= $162,889.46 without withdrawals. If they begin withdrawals at age

1 Guaranteed Lifetime Income from a Variable Annuity with a GLWB Rider (Preliminary Version) Floyd Vest, Sept. 2014 A person can get guaranteed income from their Variable Annuity with a Guaranteed Lifetime Withdrawal Benefit (GLWB) rider. Kitches says that almost no two variable annuity riders work the same, with a broad range of GLWB riders from one company to the next (kitches.com/blog). So we need to to read the fine print in the many pages of the contract and prospectus. We will review the Vanguard Variable Annuity with a GLWB rider since it is recommended by some columnists. To read about this product, go to a search engine and type in Vanguard Annuity with a guaranteed lifetime withdrawal benefit and Search, and click on the indicated site and print out the two page summary. For more information, you can call Vanguard and request a prospectus as we did. We read that when you deposit your money in the specified Variable Annuity funds and sign the GLWB rider contract, the money you deposit makes your Total Withdrawal Base (TWB). If you abide by the terms specified by the contract, the TWB can t decrease, but on the anniversary date, it can increase to a new TWB if your investment balance increases. You can leave your money in the program and let it grow, or at some date begin withdrawals at a specified yearly percentage of your current TWB based on your age. Even with withdrawals, your current TWB cannot decrease but it can increase. To figure your Maximum Annual Withdrawal (MAWA), multiply your Annual Withdrawal Percent by your TWB. For age 65 and a Joint Life Rider, the percent is 4.50%. The charge for the GLWB variable annuity rider is 1.20% of your balance plus an average annual Variable Annuity expense ratio of.70%. There are no surrender charges. Vanguard reserves the option of charging up to 2%. Commonly, this product is purchased by an investor who is near retirement, such as age 55, and expects to retire at age 65. They don t want to suffer through a severe downturn in stocks returns such as that which occurred beginning in year 2000 and running to 2010. (See Wikipedia.org, S&P 500.) You will designate your GLWB investment by choosing from three Vanguard Variable Annuities: Balanced Portfolio (60% to 70% stocks, 30% to 40% bonds), or two others: Moderate Allocation, and Conservative Allocation portfolios. As a remote example, as of Sept. 2014, a balanced portfolio of 60% stocks, 40% percent bonds, with a.26% expense ratio averaged a 8.50% return for the last ten years. As an example of a Vanguard GLWB Annuity, we might estimate a return of 8.50% +.26% - 1.20% -.70% = 6.86%. Example 1: We will not put variables in italics since they are not used in the TI 84. Consider a 55 year old who invests $100,000 at age 55 and earns 5% and at age 65 they have 100,000(1 +.05 ) 10 = $162,889.46 without withdrawals. If they begin withdrawals at age

2 65, this amount is their TWB from which they can withdraw 4.50% for a Joint Life Rider. They can receive guaranteed lifetime benefits even if withdrawals deplete the accumulated value of their account. We can run a program based on these assumptions out to age 95 and track their annual withdrawals W, their accumulated withdrawals A, and current fund balance B, with R =.05 = 5% and withdrawal percentage of Y =.045 = 4.5%. Once set at 4.5% of TWB, the annual withdrawals can never decrease but they can increase along with the current balance giving an increased TWB. Since R > Y =.047204 we will not have to revert back to an earlier locked in TWB = previous balance, but simply use the increased current balance. (See the Exercises for the.047204 = 4.7204%.) Program: GLWB : 0 A :.05 R : 1 X :.045 Y : 162889.46 B : 65 G : Lbl Z : Y B W : W + A A : B W E : Disp AGE, G : Disp A, A : Disp B, B : Pause : E (1 + R) B : G + 1 G : X + 1 X : If X = 32 : Stop : Goto Z

