Advice on a Sustainable Retirement Investment & Spending Plan - Case Study Example

Advice on a Sustainable Retirement Investment & Spending Plan The purpose of this advice is to present a best option for an investment and spending plan for our client, who is presently 63 years of age and has a retirement fund of $450,000 with which to work, so that he can be reasonably confident of having a comfortable yearly income for the rest of his life. As the client no doubt understands, there is a bit of uncertainty in calculating a plan like this, because the lifespan over which it will have to be applied and the future rates of returns on investments cannot be known. Therefore the plan is presented as a probability; the calculations required necessarily result in a risk factor of failure of the plan – that is to say, the chance that the client will run out of money before the end of his life – which is expressed as a percentage, but it may be helpful for the client to consider this from the opposite, positive point of view, the probability of success. Since we do not have current income information for the client, the assumption is made that he wishes to retire now, and will not be receiving any income apart from the returns on any investments made with his existing retirement fund. The majority of Australians surveyed feel a minimum retirement income of $30,000 is necessary for a comfortable lifestyle, and in the client’s age group, slightly more than half of those surveyed feel an income of $40,000 or more is required.1 At $40,000 a year, the client’s nest egg will last 11.25 years; at $50,000 a year, it will only last for nine years. Our client, however, can expect a retirement lifespan of between 14 and 43 years with an average life expectancy of slightly more than 20 years and a reasonable lifespan for planning purposes of 30 years (see Technical Note), so obviously some earnings must be generated from the retirement fund. The absolute upper limit of the probability of ruin – that the fund will be depleted before the end of the client’s life – is 25%2, and so our task is to present investment and spending options that: Provide an annual income of $40,000, Cover a period of 30 years or longer, and Have a risk of ruin of less than 25%, preferably very much less. The client is presented with two options: a conservative approach comprising an investment allocation of 35% to growth assets such as domestic and international equities (stocks) and properties, and 65% to safe assets such as cash instruments and bonds, and a typical balanced approach of 60% growth and 40% safe assets. Either plan will be suitable for that income level – provided it is kept constant – has very little risk of a negative return in any year, and an equally low risk of running out before the planned 30-year life cycle of the plan. Under Option A, the more conservative option, the expected return (after deduction of management fees totalling 1.12%) would be 7.06% per annum, with a range between 1.1% and 13.2% possible. Under the more risky Option B, the management fees would be slightly higher at 1.17%, the average expected return is a bit lower at 6.75%, and there is a slight although mathematically very small (see Technical Note) risk of a loss in any given year of up to 1.2%. The potential return, however, is much higher, ranging all the way up to 15.75%. The client’s level of comfort and appetite for risk will be his best guide to deciding which plan is right for him. Technical Notes Expected Lifetime: The average life expectancy for a 63-year-old Australian male is 20.14 years, with a mortality rate λx of 0.00936.3 The probability of the client living longer than the average life expectancy is given by the equation Where T is the remaining lifetime random variable and s is the average life expectancy, which yields a probability in this case of 82.8%. The expected and median values of the variable T are given by the equations E(T) = 1/λ and Median(T) = ln(2)/λ, and yield 106.84 years and 74.05 years, respectively.4 20.14 years brings our client to age 83. For