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Math 3650 Pricing Project - Helpful Hints

1. Suggested methodology:

The YRT Policy that we are selling today for females, age 40 who are smokers produces a Risk Adjusted IRR of 15.06%.  After updating your model with the assumptions for a female age 40, your YRT model should match that IRR, or you are doing something wrong.

To compare the riskiness of the proposed level premium term product to the riskiness of our existing YRT product, start by choosing a level premium (rounding to the nearest penny per thousand) that produces a risk-adjusted IRR that is as close to 15.06% as possible.  By doing this, it will be much easier to compare the sensitivity of the two product designs to changes in your key assumptions in your sensitivity tests and scenario tests. (For example, if they had equal sensitivity, the results from both the YRT and Level premium models would match after you change the assumption.).

Then, after analyzing the results of these sensitivity and scenario tests, you must make a clear, specific recommendation.

If you decide the two product designs have comparable risk overall, then you may recommend selling the level premium policy with the premium you started with, that produces a similar risk-adjusted IRR.

If you decide the level premium product design is less risky then you can recommend selling this new level premium product design at the same premium you started with, producing a similar risk-adjusted IRR as the YRT product, or even recommend a lower premium since it is less risky. You, of course, should explain how you arrived at the premium you recommend.

If you decide the level premium product design is more risky, then you may recommend selling this new level premium product design at a higher premium than you started with. This will produce a higher expected risk-adjusted IRR than the YRT product to compensate our investors for taking additional risk. You, of course, should explain how you arrived at the premium you recommend.  Or, you can decide the level premium product is too risky to sell at any price, and that our company should not sell it at all. Again, explain your reasons.

In all cases, your recommendation may be influenced by the competitive information available to you.  We know that Willimantic Life is selling the level premium term product to females age 40, smokers at a premium of $2.40 per thousand of face amount. When you give your recommendation, you should discuss how this knowledge affected your recommendation, if at all.

2. Re-read the assignment directions before you write your first draft!

3. Only perform sensitivity tests and scenario tests on the key assumptions that were assigned. (face amount, earned interest rate, mortality rates, and first-year and renewal lapse rates).  No credit will be given for sensitivity tests or scenario tests in which you change any other assumptions.  

4. Your written report must be a stand-alone document.  Do not expect me to look at your model to get needed information.  Show the key results in your written report. Summary tables of key results should be given for all sensitivity test and scenario tests you perform and discuss.

For example, in class we showed sensitivity tests for Maintenance Expenses per policy for a male non-smoker age 45.  The base-line pricing assumption for Maintenance Expense is $10 per policy.  Results for plausible changes to this assumption are given in the table below. This is the type of table you should include in your report for each sensitivity and scenario test you perform.

Maint Expense                Risk Adj. IRR-YRT        Risk-Adj IRR- Level

              Per Policy                                       

                 $7.00                                        15.79%                      16.14%                             

   $8.00                                        15.55%                          15.81%

   $9.00                                        15.32%                          15.48%

                 $10.00                                      15.09%                          15.16%

                 $11.00                                      14.85%                          14.85%                    

                 $12.00                                      14.62%                          14.54%

                 $13.00                                      14.39%                          14.24%                                 

5. Do not rely solely on graphs to display your results. Graphs can sometimes be helpful.  However, they do not provide enough detail for careful analysis, so it is essential that you provide all of your key results in numeric form, such as in a table like the example above.  If you only show your results as graphs your grade will suffer substantially.

6. Test plausible outcomes in your sensitivity and scenario tests. For example it is not reasonable that our mortality experience is going to be double what we expect every year. The range of plausible results will be different for different assumptions. You should perform more than one test in each direction. You should test the entire range of plausible changes to the assumptions, which requires showing several tests in both directions, not just one or two.

7. Use the Data Tables what-if function in EXCEL to speed up your sensitivity tests and scenario tests, and to test a range of results.   I have posted videos on HuskyCT that show you how to do this, step-by-step.  The “Simple EXCEL model” in the Pricing Project Folder on Husky CT also shows you how to do this, step by step.

8. When you conduct your sensitivity and scenario tests, consider a Risk-adjusted IRR of 13% or more to be acceptable.  In other words, while Storrs Life’s pricing hurdle rate is 15%, its opportunity cost of capital is 13%.  If at plausible extremes the Risk-adjusted IRR stays above 13%, then that variable doesn’t pose much risk to Storrs Life.  Concentrate your risk discussion on those assumptions where changes in experience can plausibly lead to outcomes with Risk Adjusted IRRs of less than 13%.  This means break-even tests should be based on the 13% opportunity cost of capital, not the 15% hurdle rate!  Also, if you choose to discuss the net present value of your results, use a 13% interest rate to calculate the NPV!

9. Be sure to pay special attention to any assumptions that affect the two policies (YRT and Level Premium) differently-meaning in different directions, or in significantly different magnitudes. Explain these results!

10.  For scenario tests, please be sure that the assumptions you select for testing are dependent on each other. Explain why a change in one assumption would likely affect the other in the magnitude and direction that you tested.  Also, test related assumptions that matter!  If a variable doesn’t affect the sensitivity test very much, then it won’t impact the scenario test very much either.  So, don’t use that variable in your scenario test.

As an example, if I had required you to do sensitivity tests on the maintenance expense per policy you would have produced the results shown in item 4 of these helpful hints.  This assumption clearly poses little risk, as the risk-adjusted IRR never falls below 14.25%, and the affect of changes in this assumption on both policies is very similar.  So, this assumption would be a very poor choice to include in a scenario test.

11. Explain your results in a clear, thoughtful way. For example, based on the Maintenance Expense sensitivity test results illustrated in Item #4, we see that the Risk-Adjusted IRR for both the YRT and Level Premium products decreases if the Maintenance Expense per policy increases.  A good explanation of this result would be as follows:

“When the Maintenance Expense per policy increases, the proportion of annual premium that is needed to cover our expenses increases which in turn decreases the proportion of premium that is left for profit.  However, as shown in the table above, changes in this assumption affect both policy designs by a very similar amount, and within the entire range of plausible results for the maintenance expense per policy, the risk adjusted IRR never falls below 14.24% for either product.  We conclude that the Maintenance Expense does not pose a significant risk.”

Of course, I purposely illustrated a rather uninteresting example that required little explanation.   I left the more interesting ones for you!  When the products are affected differently, you must explain what is causing these differences.  For example, one product may be affected significantly more than the other by a change in a particular assumption.  If that happens, you must explain why.  It is not enough just to point out that one product is affected much more than the other.  You must explain why that happens!  And you must comment on the risk and pricing implications. That’s the important (and fun) part of being an actuary!

Of course, the critical thinking skill you demonstrate in your tests and explanations is a key part of your grade.  But keep in mind, the clarity of your explanations is also a key part of your grade. Your explanations and discussions of what you learned from each of your sensitivity tests and your scenario tests should be easily understood by anyone reading the report, and not something you have to be an actuary to understand.  After you write your explanations, ask yourself this:  “If I read this to my mother, would she understand it?”  If yes, you likely have a well written paper.  If no, try again! 

12. Be sure to provide a clear, specific recommendation as to whether or not Storrs Life should begin to sell a level premium term product, and, if so, at what premium rate per $1000. Your recommendation must be supported by, and consistent with the results shown by your sensitivity and scenario tests.

13. Please refer to the suggested Outline (posted on HuskyCT) to enhance the organization of your report.  

14. Do not be shy.  If you don’t understand something in the assignment or helpful hints, or just want to discuss what you are thinking with me, be sure to ask! This is nearly 28% of your grade!