Calculation of EV

[studentyk]

Hi,
I'll be glad to have some help with understanding of EV calculation.
Chapter 13, p. 18: "If the assumptions used to calculate the supervisory reserves were exactly the same as those used to calculate the future cashflows in the Ev calculation, then the profit emerging each year would be zero. This is because net cashflow, plus investment income on the reserves would equal the release of reserves in each year."
1. What assumptions we are talking about? Mortality, RDR?
2. I can't understand why is it equal? May be you can give me numerical example of this?

Thank you very much in advance!

 

[Jian_901]

Hi yk,

This is my interpretation of the extract:
If you assume the same discount rate on the release of supervisory reserves as on the future cashflows, the supervisory reserves will have no value as it's earning and being discounted at the same rate.

Ideally the discount rate on future cashflows would be higher, reflecting a risk premium on the risks taken, the differential in discount rate will introduce a cost of capital.

Hope this helps,
Jian

 

[Mark Willder]

Hi,
I'll be glad to have some help with understanding of EV calculation.
Chapter 13, p. 18: "If the assumptions used to calculate the supervisory reserves were exactly the same as those used to calculate the future cashflows in the Ev calculation, then the profit emerging each year would be zero. This is because net cashflow, plus investment income on the reserves would equal the release of reserves in each year."
1. What assumptions we are talking about? Mortality, RDR?
2. I can't understand why is it equal? May be you can give me numerical example of this?

Thank you very much in advance!

There are two bases required for calculating an EV: the EV projection basis and the reserving basis.

The profit in each year is given by: Premium less claims less expenses plus investment return less increase in reserves.

The reserving basis is used to calculate the reserves. The EV projection basis is used to calculate the premiums/expenses/claims/investment. For there to be zero profit, we want the assumptions in both bases to be the same for all the items, ie mortality, morbidity, expenses, withdrawals and investment return.

One we have calculated the profit each year we discount it at the RDR to get the present value of future profits on the in force business. Note that if the profit is always zero, then it doesn't matter what the RDR is.

Here's a very simple numerical example for a critical illness policy with one year to go. Over the year we expect (on the EV projection basis) that claims will be 100, expenses will be 10 investment return is zero. The premium is 105.

The reserve just before the payment of the premium at the start of the year is 100 + 10 - 105 = 5 if we assume exactly the same basis for reserves as for the EV projection. The reserve at the end of the year is zero, as the policy finishes. So the increases in reserves over the year is actually negative, ie -5.

So the profit is 105 - 100 - 10 + 0 -(-5) = 0

I hope this helps.

Best wishes

Mark

 

[Jian_901]

There are two bases required for calculating an EV: the EV projection basis and the reserving basis.

The profit in each year is given by: Premium less claims less expenses plus investment return less increase in reserves.

The reserving basis is used to calculate the reserves. The EV projection basis is used to calculate the premiums/expenses/claims/investment. For there to be zero profit, we want the assumptions in both bases to be the same for all the items, ie mortality, morbidity, expenses, withdrawals and investment return.

One we have calculated the profit each year we discount it at the RDR to get the present value of future profits on the in force business. Note that if the profit is always zero, then it doesn't matter what the RDR is.

Here's a very simple numerical example for a critical illness policy with one year to go. Over the year we expect (on the EV projection basis) that claims will be 100, expenses will be 10 investment return is zero. The premium is 105.

The reserve just before the payment of the premium at the start of the year is 100 + 10 - 105 = 5 if we assume exactly the same basis for reserves as for the EV projection. The reserve at the end of the year is zero, as the policy finishes. So the increases in reserves over the year is actually negative, ie -5.

So the profit is 105 - 100 - 10 + 0 -(-5) = 0

I hope this helps.

Best wishes

Mark

Hi Mark

This is an interesting example you've raised.

In my opinion, the profit you make on this policy should be -5, which is equivalent to the capital needed to fund the loss up front.
The capital is used to pay for claims and expenses and is never released.

In addition, the numerical example you provided, if workable, applies to any numbers and arrives at a $0 profit.

I believe what you are trying to say, however, is that the release of the reserve has no value to shareholders, if reserving and EV bases are the same.

Jian

 

[Mark Willder]

Hi Mark

This is an interesting example you've raised.

In my opinion, the profit you make on this policy should be -5, which is equivalent to the capital needed to fund the loss up front.
The capital is used to pay for claims and expenses and is never released.

In addition, the numerical example you provided, if workable, applies to any numbers and arrives at a $0 profit.

I believe what you are trying to say, however, is that the release of the reserve has no value to shareholders, if reserving and EV bases are the same.

Jian

Hi Jian

EV only looks at future years. In this case the future profit is zero. EV does not measure the overall profitability of a contract over its full term.

Yes, I agree that at some point in the past there has been a cost of 5 to set up the reserves.

However, we would expect claims costs to rise with age. So we would expect the premium to be less than the claims and expenses near the end of the contract. But in the earlier years of the contract the reverse should be true, and some of the excess premium can be used to set up the reserve. So overall this contract may well have been profitable.

Best wishes

Mark

 

[Jian_901]

Hi Mark

I agree that the PVFP component should be 0. In mathematical terms:
PVFP = PV (future profit) + release of capital

Assuming interest rate is 0%, this is $-5 + $5 = 0.

However, it's still my submission that the EV takes a hit of -5, as the $5 comes out of the free assets (in my country it's called the Adjusted Net Worth which is pretty much free assets above regulatory capital requirement), as EV is the sum of PVFP and the 'free assets'.

Using the same example assuming the free assets at time 0 is 10. The EV would have been (10 - 5 ) + PVFP (0 per above) = 5.

If we adjust the expense down by 5, the EV would have been (10 - 0) + PVFP (still 0, as cashflow is 0 and release of capital is 0 as capital is not required) = 10.

Please let me know if this makes sense.

Regards,
Jian

 

[Muppet]

EV takes a hit of -5, as the $5 comes out of the free assets

A few pointers:

original post was asking about future profis, not the overall impact of EV
If you were looking at the impact of the above being a 1-year policy then yes, overall we'd expect to make a loss and so overall EV would take the hit somewhere
But the above example wasn't a 1-year policy, it was a policy with one year to go. We don't know what's happened in the past, just that reserves at the start of the year are 5.
So for example, perhaps last year we received another premium of 105 and only paid out claims and expenses totalling 100. The +5 cashflow would have covered the reserve we needed for the future.

 

[Mark Willder]

A few pointers:

original post was asking about future profis, not the overall impact of EV
If you were looking at the impact of the above being a 1-year policy then yes, overall we'd expect to make a loss and so overall EV would take the hit somewhere
But the above example wasn't a 1-year policy, it was a policy with one year to go. We don't know what's happened in the past, just that reserves at the start of the year are 5.
So for example, perhaps last year we received another premium of 105 and only paid out claims and expenses totalling 100. The +5 cashflow would have covered the reserve we needed for the future.

Hi Jian

Yes, you are right that there are two parts to the EV: net assets and present value of future profits (PVFP). We've only been looking at present value of future profits above.

We can calculate the EV profit for the year as the change in the net assets plus the change in the present value of future profits. This would require us to know what the net assets and the PVFP were last year - we've not discussed these above.

Remember that we are only looking at future profits in the example. It is possible that in the previous year that the premiums were 5 bigger than the claims and expenses which allowed the company to set up the reserves of 5 as required. So overall the contract makes neither a profit or loss. Without knowing the previous years position we cannot comment further - we just know that the profit in the final year is 0.

Best wishes

Mark