the client’s overall plan, any risk of ruin over 25% is considered unacceptable, so if that same probability is applied to the expected lifetime, a result of 75% from the above equation is reached between ages 93 (75.5%) and 94 (74.8%). Hence, the 30-year expected lifespan of the overall plan. Asset Allocation, Expected Returns, and Volatility: The two investment options presented are typical of those offered by most fund managers.5 Table 1 shows the average yearly returns over a 16-year period and the volatility for various assets. Volatility is an annualised function, usually calculated on a daily, weekly, or monthly basis. Using Microsoft Excel, volatility for any given set of returns can be easily calculated using the formula (=STDDEV(cell:cell)*SQRT(n)), where n represents the interval of the return (daily, weekly, monthly) in a year-long period. This Excel notation is an expression of the equation6 Volatility is calculated from the historical monthly asset returns data provided for this report. Yearly Average Returns & Volatility for Historical Assets International Equities Australian Equities Australian Property Australian Bonds Cash Consumer Price Inflation AC World index -ex Australia DS-calc S&P property UBS composite UBS Bank bills Interpolated Yearly % Return Yearly % Return Yearly % Return Yearly % Return Yearly % Return Yearly % Change Year 1990 -12.5222% -11.9130% -4.0251% 17.6517% 15.1498% 0.5948% 1991 21.1663% 36.9351% 12.1875% 22.3890% 10.6631% 0.3017% 1992 6.4129% -0.7911% -3.4551% 10.1649% 6.7099% 0.0904% 1993 24.1233% 35.8002% 21.7392% 15.2817% 5.2610% 0.1384% 1994 -7.8908% -5.8087% -15.9958% -4.6425% 5.2129% 0.1523% 1995 22.7530% 20.5034% 5.7202% 17.3565% 7.7323% 0.3614% 1996 5.8815% 14.6577% 5.0007% 11.3632% 7.3579% 0.2396% 1997 35.9581% 15.9211% 13.2544% 11.6680% 5.4945% 0.0331% 1998 27.5632% 17.8393% 14.9511% 9.2568% 5.0238% 0.0582% 1999 17.5480% 16.6954% -14.7817% -1.1879% 4.8971% 0.1197% 2000 1.9097% 2.1697% 12.0701% 11.4580% 6.0664% 0.3372% 2001 -8.1260% 9.7017% 6.2166% 5.4229% 5.1549% 0.3777% 2002 -29.2212% -9.2845% 4.1906% 8.5188% 4.6664% 0.2475% 2003 1.0372% 13.3873% 1.0334% 3.0523% 4.7926% 0.2327% 2004 11.0719% 23.5096% 24.6404% 6.7721% 5.4782% 0.1916% 2005 17.5396% 20.2341% 3.2354% 5.6586% 5.5804% 0.2182% 16-year average 8.4503% 12.4723% 5.3739% 9.3865% 6.5776% 0.2309% Volatility 14.1242% 12.5918% 10.4214% 4.4078% 0.8021% Table 1: Average annual returns and volatility of historical assets Option A 35% growth assets 65% safe assets Option B 60% growth assets 40% safe assets In either option, growth assets will have an expected annual return of 8.7655% (average of the returns on Australian and International Equities and Property over the 16-year historical period), and an expected volatility of 12.3791% (average of those three categories over the same period). The safe assets will have an expected annual return of 7.9821%, and an expected volatility of 2.6050%. The difference between the two options is, of course, the proportions of the total investment to which these expected return and volatility figures apply. Option A has an expected overall annual return of 8.2563% with a volatility of 6.0259%, and Option B has an expected overall annual return of 8.4521% with a volatility of 8.4695%. Including management fees of 0.5% p.a. for cash funds and 2.5% p.a. for growth funds reduces the returns for Options A and B to 7.0563% and 6.7521%, respectively. Expected Stochastic Present Value (SPV) of the Portfolio Options: We now have the figures necessary to compute the expected SPV and the probability that the SPV is greater than the initial investment amount of $450,000, using the equation7 For the probability (using the cumulative gamma distribution function of Excel to save time), and For the expected SPV, where w = the initial investment ($450,000) μ = the expected annual return (either .070563 or .067521) σ = the expected volatility (either .060259 or .084695), and λ = the implied mortality rate, which is equal to ln(2)/14.05, or 0.0493. The expected value of SPV is equal to 8.6059 for Option A and 1.3940 