Some arithmetic on retirement income

I’ve been thinking about the impact of the financial crisis on retirement income policy and individual strategies, and have come up with a reasonably simple way (I hope) to illustrate the core problem. Pre-crisis, it seemed reasonable to base a retirement strategy on the idea that a long-term investor, focusing on stocks could average a 7 per cent real return over 30 years, with relatively little risk. Now it’s clear that assumption has been proved wrong for lots of people. So it seems reasonable to ask how retirement strategy would look if, instead, you assumed a 2 per cent real return (what you might get with a portfolio of government bonds and the safest stocks).

To answer this question, we can use the magic of compound interest. At 7 per cent, money doubles in 10 years (the rule of 70), so a dollar invested today will be worth 8 dollars in thirty years time. That means someone with a stable real income, who starts saving 10 per cent of their income at age 25 and retires 30 years later at age 55, with a further life expectation of 30 years, can retire on 80 per cent of their pre-retirement income, as compared to 90 per cent net of saving in the working years. Quite attractive!

At 2 per cent, though, money doubles in 35 years. To get a more less stable consumption stream you need to change the balance above by a factor of four. A simple way to do this is to double contributions, to 20 per cent of income and shift the work-retirement balance, so that you work from 25 to 65 to finance an expected 20 years of retirement income.

Among other things, this means that the flow of savings into superannuation will have to increase a lot in the medium term which may help to resolve some of our many macroeconomic imbalances. But how this is to be brought about remains to be seen.

22 thoughts on “Some arithmetic on retirement income

  1. The assumption is that the lower yield investing institution will not eventually renege on interest or dividends. So far the failures have been with higher yield firms. However the contagion may spread to banks, deposit takers and equity we now regard as safe. If increasingly welfare has to top up underperforming superannuation then the burden on the government may be unsustainable. That’s another reason not to squander the recent surpluses.

  2. As you have your calculator out JQ, here is another possibility to explore.

    A couple starting a family with the resources to safely buy a house from their income take out out a mortgage for that purpose. Then in this proposal they have their 9% employer superannuation contribution payed into their mortgage fund along with their standard payments. The added funds accelerate the principle repayment and the mortgage term is significantly reduced. Once the property is freehold the couple continue to pay the same amount as their mortgage payment along with the employer contribution into an investment fund which rapidly accumulates to a realistic holding over the next 15 years.

    There are disadvantages of course. The house is treated as a retirement asset and cannot be sold or drawn down on for expences until the couple reach a certain age (many would call that an advantage). The property can be sold and divided as can a retirement fud but the funds must be retained in a suitable manner for retirement purposes.

    The main advantage of this is that the asset is very tangible to the investors. It is their house, they can see it and feel it. Rather than just believe that there is an asset backing for their retirement funds as at present, which we now know in the light of the financial collapse is not necessarily true.

    I have tested this idea on many people. Some have already thought this through exactly as above, others are very positive. The Commonwealth Bank made no real comment, although they saw the potential.

  3. I don’t what to have read a text book about the capital asset pricing model but where does the long term 7%pa come from? Given that the Australian GDP has been growing at under 3%pa.

    See URL:

    Then how does the share market grow at 7%pa?

    Is it because the proportion of the economy represented by the share market is growing?

    Is there some sort of giant Ponzi scheme going on? (Growth is debt is funding the difference between economic growth and growth in share market returns).

    I just can’t see how a market can sustainable grow at 7% when its underlying economy is growing at 2.5%.

  4. Re: 7 – Yes Peter it is a classic Ponzi scheme. It has functioned well as the 33% “more than normal” baby-boomers have invested their savings, which has inflated the price of assets.
    It is now just beginning that the baby boomers want their money. Invested in Real Estate trust – sorry can’t have it. Invested in the sharemarket – thats a 50% off.
    Its apparently all OK though, the market will all be “back to normal” next week, (ha ha, ha ha)

  5. Money chasing activity.

    When you had large investments, chasing large amounts of activity (baby boomers putting in their “prime of life” superannuation – and also being in the workforce) then the market goes through the roof.

    We will be changing to large amounts of money (the baby boomer super nest eggs) chasing smaller amounts of activity. In other words the retiree/workee equation will be changing rapidly, while somehow the concept that “money” is the important aspect has overridden the basic concept that the number of people conducting adequate activity is the important part.

