test, we will use the premium and look at: Profit = Premium + Interest - Expenses - Increase in reserve.
It follows then that this profit must be discounted backwards. What rate should be used then? - I assume that our net present value of profits will be lower (if not below zero) if we continue to use the required rate of return as the RDR since we now have the cost of reserves.
[Please address the profit testing with regard to new policies and existing ones]

Hi

If we use an equation of value (PV(Premiums) = PV(Benefits) + PV(Expenses)) to calculate premiums then we ignore the cost of capital. So we wouldn't use a RDR at all in this calculation. Instead we need to use an investment return assumption (to be prudent this would need to be a low investment return). For that reason I wouldn't use any of the 3 approaches you suggest. We could either use prudent assumptions (high expenses and claims and low investment returns), or best estimate assumptions with an explicit profit loading.

Yes, if we use a profit test then we use the equation Profit = Premium + Interest - Expenses - Increase in reserve. The basic idea is no different whether we are valuing new policies in pricing or existing policies in an embedded value. It is these profits that we discount at a RDR.

Best wishes

Mark