[ILA Track] Intro to ILA Module Exercise Task 3: Actuarial Pricing Memo

[Steve Zeske]

Task 3: Actuarial Pricing Memo of the Intro to ILA Module Exercise asks you to calculate ROI, Embedded Value (EV), and New Business Strain as a % of net premium under a baseline and multiple scenarios. I found one reading from Section 4 of the module that describes all 3 of these profit measures. The reading is Life Insurance Products and Finance: Charting a Clear Course (Atkinson and Dallas, 2000).

A huge concern of mine though is that this reading does not use a typical definition of ROI. The reading describes ROI like most people describe IRR: “a solved for discount rate that causes the present value of profits to equal zero.” Since there are 3 sign changes in the stream of distributable earnings over 40 years of the product given in the task, that means there are 3 possible ROIs by the author’s definition. How would I know which one to enter as the solution?

If, on the other hand, the question writer was not thinking about this reading and meant for ROI to be calculated in a more typical manner, like the PV(Distributable Earnings) divided by first-year expenses including commissions (i.e. acquisition expenses), then there would only be 1 solution.

The reading also mentions using a discount rate other than the Hurdle Rate to discount distributable earnings when they are negative. There are negative distributable earnings in years 1, 20, and 21 of the pricing projection. The given information includes a Hurdle Rate but is not clear about which discount rate to use for negative distributable earnings, although it does mentions 4% as the pricing interest rate assumption.

Is anyone else struggling with this task? What are your thoughts?
How are you calculating ROI?
Are you using a different discount rate to discount the negative distributable earnings? If so, which one?

This does feel like a make-or-break decision since the entirety of Task #3 deals with repeating these same profit calculations for a baseline + scenarios and then discussing them.

[nicktheactuary]

I am working on this module assignment and also am stuck on this task. Were you able to figure it out?

[Steve Zeske]

I went forward and calculated ROI how the Atkinson & Dallas book defines it. I got an ROI around 11% for the baseline 40-year pricing horizon. I did not go ahead and try to determine the other 2 possible solutions that would solve PV(Profits) = 0 since 11% seemed like a reasonable value. Generally, the other possible solutions to an IRR equation are unreasonable like <0% or >100%.  I used the same ROI definition for the sensitivities to stay consistent.

I used the 4% pricing discount rate to discount negative distributable earnings, also consistent with the methodology in the Atkinson & Dallas book. I’m still just unsure if this is the right rate, but I don’t see any other logical value to use.

I have not actually submitted the module exercise yet. Since I’m in no hurry, I decided to wait for a reply on this post.

What were you thinking?

[nicktheactuary]

It sounds like we did it similarly. I used the hurdle rate instead of the the investment rate because in the profit measures reading (may be the what you are referencing) one of the examples mentioned used 7%, which was the hurdle rate, to discount when DE is negative. To solve for the ROI, I used formula 11.5.3 that was referenced in the reading. For the baseline 40-year horizon, I got 11.2% as the ROI.

For Embedded Value, I used the 4% to discount when DE are negative and then the 10% hurdle rate when positive because the section on PV said that the discount rate to use for negative DE is typically set less than the hurdle rate and is typically set to the investment rate. For the baseline 40-year horizon, I got 14.64.

Let me know if that sounds reasonable.

Also, I am having a little trouble figuring out how to calculate NB strain as a % of premium, is it simply first DE (cell C43) divided by first year premium (cell C27)?

[Steve Zeske]

If you read the two paragraphs in section 11.6.2.3 following the example in the textbook where both positive and negative cashflows are discounted using the 7% hurdle rate, it says it is wrong to use the same rate for discounting both types of cashflows. Instead, it says to use the more generalized 11.5.3 formula, which allows for different discount rates. It sounds like you ended up using that formula anyway.

I got 11.3% (after rounding) for the ROI, so we’re only off by 0.1%. I used the IRR function in Excel to calculate ROI since the ROI in the textbook is essentially an IRR measure. I did not directly use the 11.5.3 formula for ROI. It’s possible that there are timing differences in the Excel IRR formula (cashflows assumed to be at the beginning of the year v. end of the year) that may result in the small difference.