    In other words, the GFC has more to do with demographic collapse rather then market failure or business incompetence.

  6. re:9 – Thank you veltyin, very well put. Money as a store of wealth is only good when the demographics remain constant. When the demographics are rising we get asset inflation. When the demographics start falling we will have asset deflation – (either with a stable currency and lower prices or with an inflated currency and seemingly stable prices).
    When we have one following the other – which we now have – we have what may be termed “a problem”

  7. PRQ
    with respect I think the flow of savings into superannuation has become a force feed of the financial markets and has contributed to teh crisis. A plain old government force feed of one sector that grew into a monster and as usual its now enternched in bureaucratic process and no one is even examing whether it played a part. All that liquidity chasing higher and higher returns gave us the GFC. The financial managers as ludicrous as it sounds, just responded to the environment by multiplying and inventing lots of deals to process that liquidity. Is it much different to the goldrush and then immmigration led (money in pockets)more money = land values up = investment in farm buildings up = boom of the 1880s when the banks bred like rabbits and then most fell over in the 1890s crash.

    Super money over the past two decades (some of it) may have been better spent on the family home for some underlying stability in Australia (I still think a lot of ordinary people are carrying a too big mortgage burden – its not the baby boomers, its the rest after).

    Too many people out there have huge mortgages and little superannuatuion. If they print all this 7 trillion what will happen to inflation?? I think a superannuation amnesty (or a cut back) with far greater freedom as to what constitutes “savings for retirement” and greater freedom to put it in the control of the individual’s hands and off his mortgage if needs be (rather than this fund or that fund) to stimulate after housing costs income and spending would be a much better idea.

    More super is just giving it back to the gamblers to play another round.

  8. That is easy PeterM, A classic case is the NZ aluminium smelter where there is strong investment much commercial activity within the area of the smelter’s influence, but the product is shipped out of NZ totally and at cost or lower. Net gain to the NZ economy? OK growth. Net gain to the Head Office country? much better.

    Equally if all of the retirees take the returns on their investments and spend it in Las Vegas, The markets that generated the growth returns will appear to be more dynamic than the country in which those markets perform their activity.

  9. I just had an unusual experience. I’ve had a couple of mice in my factory for a while, and I’ve wondered what was keeping them here. Yesterday I found a jar of oats in the kitchen where the end of the container was broken, but out of site. Fixed that, so now the mice are roaming looking for a food source. I’m sitting here looking at JQ’s thread, with my hand on the computer mouse when one of the real mice appears from behind the modem router and stares at me. I kept perfectly still. The mouse continued all the way over to my hand holding the computer mouse. Do you think that I could get my hand from the computer mouse and onto the real one? Now I know that I am getting old. It is all in the mind though. I see now that I should have thought of the mouse as a bundle of retirement cash.

  10. I suppose another factor that needs to be considered is that the more the rate of national savings is increased, the more that returns must decline. Simply, the greater the supply of capital that is available for investment the more that returns must decline.

    Declining returns on investments should encourage people to consume more and not save as much. But then if people are forced to save, they cannot adjust their behaviour accordingly.

  11. PeterM Says:

    Given that the Australian GDP has been growing at under 3%pa…

    Then how does the share market grow at 7%pa?

    The 7% return doesn’t imply sharemarket growth of 7%.

    Return includes both dividends and capital appreciation. So dividends could be 7% with no change in the level of share price index, or dividends could be zero with a 7% increase in share price index, or anything in between. In fact, an annual share price index decline of, say 10% combined with dividends of 17% would still fit.

    A particular return on equity doesn’t necessarily imply anything about GDP growth.

  12. MU,

    The increase in capital sloshing around the world is partly to blame for the credit crunch. It has resulted in people buying the safest assets but in such quantities that it drove down the premium for these assets. Then additional capital moved to the corporate sector and so on. So what happened is the sheer volume of cash for investment actually distorted the risk premium requested.

    This is larger than merely Australian super and incorporates the high savings countries in Australia and the Mid East.

  13. It is impossible to work out any form of rational investment strategy while we have dysfunctional markets and while we have currencies where the controllers of the currency not only tolerate inflation but have targets!

    See my post under weekend reflections to see how to eliminate inflation.

    Eliminating inflation may also have the effect of removing the so called business cycle which is likely to be caused by the system purging itself of excessive debt before regorging on debt.

