Notes and References
Introduction
1. Eckhart Tolle, The Power of Now (New World Library, 1997).
2. Daniel Kahneman, Thinking, Fast and Slow (Penguin Books, 2011).
3. Shane Frederick, George Lowenstein, and Ted O’Donoghue, “Time Discounting and Time Preference: A Critical Review.” Journal of Economic Literature Vol. XL (June 2002): 351–401.
Chapter 1
4. The most important of the many was Stephen G. Kellison, The Theory of Interest (R. D. Irwin, 1970).
5. All the details on what it takes to become an actuary can be found at the Society of Actuaries website (www.soa.org).
Chapter 2
6. Some readers have pointed out that I left out the fact that by buying a new refrigerator I was accelerating the point where I would need to buy another one (and another one after that). In other words I should have been calculating “the Present Value of all future refrigerator expenses.” It turns out that, while true, this has a very minor impact on the analysis and doesn’t change the result, especially when you consider that discount rates for the distant future (at least mine) are higher than 5%. This point also is true for the “air duct” example a little later on.
7. To my mind, Steve Vernon’s books provide the best (and least biased) advice available on saving for and planning your retirement. He has written five of them and they can all be obtained (as well as other good information) at his website (www.restoflife.com).
Chapter 3
8. The world has changed somewhat, but even as of 2005 there were 31 credentialed actuaries disclosed in SEC proxy information as being in the “top 5” of major insurance companies, and by the nature of the industry, high positions in Finance and other technical departments almost, of necessity have to be filled by actuaries. See for example (http://actuarialoutpost.com.actuarial_discussion_forum/showthread.php?t=12658).
9. For a succinct and well-presented history of the actuarial profession and its role in founding the insurance industry see http://www.actuaries.org.uk/research-and-resources/pages/actuarial-history-research and download Chris Lewin’s 2007 seminar presentation on the subject.
Chapter 4
10. For those more quantitatively inclined, this note will give you more of the math behind Present Value. To derive the full general formula for a Present Value, let’s first consider one of the most prevalent examples of present value that we see in the world, specifically the determination of our monthly payments when we buy a house and take out a mortgage.
Your Mortgage—Present Value When Payments are Certain
Most people understand that when you take out a 30-year mortgage, the higher the interest rate, the higher your monthly payments will be, but few people understand how those monthly payments are calculated. In fact calculating loan repayments is just the mirror image of a Present Value calculation, and an expansion of the above formula to consider multiple payments. If I take out a thirty-year mortgage on a $400,000 loan and the interest rate I get is 5%, my monthly payments will be about $2500 or $30,000 per year. If instead I look at it the other way and ask the question “what is the Present Value (using a 5% discount rate) of 30 years of monthly payments of $2500 per month?” The answer is $400,000. The way to see this is to think about each of those 360 monthly payments as separate present value calculations that when they are all added up sum to the amount of the loan. So even though the sum of all those payments equals $900,000 (i.e., 360 × $2500), the present value of the payments is exactly equal to the $400,000 you borrowed. Oversimplifying a little (by assuming each year’s payments are paid in a lump sum at the end of the year) we can show this in numerical terms as follows:
$30,000 × (1/1.05) + $30,000 × (1/1.05)2 + …
+ $30,000 × (1/1.05)30 = $400,000
Now consider what happens if mortgage rates go down to 4%. Everyone knows that when rates go down you should refinance to reduce your monthly payments, but the other way of looking at it is that because discount rates have gone down, the Present Value of all those future payments is now more than the $400,000 that you borrowed and you need to do something about it. You can check this for yourself by changing 1.05 to 1.04 in the above equation.
