Chapter 21 - Surrender Values Practice question

[jack]

Hi,

looking at practice question 21.3 part (iii) we are asked to describe the problems caused by a share increase in interest rates.

We are told the earned asset share may fall as the market value of assets will fall?
we are also told in the answer “ current premium rates me be lower”

question:
1) why does a rise in the interest rate cause a fall in the market value of assets. And hence why would this fall in the market value of assets cause the asset share to fall. We use AS(t+1) = AS(t) * (1+i) ….
So I think I am confused here as I thought the increase in interest rates would actually increase the asset share.

2) why would premium rates be lower now as a result of this interest rate rise ?

thanks for your help

 

[Lynn Birchall]

Hi Jack

(1) Remember that in the asset share formula you mention, the i is not referring to interest rates. For the asset share accumulation i is investment returns - this includes gains/losses due to changes in market values of assets held.
The assets backing these without-profit policies are likely fixed-interest bonds. So, the argument is along the lines that a sharp increase in interest rates suggests higher bond yields & so falls in bond values.

(2) If we consider pricing by equating the present value of benefits/expenses with present value of premiums, then using a higher interest rate in discounting would result in a lower premium. Intuitively, if future premiums are assumed to earn a higher return when invested, then the premium needed to cover the benefits/expenses will be lower.

Hope these help!
Lynn

 

[Priyanka Malhotra]

Hi Jack

(1) Remember that in the asset share formula you mention, the i is not referring to interest rates. For the asset share accumulation i is investment returns - this includes gains/losses due to changes in market values of assets held.
The assets backing these without-profit policies are likely fixed-interest bonds. So, the argument is along the lines that a sharp increase in interest rates suggests higher bond yields & so falls in bond values.

(2) If we consider pricing by equating the present value of benefits/expenses with present value of premiums, then using a higher interest rate in discounting would result in a lower premium. Intuitively, if future premiums are assumed to earn a higher return when invested, then the premium needed to cover the benefits/expenses will be lower.

Hope these help!
Lynn

Hi,

Could someone please help me understand the rest of the answer as well…
1)Why is it stated that using prospective method loss would be avoided ( at best estimate basis)

2) why realistic interest rate should be higher than the premium basis interest rate..?

3) if Company is mismatched due to being invested too long … why would this mismatching arise and how does this affect the surrender values

thanks in advance

 

[Mark Willder]

Hi,

Could someone please help me understand the rest of the answer as well…
1)Why is it stated that using prospective method loss would be avoided ( at best estimate basis)

2) why realistic interest rate should be higher than the premium basis interest rate..?

3) if Company is mismatched due to being invested too long … why would this mismatching arise and how does this affect the surrender values

thanks in advance

Hi Priyanka

I'll answer each of your questions in turn.

1) The solution says:

"… the realistic prospective method should avoid loss by valuing future benefits at the new higher market-related interest rate."

Using the new higher interest rate will result in a lower prospective value and hence a lower surrender value. This avoids the loss that would be made if the surrender value had been too high because it used the original higher interest rate.

2) The solution says:

"The realistic interest rate should be higher than the interest rate assumed in new premium rates (which would include a margin for reinvestment risk)"

The pricing basis starts with the realistic interest rate and then deducts a risk margin. Using a lower interest rate in this way leads to a higher premium. Higher premiums are more likely to make a profit, eg the insurer should still make a profit even if interest rates turn out to be a little lower than the realistic estimate.

3) Mismatching may occur if assets of a suitable term are not available. Alternatively mismatching may be a deliberate strategy if the insurer thinks that the assets it chooses will give a higher return than the matching assets.

The solution says

"If the company is mismatched due to being invested too long, and interest rates were to rise, then the earned asset share would fall by more than the prospective value, even if the latter were calculated at the new proposed higher interest rate. If this were the case, the company might want to reduce all surrender values further to try to recoup the loss it made."

So mismatching with assets too long will result in a loss unless the insurer reduces its surrender value to be even lower than the realistic surrender value.

Best wishes

Mark

 

[Priyanka Malhotra]

Than

Hi Priyanka

I'll answer each of your questions in turn.

