Conflicting statements

[Meher]

Hi,
I am referencing Chapter 13 Course Notes 2019:
1. Page 11 Section 3.2 states: <<Decreasing the discount rate increases the degree of prudence for a positive reserve>>
In contrast we have the following two
2. Page 15 Section 4.1 states: << The risk discount rate (to calculate profitability on EB) will probably be lower than in the pricing basis.>> In relation to the lower risk for EB business as there is no uncertainty of new business.
3. Page 17 Section 4.3 states: << All else being equal, (for EV calculations) increasing the discount rate increases the degree of prudence. So, one possible way of allowing for risk is to use a risk discount rate that is higher than the risk‐free rate.>>

Is the risk discount rate referred in all of the above the same? i.e. used to discount cashflows. Then decreasing discount rate would imply higher Present value and hence more prudence which is statement 1. How is it that higher rdr in statement 2 and 3 implies higher risk/prudence?

 

[Trevor]

Hi Meher, I used to have the same confusion as you do! I sort of thought through it, though not sure this is the correct explanation:

Reducing the risk discount rate (denominator) definitely makes the present value larger. However:

1. In the purpose of reserving, Assets and Liabilities are calculated separately. Assets will be market value of assets, no discounting involved. Liability is PV of future (negative) cashflows.
Reducing rdr will inflate the PV negative cashflows, leading to higher reserves. Therefore more prudent.

2. Profitability is usually assessed in a cashflow projection. Whereby in each projection period, the income and outgo will be considered together:
Profit(t) = [ (Premium(t)-Expense(t))*(1+i) - Claims(t) ] / (1+r)
where i is the investment return on assets, r is the risk discount rate
Profit is a "good thing" that we want it to be high. if we increase r, we are shrinking the PV future profit. We are understating profit hence more prudent.

3. Same as item 2, for the PVIF component of EV, the net cashflow is a "good thing":
Net cashflow(t) = [ (Premium(t)-Expense(t))*(1+i) - Claims(t) - increase in reserves(t)] / (1+r)
Increasing r is shrinking the Net cash flow, so we are understating PVIF (and hence EV). Therefore more prudent.

To summarise, decreasing rdr will definitely inflate something, but is it prudent or not to increase it.

This is based on my own understanding. Can any ActEd tutor confirm this?

Thanks,
Trevor

 

[Trevor]

To add on, we know from the core reading that:

1. To calculate reserves, insurers can usually add on an illiquidity premium / Matching Adjustment onto the prescribed risk free rate. This add on will increase the overall risk discount rate to be less prudent (reducing reserves), subject to regulatory approval.
Again, the above explanation agrees with this: lower rdr is more prudent.

2. For pricing purposes, the risk discount rate will incorporate the inherent risk of the product and shareholder's cost of capital
The higher the risk, the higher the rdr, which reduces the PV profit, or at least make the required premium higher to achieve the profit criterion.
The above explanation agrees with this: higher rdr is more prudent

 

[Mark Willder]

Hi,
I am referencing Chapter 13 Course Notes 2019:
1. Page 11 Section 3.2 states: <<Decreasing the discount rate increases the degree of prudence for a positive reserve>>
In contrast we have the following two
2. Page 15 Section 4.1 states: << The risk discount rate (to calculate profitability on EB) will probably be lower than in the pricing basis.>> In relation to the lower risk for EB business as there is no uncertainty of new business.
3. Page 17 Section 4.3 states: << All else being equal, (for EV calculations) increasing the discount rate increases the degree of prudence. So, one possible way of allowing for risk is to use a risk discount rate that is higher than the risk‐free rate.>>

Is the risk discount rate referred in all of the above the same? i.e. used to discount cashflows. Then decreasing discount rate would imply higher Present value and hence more prudence which is statement 1. How is it that higher rdr in statement 2 and 3 implies higher risk/prudence?

Hi Meher

Have a look at Trevor's reply. He's quite right. It depends on what it is that you are discounting, ie is it profits (a good thing), or negative cashflows (a bad thing).

Best wishes

Mark

 

[Mark Willder]

Hi Meher, I used to have the same confusion as you do! I sort of thought through it, though not sure this is the correct explanation:

Reducing the risk discount rate (denominator) definitely makes the present value larger. However:

1. In the purpose of reserving, Assets and Liabilities are calculated separately. Assets will be market value of assets, no discounting involved. Liability is PV of future (negative) cashflows.
Reducing rdr will inflate the PV negative cashflows, leading to higher reserves. Therefore more prudent.

2. Profitability is usually assessed in a cashflow projection. Whereby in each projection period, the income and outgo will be considered together:
Profit(t) = [ (Premium(t)-Expense(t))*(1+i) - Claims(t) ] / (1+r)
where i is the investment return on assets, r is the risk discount rate
Profit is a "good thing" that we want it to be high. if we increase r, we are shrinking the PV future profit. We are understating profit hence more prudent.

3. Same as item 2, for the PVIF component of EV, the net cashflow is a "good thing":
Net cashflow(t) = [ (Premium(t)-Expense(t))*(1+i) - Claims(t) - increase in reserves(t)] / (1+r)
Increasing r is shrinking the Net cash flow, so we are understating PVIF (and hence EV). Therefore more prudent.

To summarise, decreasing rdr will definitely inflate something, but is it prudent or not to increase it.

This is based on my own understanding. Can any ActEd tutor confirm this?

Thanks,
Trevor

Hi Trevor

Yes, this is a nice way of thinking about it. Being prudent is about making good things smaller and bad things bigger.

So if we are calculating reserves, we are discounting negative cashflows (a bad thing) so we use a low discount rate as it makes them bigger.

But if we are calculating embedded values, we are discounting profits (a good thing) so we use a big discount rate as it makes them smaller.

Best wishes

Mark

 

[Mark Willder]

To add on, we know from the core reading that:

1. To calculate reserves, insurers can usually add on an illiquidity premium / Matching Adjustment onto the prescribed risk free rate. This add on will increase the overall risk discount rate to be less prudent (reducing reserves), subject to regulatory approval.
Again, the above explanation agrees with this: lower rdr is more prudent.

2. For pricing purposes, the risk discount rate will incorporate the inherent risk of the product and shareholder's cost of capital
The higher the risk, the higher the rdr, which reduces the PV profit, or at least make the required premium higher to achieve the profit criterion.
The above explanation agrees with this: higher rdr is more prudent

Hi Trevor

1. Yes, it would be more prudent to ignore the illiquidity premium.

2. Yes, increasing the RDR means that we need to increase the premium to achieve our desired profit.

Best wishes

Mark

 

[Meher]

Hi guys,
Thank you for your responses. Great help!
Regards,
M