3 Reading the above Program GLWB you can see that Age = G starts at age 65. Y B (balance in fund) = W (withdrawal). W + A = A accumulates the sum of annual withdrawals. B W = E is balance after withdrawal. E (1+R) = B is new balance for the next year. The program reports: AGE G, A A, B B. There is a Pause for the end of each year. To pass Pause, Press Enter. When you run Program GLWB, you will see B 162889.46, After Enter, you will see AGE 65, A 7330.03, B 155559.43. After Pause, you will see AGE 66, A 14680.21, B 155987.22. (See the Exercises (?#17) for the development of this investigation in term of mathematical formulas.) The funds in the variable annuity accumulate tax free, and the percentage withdrawals are taxed depending on what type of funds were invested. If all funds are withdrawn, the investor receives the account balance )page 32 of the Vanguard Prospectus). If IRS mandatory withdrawals are required, this may cause complications. You Try It #1 Write Program GLWB in your TI 84 or other device. For the programming in the TI 84, see Chapter 16 of the manual, and for If x = 32, see page 2-25 for the Relational Test Menu. You may prefer to write a better, more general, more informative program, or spreadsheet. Run the program and (a) Report the first withdrawal W + 0 A, (b) Report the A including the second withdrawal, (c) Does the account balance B and the TWB increase? (d) What is the accumulation of withdrawals A at age 95? (e) What is the account balance B at age 95? (f) What is the rate of return on the investment? (g) At what rate do the balance and withdrawals increase? Do they keep up with your estimate of inflation? A person could write a program with R <.047204 and an inequality test going back to the latest and guaranteed TWB and resulting in a first withdrawal which continues constant for the duration of the program. One would also trace the accumulated A and the declining balance B. (See the Exercises.) An alternative is to investigate the historical annual returns for a portfolio and build a spreadsheet giving fund Balance, Withdrawals, Accumulated Withdrawals, TWB, AGE, after the above expenses for the GLWB and a fund expense ratio. Such a program would include an inequality test and a loop. Side Bar Notes: Are you under estimating your lifespan? Once you reach age 65, there is a 58% chance you will live to age 85, a 38% change you will live to age 90, and a 19% you will live to age 95 (TIAA Participant, Nov. 1990). Time discounting in Utility Theory refers to whether a person prefers a benefit now or prefers a better benefit in the future. In a Washington University study, of employees who invested in a 401k and those that did not, there was a positive correlation between investing in a 401k and better health practices, and good blood tests (blood sugar, cholesterol, etc.) (AAII Journal, Aug. 2014, p. 5).

4 GLWB insurance riders can cost an extra 3% above the variable annuity which could have an expense ratio of 2%. Kitches (Kitches.com/blog) says that no two variable annuity riders work the same, with a broad range of their own unique features and benefits. As a result, there is pressure on the investor and the salesman to read carefully the more than 200 pages of details. Notice that the above Vanguard rider did not require a salesman. Many programs include a phantom benefit base which does not have a liquid cash value. This fact could be overlooked by the investor and the sales presentation. Securities and Exchange Commission sends enforcement referrals to 20% of broker dealers, and for less serious offences 50% received deficiency letters. For registered investment advisors, 90% received deficiency letters (Mutual Funds magazine, June 2000, page 90). What false impression does the following ad give? For a single contribution of $2000 invested for twenty years, for a Roth IRA you pay $778 in taxes, for a Traditional IRA you pay $2610 in taxes. Can you make their numbers work? The money earns 8% and the tax rate on a lump sum withdrawal is 28%. See the article in this course Does T. M. Need a Roth? Stock earnings expectations too high. From Mutual Funds magazine, May 1998, page 17: when investors were asked for expectations for the next ten years, they averaged 13%. This was after S&P 500 total returns of 37.58% in 1995, 22.96% in 1996, and 33.36% in 1997. From the end of 1997 for $30.48 invested in the S&P 500, it by the end of 2007 grew to $54.12. What was the total return rate for these ten years? Unloved mutual funds. (Smart Money, March 1998, page 46) Since 1987 funds that lost the most assets in any particular year because investors yanked their cash out proceeded 78 percent of the time to beat the average equity fund over the next one, two and three years. They did even better when compared with popular funds that received more investor cash, posting a higher return 89 percent of the time. Funds that investors craved in any one year fell behind the average equity fund 70 percent of the time over the next few years. More reward, less risk. (Mutual Funds magazine, April 1998, page 56) Over the past five years, the S&P 500 produced an astounding annualized return of 20%, twice its historical norm. Over that period, only 3% of all equity funds 99 in all beat the index. But even among the 99 winners, most carried far more risk than the S&P 500. Exercises: Show your work. Label answers, numbers, and variables. Conduct discussions in complete sentences. Provide documentation for your programs. #1. Show that with Y =.045, if (1 + R)(1 Y) = 1 + 0, then R =.0471204. Interpret. For Program GLWB, if R <.0471204 what happens? #4. If B remains a constant $162,839.46 each year, how much does the insurance company and variable annuity collect each year? If B increases at the rate K, give a formula for K. #5. If R > Y, give a formula for the rate at which withdrawals increase, and the rate at which the balance increases. What rate R would the investor have to earn for withdrawals to keep up with 2.25% inflation?