1) The solution says:

"… the realistic prospective method should avoid loss by valuing future benefits at the new higher market-related interest rate."

Using the new higher interest rate will result in a lower prospective value and hence a lower surrender value. This avoids the loss that would be made if the surrender value had been too high because it used the original higher interest rate.

2) The solution says:

"The realistic interest rate should be higher than the interest rate assumed in new premium rates (which would include a margin for reinvestment risk)"

The pricing basis starts with the realistic interest rate and then deducts a risk margin. Using a lower interest rate in this way leads to a higher premium. Higher premiums are more likely to make a profit, eg the insurer should still make a profit even if interest rates turn out to be a little lower than the realistic estimate.

3) Mismatching may occur if assets of a suitable term are not available. Alternatively mismatching may be a deliberate strategy if the insurer thinks that the assets it chooses will give a higher return than the matching assets.

The solution says

"If the company is mismatched due to being invested too long, and interest rates were to rise, then the earned asset share would fall by more than the prospective value, even if the latter were calculated at the new proposed higher interest rate. If this were the case, the company might want to reduce all surrender values further to try to recoup the loss it made."

So mismatching with assets too long will result in a loss unless the insurer reduces its surrender value to be even lower than the realistic surrender value.

Best wishes

Mark

Thanks for the explanation!

in point 3 above, solution says asset share will fall more than the prospective value , is it because due to being invested for too long asset share will be valued at a rate of interest lower than the prospective because of illiquidity premium?

also the solution says that “
The realistic interest rate should be higher than the interest rate assumed in new premium rates (which would include a margin for reinvestment risk), thereby avoiding the surrender and re-entry option”

so does this mean that a company will resort to not decreasing the surrender value in the case when assets and liabilities and well matched?

And take care of lapse and re entry by updating the premium rates at current rate of interest deducting for appropriate reinvestment risk margin? Which would lead to lower premium basis rate of interest as compared to the prospective basis?


And when solution talks about assets liabilities not being well matched then reducing the surrender value is the option insurance company might resort to ?



thanks in advance!

 

[Mark Willder]

Than

Thanks for the explanation!

in point 3 above, solution says asset share will fall more than the prospective value , is it because due to being invested for too long asset share will be valued at a rate of interest lower than the prospective because of illiquidity premium?

also the solution says that “
The realistic interest rate should be higher than the interest rate assumed in new premium rates (which would include a margin for reinvestment risk), thereby avoiding the surrender and re-entry option”

so does this mean that a company will resort to not decreasing the surrender value in the case when assets and liabilities and well matched?

And take care of lapse and re entry by updating the premium rates at current rate of interest deducting for appropriate reinvestment risk margin? Which would lead to lower premium basis rate of interest as compared to the prospective basis?


And when solution talks about assets liabilities not being well matched then reducing the surrender value is the option insurance company might resort to ?



thanks in advance!

Hi Priyanka

We don't need to consider the illiquidity premium here.

The asset share will fall by more than the prospective value because the assets are too long. An increase in interest rate makes the price of long assets fall by more than short assets as we are discounting for more years.

The surrender value will need to reduce if interest rates go up (whether the assets are matched or not) because the asset share falls when interest rates rise. But if the insurer has invested its assets long, then it will need to reduce the surrender value even more in order to avoid a loss.

Higher interest rates will make new policies cheaper, so the insurer will need to reprice. Existing customers would then want to lapse their expensive old policy to buy the cheap new policy. However, by reducing the surrender value for the old policy the insurer makes the lapse and re-entry option less attractive.

Best wishes

Mark

 

[Priyanka Malhotra]

Thank you so much for the explanation!

One question, does “short assets” mean assets invested for shorter term and similarly for “long assets” investments held for longer term?

thanks!!

 

[Mark Willder]

Thank you so much for the explanation!

One question, does “short assets” mean assets invested for shorter term and similarly for “long assets” investments held for longer term?

thanks!!

Hi Priyanka

In the explanation above, short assets refers to a bond with a short term to maturity, perhaps 5 years. Long assets refers to a bond with a long term to maturity, perhaps 20 years.

Best wishes

Mark