For the baseline 40-year horizon EV, I used the 11.5.3 formula directly and got $16.10. I assumed distributable earnings occurred at the beginning of the year so I could use the 11.5.3 formula exactly as it is in the textbook. Although, I’m not sure this is the exact right approach because the projections assume some cashflows occur at the beginning of the year and some occur in the middle of the year. What cashflow timing assumption did you use? If you assumed middle or end of the year earnings, your distributable earnings would be discounted more. That may explain why your EV is a bit less than mine: $14.64.

For NB Strain, I calculated it exactly as you described.

[nicktheactuary]

Yeah the example in section 11.6.2.3 is the one I used to base my answer off of. I did not use the IRR function. Instead I used used formula 11.5.3 and used 10% when discounting negative cashflows and then used goal seek to determine the ROI such that the PV at 0 was 0.

For the EV, I also used 11.5.3 directly just as the textbook did it. I see where you got your 16.10. I did the calculation 1 more time. You stopped in column C when I applied the formula one more time to get to 14.64 to get to time 0. Since I applied the formula one more time than you, then I would be assumed DE occur at end of year. Based on example, 11.6.4 I feel like my way may be correct.

One last question about NB strain, since DE in year 1 is negative, you get a negative percentage (-57.9%). Did you leave it as negative or take the absolute value?

[Steve Zeske]

Ah, I see. I think you’re right to assume end-of-year distributable earnings because pieces of distributable earnings in the projection, like Investment Income on Required Capital, require a full year to achieve the full return. Mid-year earnings would probably be an acceptable solution too, although it would require modifications to the 11.5.3 formula. Beginning of the year distributable earnings is probably not acceptable. I’ve reworked my EV calculations to assume end-of-the-year timing and got your answer.

I also verified the PV(Distributable Earnings) = 0 at time 0 using the ROIs calculated by Excel’s IRR function. So I did not change my answer there. PV(Distributable Earnings) = 0 at time 1 as well. Discounting 0 at time 1 is still 0 at time 0.

For NB strain, yes, I left the percentage negative. The textbook does not say to take the absolute value so I did not. Admittedly, this did make it more difficult to describe in words whether the sensitivities made new business more or less strained.

[nicktheactuary]

Okay sounds good. Thanks for discussing this through, Steve. I feel better about my answers. I think for ROI either of our answers should be acceptable as long as we explain our logic.

FYI, here is a link to a google group. Not sure how active it is but there may be other questions you had that may already be answered:
https://groups.google.com/g/Introduction-to-ILA-Module

[Steve Zeske]

Thanks to you too. I also feel better about my answers.

[nicktheactuary]

Hopefully, this is my last question. For the coinsurance tab, are your EV results 26.66 and 17.21 for the 20-year and 40-year time horizons? I think its weird that the 40-year horizon has a higher EV value than the baseline group.

[Steve Zeske]

Yes, I got those results. The EV is higher than the baseline group for the 40-year pricing horizon because the reinsurer absorbs some of the costs of the shock lapse event in year 21.

[nicktheactuary]

I agree. I looked at it more and was thinking the same thing. Thanks again!

[Ally]

I must be interpreting the 11.5.3 EV formula wrong. For example, at time 39, I have my formula performing (since Profit(40) > 0) do Profit(40)/(1.1) + Profit(39), where Profit = Distributable Earnings. I copied this formula all the way to time 1. Now what? I feel like I’m missing something. Any help is greatly appreciated!

[nicktheactuary]

We used 4% when the DE is negative in the EV formula and applied the formula one more time to bring it back to time 0

[Alex_FSACand]

For the baseline EV calculation I used 11.5.3 formula

At time 39: DE(40)/1.1 + DE(39) = 48.27

at time 38: 48.27/1.1 + 24.65 = 68.53

Using this formula all the way to time 1 with 4% discount rate at t=1, 20,21

i get 42.01

Don’t know what I doing wrong

any ideas?

[Steve Zeske]

I’ve already submitted my module exercise so I haven’t been paying close attention to this thread. My answer here may be too late, but you need to use the 4% discount rate when PVFP(t) < 0, not when DE(t) < 0. This should occur at t= 17-21.

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