5 #6. Write a program reporting for each year W, B, A, and age, somewhat similar to Program GLWB, with the beginning balance of $162,889.46, the rate of withdrawal of 4.5%, the rate of return on the fund of 4%. What is the balance B in the fund at age 95, and the accumulate withdrawals? #7. If W s increase at the rate K, give a formula for the sum A of W s after n years. #8. Assume 100 people each contribute $100,000 to an insurance company at age 65. Each receives $10,000 at the end of each year up to and including their birthday. Assume 42 die on their 85 th birthday, 20 die on their 90 th birthday, 19 die on their 95 th birthday, and 19 die on their 98 th birthday. How much did the insurance company collect from these people? What is the expected payout? What is the difference? Discuss this difference. Discuss what happens if the insurance company makes 6% on the outstanding funds. #9. The AAII Journal reported from Jeremy Siegel, The Future of Investors that from Jan. 1802 to Dec. 2013, the real rate of return on the dollar was -1.4% per year. What was the average annual rate I of inflation? For the same period, the real rate of return for stocks was 6.7%. What was the average nominal rate of return? Their graph indicates that the real value of $1 in stocks increased to $930,550. Check their figure. According to their graph, inflation didn t set in until about 1940. Previous to 1911, there were long periods of deflation. What economic event might have started inflation? #8. A 65-year-old man can invest $100,000 in a deferred income annuity which pays $28,695 a year for life when he reaches age 80. Calculate the internal rate of return (irr) if he live to age 95 and collects for 15 years, and collects nothing for the first 15 years. On the TI 84, you can use the irr( function. If he selects a 3% annual increase in payments beginning at age 80, his first payment is $24,300. If he lives to age 95, does he still make 6.73%? If he selects a return of premium benefit, if he dies before age 80, the payment is reduced to $21,601. (Kiplinger s Personal Finance, 10/2014, page 58) What is the probability that he will live to age 95? Estimate the probability he will live to age 80. What percent don t live to age 85? What percent don t live to age 95? #9. Scott Burns (Denton Record Chronicle, Aug. 31, 2014) gives an example of a lady who on her 55 th birthday, invests $100,000 in a GLWB rider with an insurance company which guarantees to double her money to $200,000 in a benefit base in ten years. On her 66 th birthday she can begin withdrawing 5% of her benefit base which is $10,000 per year for life and more if her fund increases. Scott estimates that the actual cash value at age 65 is $148,000. (a) What is her irr if she live to age 81? To age 82? To age 85? To age 75? You may need to write a Program: SCOTT to answer these questions. (b) If the fund earns 4% on the cash value, at what age is the cash value depleted? If the benefit base earns 4%, at what age is the benefit base depleted? What happens if these are depleted? (c) Scott says that the insurance company will make 4% on Cash Value each year. By the time the Cash Value is depleted, how much has the insurance company collected? #10. Examine the value of one dollar invested in the S&P 500 Index of stocks from 2000 through 2010. (See Wikipedia.org, S&P 500.) What was the rate of return? Did it keep up with inflation? In what year did the total return of the S&P 500 catch up with inflation? When were the bad losses and by how much? What was considered to be the causes? (See the article

6 in this course, Three Sigma Events. ) What has the S&P 500 done at the time you are working this problem? #11. You can learn about various guaranteed income programs from many sources. For example consider cbsnews.com/news. Search Retirement income, GLWB, or Search one of their authors Steve Vemon. Another author is Wade Pfau. Another is Michael Kitces. List and discuss the advantages and disadvantages of various programs such as fixed accounts, insurance policies, immediate annuities, GMIB riders, indexed annuities, inflation adjusted annuities, for a few. Some sites specialize in annuities. One site says, I hate annuities. #12. The sequencing effect. From 1968 to 1998 an investment averaged 11.7% and $250,000 is calculated to pay for the first year $21,250 and increasing at 3% per year for 30 years. But it actually paid out for only 13 years. (a) Verify their calculations. (b) Why with an average of 11.7%, did the investment historically only pay 13 years. See articles in this course about the sequencing effect such as The 4% Rule for Retirement Withdrawals. (c) Graph the curve of the remaining value of the retirement fund for their calculations. (d) See if you can construct a similar historical example. (Mutual Funds magazine, page 75) #13. Two-to-one leverage. From Mutual Funds magazine, May, 1998, page 48: Example: Say the market advances 10%, then declines 10%, then advances 20%, and then falls 10%. If you own an index fund that tracks the market precisely, your total return is 6.9%. (a) Check the above results. Now, say you own a mutual fund, Pro Fund UltraBull, with two-to-one leverage, gains and losses are magnified by two. The above returns would produce +20%, -20%, +40%, and -20%. Compounding yields 7and ½ percent total return. (b) Check these results. Discuss both results (a) and (b). (c) Say the market advances 11.1% and then falls 10%. The total return is 0%. Check these results. (d) A mutual fund providing twice the above market s volatility would produce a 2.2% loss. Check this figure and generalize. (e) Say the market advances 25%, and loses 20%, the total return is 0%. Check this result. What return does twoto-one leverage produce? (f) What happens if the market moves straight up or straight down? Do some examples and generalize. #14. No-Load Funds and Load Funds. Load funds typically charge a sales commission to purchase. No-load funds don t charge a sales commission. In a study from 1993 to 1997 inclusive, for average annual returns, 1993 1994 1995 1996 1997 No-Load Funds 13.11% -1.04% 31.64% 20.26% 25.07% Load Funds 13.32% -1.60% 31.41% 19.25% 23.65% No-Load Advantage -0.21% 0.56% 0.23% 1.01% 1.42% For load funds the expense ratio averaged 1.64% and for no-load funds it average 1.15%. (a) From the table, calculate the average total returns for no-load and load funds. (b) If the market averages 9.5%, calculate the after expense ratios accumulation of $10,000 over 35 years.