Life Insurance—Present Value When the Payment is Uncertain
The example of mortgage payments illustrates how to project the future and discount it back to the present to produce a Present Value when we are sure about what is going to be paid and when. But what if we are not? The simplest example of such a case is when you buy a single premium life insurance policy. Let’s say you are thirty-five years old and you have a three-year old child. Suddenly you realize that even though you are planning your financial life in such a way that you will be able to save enough to put her through college, you need to do something about the risk that you might die before then. In particular let’s say you expect that fifteen years from now you will have accumulated the $400,000 you think you will need to pay for four years of college, but if you die before then you won’t have saved enough. Putting aside the complexities of exactly how much the actual shortfall would be and how much insurance you really need, let’s say you decide to keep it simple and buy a life insurance policy that will pay your spouse $400,000 if you die some time in the next fifteen years and therefore be able to send your daughter to college. Let’s further say that you just want to pay the insurance company one single premium that will cover you for the whole fifteen years. How much will such a policy cost and how does the insurance company determine it? To see how, we have to first understand that the amount of the premium should be the Present Value of all the future possible death benefit payments the insurance company might have to make if you were to die sometime in the next fifteen years. Now one approach to this might be to figure out the probability that you will die between the ages of thirty-five and fifty (about 5%) and apply that to the $400,000 to get the premium. But $20,000 (5% of $400,000) is too much because the $400,000 payment might not have to be made until fourteen years from now and we’ve already seen that $400,000 payable many years in the future is worth a lot less than $400,000 today. So what we need to do is to reflect both the uncertainty of the payment itself and the discount for the fact that if the payment is made, it will be made some time in the future. So much like we did with our mortgage payments, we need to evaluate the present value of each possible payment and then add them up. Specifically we first define the term q(x), or simply qx, as the probability of someone age x dying before she reaches age x + 1. So q35 would be the probability of dying between ages thirty-five and thirty-six. Then assuming a 5% discount rate we calculate the premium as follows:
Premium = ($400,000 × q35) + ($400,000 × q36 × (1/1.05)) + ($400,000 × q37 × (1/1.05)2)+ … + ($400,000 × q49 × (1/1.05)14)
If you can understand the above equation, you understand present value. In fact the basic equation for present value in its general form can be expressed as:
SUM (t = 0 to N) of CF(t) × P(t) × (1/(1+i))t where
N = the number of years that is being considered in the calculation CF(t) = the payment that is expected in year t (assuming it is made)
P(t) = the probability that the payment in year t is actually made i = assumed interest/discount rate
and “SUM (t = 0 to N)” is usually written as: 
, so that the whole formula with this notation is: 
The above equation is the complete and general formula for calculating Present Value.
Chapter 5
11. Mark is not his real name. Throughout this book I have tried to be as faithful to history as possible by contacting the people I am writing about directly. In this case, my friend objected to his actual name being used, so, at his request I have changed his name and occupation but not the essential facts of the story.
Chapter 6
12. Kurt Vonnegut, Slaughterhouse-Five (Delacorte, 1969).
13. Fritz Leiber, The Big Time (Ace Book, Inc, 1961).
14. Isaac Asimov, Foundation (The Foundation Series) (Spectra [Revised edition], 1991).
15. James Gleick, Chaos (Penguin Books [Revised edition], 2008).
16. Robert Pirsig, Zen and the Art of Motorcycle Maintenance (Bantam Books [New Age edition], 1981) p. 255.
17. Ibid. pp. 28–32.
18. For a description of the match, see www.chessgames.com/perl/chess.pl?tid=54195
Chapter 7
19. See for example chapter 11 of Nassim N. Taleb’s Fooled by Randomness (Random House [Trade Paperback Edition], 2005), in which the author discusses a myriad of ways where we fail to accurately assess the probability of events and describes, in some detail, the groundbreaking work that Kahneman and Tversky have done in this area.
20. According to www.baseball-reference.com, over his career, Pedro Martinez gave up only 760 walks, putting him a lowly 286th on the all time list, but he hit 141 batters putting him comfortably in the top thirty of all time. As far as I can tell, his ratio of .186 is by far the highest of anyone with more than 100 HBPs. Interestingly, Greg Maddux at .137 (137/999) is not too shabby, either, as he is one of only a handful of other pitchers with both more than 100 HBP and less than 1000 BBs over his career.
21. See again the Chris Lewin presentation mentioned in note 9.
22. Among other things, David’s most important work on the appropriate way of funding a pension plan (“Objectives and methods for funding defined benefit pension schemes,” Journal of the Institute of Actuaries, September 1987: 155–225) was never, in my opinion given the credit it deserves, and to this day very few actuaries have heard of the DABM (Defined Accrued Benefit Method).
23. See en.wikipedia.org/wiki/Bell_System
24. See en.wikipedia.org/wiki/Econometric_model
25. Nassim N. Taleb, Fooled by Randomness, Random House (Trade Paperback Edition), 2005.
26. Ibid. pp. 113–115.
27. Ibid. pp. 116–131.
28. Ibid. pp. 126–127.
29. See en.wikipedia.org/wiki/General_equilibrium_theory
30. See FCC Record, Volume 07, No. 09, p. 2724, April 20–May 1, 1992.
31. Nassim N. Taleb, The Black Swan (Random House [Trade Paperback edition], 2010).
32. From 1/1/1982 to 1/1/2000 the S&P 500 rose from 122.55 to 1469.25, a return of almost 15%/year
33. Taleb, Fooled by Randomness, 113–115.
34. There were countless postmortems after the LTCM collapse. See for example: Philippe Jorion, “Risk Management Lessons from Long-Term Capital Management,” European Financial Management 6 (September 2000): 277–300.