for Option B. In either case, the probability that the SPV is greater than the initial investment amount is positive, but infinitesimally so (values of 1.928 x 10-29 and 9.474 x 10-23, respectively). When the volatility is taken into consideration, it would be possible that the client could lose money in any given year under the riskier Option B, but there is a potential for a return of up to 15.75%; under Option A, earnings would be a minimum of 1.11%, and range upward to about 13.16%. To test the risk of the investment earning a negative return in any year, we apply the probability law for the total return Rt with the equation8 Where t is the 30-year timeframe of the plan, and x = 0. This is a cumulative normal distribution function which can also easily be done with Excel. In both cases, the risk of a negative return is so low (2.08 x 10-8 % for Option A and 1.78 x 10-3 % for Option B), that it can be virtually disregarded. What is not accounted for by the Stochastic Present Value method, however, is the increase in spending that might occur due to the increase in consumer prices, which as can be seen in Table 1 vary greatly, but have a long-term annual average increase of 0.2309%. If that rate remains constant over the 30-year term, and if the client increases spending to match inflation, at five years his withdrawal from the funds will equal $40,368; at 10 years, $40,647; at 20 years, $41,782; and at 24 years Option B will become unsustainable, with Option A falling into ruin in Year 25: Year A B 7.0563% 6.7521% Withdrawn Balance A Balance B 0 450000 481753 480384 481753 480384 1 481753 480384 515746 512820 40000 475746 472820 2 475746 472820 509316 504745 40092 469224 464653 3 469224 464653 502333 496026 40184 462149 455842 4 462149 455842 494759 486620 40276 454483 446344 5 454483 446344 488855 476481 40368 448487 436113 6 448487 436113 480133 465559 40461 439672 425098 7 439672 425098 470696 453801 40554 430142 413247 8 430142 413247 460494 441149 40647 419847 400502 9 419847 400502 449472 427544 40740 408732 386804 10 408732 386804 437573 412921 40834 396739 372087 11 396739 372087 424734 397210 40928 383806 356282 12 383806 356282 410888 380338 41022 369866 339316 13 369866 339316 395964 362226 41116 354848 321110 14 354848 321110 379887 342791 41210 338677 301581 15 338677 301581 362575 321944 41305 321270 280639 16 321270 280639 343939 299588 41400 279870 258188 17 279870 258188 299618 275621 41495 258123 234126 18 258123 234126 276336 249934 41590 234746 208344 19 234746 208344 251310 222411 41686 209624 180725 20 209624 180725 224415 192927 41782 182633 151145 21 182633 151145 195520 161350 41878 153642 119472 22 153642 119472 164483 127538 41974 122509 85564 23 122509 85564 131153 91341 42070 89083 49271 24 89083 49271 95368 52597 42167 53201 10430 25 53201 56955 42264 14691 26 42361 27 42459 28 43439 29 43540 30 43640 Table 2: Spending Plan with Inflation There are, however, a couple mitigating factors. If the client maintains a constant spending rate, he will effectively be spending less as time passes, but the natural tendency is for spending to decrease with age, and so the effect will likely not be noticeable. Under the constant $40,000-per-year scheme, either plan will last the entire 30 years. References Australian Government Actuary. Australian Life Tables 2005-07, Department of the Treasury, 2009, retrieved 2 Many 2010, . Clare, R. ‘Community attitudes to superannuation, retirement income adequacy and government policies on superannuation’, Association of Superannuation Funds of Australia, January 2010, retrieved 2 May 2010, . ING Australia. ‘MoneyForLife’, website, 2010, retrieved 2 May 2010, . Kotzé, A.A. ‘Stock Price Volatility: A Primer’, Doornfontein, S. Africa: Financial Chaos Theory, 2005, retrieved 2 May 2010, . Milevsky, M. A. ‘Sustainable Spending at Retirement’ in The Calculus of Retirement Income, Cambridge University Press, 2006, pp. 185-214. Milevsky, M.A., and Robinson, C. ‘A Sustainable Spending Rate without Simulation’, Financial Analysts Journal, vol. 61, no. 6, 2006, pp. 89-100. Read More