7 Discuss. (c) What would be the advantage of a load fund? A commission is what percent of a mutual fund purchase? At the time of the above report, two-thirds of money invested in mutual funds has come through financial advisors who charge commissions or loads. (Mutual Funds magazine, May 1998, page 75) #15. Invesco Asian Growth mutual fund lost 38% of NAV. It was hit by mass redemptions taking their profits. As a result of selling stocks to pay the redemptions, it reported taxable gains of 21% of NAV. What percent of NAV was lost by a person who invested just before these events assuming taxable gains were taxed at 15%? Several cases have been much worse. (Mutual Funds magazine, May 1998, page 63) If they invested $100,000, how much did they lose? #16. In 1999, the Nasdaq-100 stocks had an average Price to Earnings Ratio (P/E) of the atmospheric figure of 200. Jeremy Siegel, Finance Professor at Wharton School of Business said The Nasdaq is not worthy of this run-up, as great as these companies are. I m afraid it won t end well. (Mutual Funds magazine, 1999, page 23) Go to Wikipedia.org and trace the Nasdaq- 100 since 12-31-1999. See also finance.yahoo.com. Discuss the history and names of the events. Do some mathematical examples. Name some of the components of the Nasdaq-100. What type of companies are they? Where is the Nasdaq-100 at the time you are working this problem. What is the average P/E? What happened to CISCO stock and where is it now? What is the average P/E for the S&P 500? What happened to the Nifty Fifty stocks in 1973. What happened to some of the companies? #17. Replace Program GLWB with a set of equivalent variables with general equations and general assumptions. Use an index n starting at B 0 = the beginning balance. W 0 is the first withdrawal equal to Y B 0. W n is the nth withdrawal after W 0. B n is the nth balance after B 0. A1 W0 W1. An An 1 Wn. At Age 65, n = 0, at Age 66, n = 1. At Age n G, G n = 65 + n. R and Y have the same meanings as in the program. Given Y, there is a general assumption about R. References: Notice that in Program GLWB, we used 4.50% annual withdrawals. For the 4% rule for retirement withdrawals, see in this course The 4% Rule for Retirement Withdrawals and similar articles. For a discussion of variable annuities, see the article Investing in Tax Deferred Variable Annuities. For the history of the stock market earnings, see The S&P 500 Index of Stocks, and the article Three Sigma Events. For evaluation of different retirement withdrawal strategies see Evaluation of Five Methods of Retirement Withdrawals, which includes Table 2 of 5% life expectancy for a couple age 65 to 95:

8 Age 65 70 75 80 85 90 95 5% Life expectancy in years 37 33 27.7 22.2 16.9 11 5.5 Fit a line to this data for purpose of interpolation. You will be surprised at R and 2 R. For mortality considerations in life insurance, see Mortality and Money, Mathematics and Life Insurance. For more information on the Vanguard Variable Annuity GLWB rider, Search Vanguard Variable Annuity Guaranteed Lifetime Withdrawal Benefit on the internet which includes a table of annual percentage withdrawals for different ages. For a technical, mathematical analysis of when to begin withdrawals from a GLWB rider, see Optimal Initiation of a GLWB in a Variable Annuity which is hot linked in kitces.com/blog. For a free course in financial mathematics, with emphasis on personal finance, for upper high school and undergraduate college, see COMAP.com. Register and they will e-mail you a password. Simply click on an article in the annotated bibliography, download it, and teach it. Unit 1: The Basics of Mathematics of Finance, Unit 2: Managing Your Money, Unit 3: Long- Term Financial Planning, Unit 4: Investing in Bonds and Stocks, Unit 5: Investing in Real Estate, Unit 6: Solving Financial Formulas for Interest Rate, Unit 7: More Advanced or Technical. For about thirteen more advance or technical articles, see the UMAP Journal at COMAP. The last section is Additional Articles on Financial Mathematics or Related to Personal Finance. In all, there are about eighty articles.