Chapter 8
35. Peter Neuwirth, “The Time Value of Time.” Contingencies, Vol. 9 No.1 January/February 1997: 47–50.
36. Frederick, Shane, George Lowenstein, and Ted O’Donoghue, “Time Discounting and Time Preference: A Critical Review.” Journal of Economic Literature 40: 351–401.
37. Their website is at disability-insurance-specialists.com
38. One measure of this slipperiness can be seen by the extremely strong correlation between economic downturns and the level of disability payments made. This is not just with respect to applications for disability benefits, as one would expect when people experience economic hardship and seek income from other sources, but it turns out that when times are tough, the actual rates of disability increase as well. See for example the Statement of Stephen Goss (Chief Actuary of the Social Security Administration) given before the House Committee on Ways and Means on March 14, 2013 (www.ssa.gov/legislation/testimony_031413a.html).
39. See en.wikipedia.org/wiki/Discounted_cash_flow
40. Nassim N. Taleb, The Black Swan (Random House [Trade Paperback edition], 2010).
41. Frederick, Shane, George Lowenstein, and Ted O’Donoghue, “Time Discounting and Time Preference: A Critical Review.” Journal of Economic Literature 40: 351–401.
42. See, for example www.forbes.com/sites/joannmuller/2014/02/21/pensions-spared-worst-pain-in-detroit-recovery-plan/.
43. See, for example www.nytimes.com/2013/12/04/us/politics/illinois-legislature-approves-benefit-cuts-in-troubled-pension-system.html?_r=0.
44. See www.oregon.gov/pers/docs/earnings_crediting1946-2012.pdf
45. See www.oregonlive.com/politics/index.ssf/2012/11/oregon_pers_money_match_pensio.html for an excellent article by Ted Sickinger, which includes a general description of how the Plan works as well as the history of how the Money Match arose and what steps were taken to remedy the problems that were created.
46. See www.oregon.gov/pers/docs/earnings_crediting1946-2012.pdf and find the amounts credited on “Money Match” accounts under the column headed “Tier One – Credited %.”
47. In 2000 the average PERS participant retiring with thirty years of service received 100% of his pre-retirement income. This can be seen on page 5 of “PERS by the Numbers” September 2012 available at www.oregon.gov/pers/docs/general_information/pers_by_the_numbers9-2012.pdf
48. Ibid. p. 17.
49. See for example Justin Falk, “Comparing Benefits and Total Compensation in the Federal Government and Private Sector” Working Paper Series of the Congressional Budget Office, Washington, DC, January 2012.
50. See page 3 of “PERS by the Numbers” described in note 47.
Chapter 11
51. The test was Chronic Villus Sampling (CVS) and you can read about it at americanpregnancy.org/prenataltesting/cvs.html. The 1% probability of miscarriage is mentioned.
52. The probabilities of having a child with Down syndrome at different ages are can be seen at www.marchofdimes.com/baby/down-syndrome.aspx
53. See for example Steve Vernon, Money for Life (Rest-of-Life Communications, Oxnard, California, 2012), pp. 55–58.
54. This is explained in concept on the American Council for Gift Annuities website at www.acga-web.org/about-gift-annuities-top/the-philosophy-of-gift-annuity-agreements.
55. Robert B. Avery and Michael S. Rendall, “Estimating the Size and Distribution of Baby Boomers’ Prospective Inheritances,” American Statistical Association, Proceedings of the Social Statistics Section, 1993. pp.11–19.
56. Charitable Remainder Trusts are explained in detail on the Planned Giving Design Center’s website at www.pgdc.com/pgdc/charitable-remainder-trusts.
Chapter 13
57. One of the best discussions of how the retirement crisis arose can be found in Sylvester Scheiber, The Predictable Surprise (Oxford University Press, New York, 2012).
58. There is a wealth of data on this point available on the Towers Watson website (www.towerswatson.com).
59. “More U.S. Workers Willing to Trade Pay for Extra Security and Richer Retirement Benefits, Towers Watson Survey Finds,” from www.towerswatson.com, February 27, 2012.
60. The fact that the predominant retirement program at most companies is now defined contribution and how those plans are managed is discussed in “The Defined Contribution Plans of Fortune 100 Companies” from www.towerswatson.com, February 2011.
61. Steve Vernon, Don’t Work Forever (Wiley, 1995).
62. Steve Vernon, Live Long and Prosper (Wiley, 2004).
63. In addition to the two above, Steve’s other books include The Quest (Rest-of-Life Communications, 2007), Money for Life (Rest-of-Life Communications, 2012), and Recession-Proof Your Retirement Years (Rest-of-Life Communications, Fourth Edition, 2014).