    We can make markets so that they operate the way they are meant to work – e.g. increase supply, price drops, demand goes up – and where the suppliers get a positive return on their investments by changing the way the rules inside the market work.

    These things are possible if we look more at the rules associated with individual transactions and observe the emergent properties of the systems we create and change the rules of the individual transactions to influence the emergent properties rather than try to put rules on the emergent properties which are symptoms rather than causal.

    For example, rather then try to put rules on executive salaries (like disclosure and limits) put the rules around the way executive salaries are set and observe the results.

  14. Sorry you lose the subscripts and powers but this is the derivation of the formula you need. Tidy it up and plug in what you want.

    Treat the contributions as yearly payments and compound the return.
    Amount at period 0:
    Amount at period 1:
    P1 = P0 + P0 * r + c ( principle + interest + contribution)
    P1 = P0(1 + r) + c (equation 1)
    Amount at period 2:
    P2 = P1(1 + r) + c
    Using equation 1 for P1
    P2 = (P0(1 + r) + c)(1 + r) + c
    P2 = P0(1 + r)2 + c(1 + r) + c (equation 2)
    Amount at period 3:
    P3 = P2(1 + r) + c
    Using equation 2 for P2
    P3 = (P0(1 + r)2 + c(1 + r) + c)(1 + r) + c
    P3 = P0(1 + r)3 + c(1 + r)2 + c(1 + r) + c
    Amount at period N:
    PN = PN ? 1(1 + r) + c
    PN = P0(1 + r)N + c(1 + r)N ? 1 + c(1 + r)N ? 2…. + c
    PN = P0(1 + r)N + c((1 + r)N ? 1 + (1 + r)N ? 2…. + 1)
    PN = P0(1 + r)N + c(S) (equation 3)
    Where S = (1 + r)N ? 1 + (1 + r)N ? 2…. + 1 (equation 4)
    S(1 + r) = (1 + r)N + (1 + r)N ? 1…. + (1 + r) (equation 5)
    With the exception of two terms the S and S(1 + r) series are the same so when you subtract all but two terms cancel:
    Using equation 4 and 5
    S(1 + r) ? S = (1 + r)N ? 1
    S((1 + r) ? 1) = (1 + r)N ? 1
    S(r) = (1 + r)N ? 1
    S = ((1 + r)N ? 1) / r (equation 6)
    Equation 6 into 3.
    PN = P0(1 + r)N + c(((1 + r)N ? 1) / r )

  15. I am not sure if Pr Q has seen Pr K’s recent article on GWB’s parting gift to Wall St. It turns out that GWB left one last little mess for Obama to clean up. He, or his agents, instructed the Social Security department to weight the governments investment in financial instruments much more heavily towards stocks rather than bonds. Right at the peak of the boom 2007. Talking Points Memo quotes the Boston Globe:

    Just months before the start of last year’s stock market collapse, the federal agency that insures the retirement funds of 44 million Americans departed from its conservative investment strategy and decided to put much of its $64 billion insurance fund into stocks.

    Switching from a heavy reliance on bonds, the Pension Benefit Guaranty Corporation decided to pour billions of dollars into speculative investments such as stocks in emerging foreign markets, real estate, and private equity funds.

    Who was responsible for the switch? Meet Charles Millard, a former Lehman exec (great pedigree there) who ran the agency from 2007 until the end of the Bush administration.

    Millard told the Globe: “The new investment policy is not riskier than the old one,” and added that a riskier strategy was justified to give the agency a chance to raise enough money to eliminate its deficit.

    It appears to have had the opposite effect though. The agency’s stock-related investments were down 23 percent since the end of last September. But as the Globe notes, that was before the major downturn in the market triggered by the financial crisis. So the losses now are probably considerably higher.

    “This could be huge,” Zvi Bodie, a finance professor who in 2002 advised the agency to rely on bonds, told the Globe. “This has the potential to be another several hundred billion dollars.”

    A few hundred billion here, a few hundred billion there. Pretty soon you are talking real money.

    All captured by those insiders who sold out at the top of the boom.

    I remember that Bush poked fun at Gore for questioning the REPs “risky schemes” in Social Security and so on. Hows that going now?

  16. Jack#20

    Bush was just giving away taxpayers money to his mates. He gave (taxpayers) government war funds to his mates. Why wouldnt he give (taxpayers) social security money to his mates. Its a wonder he didnt give the white house itself (or the taxpayers themselves) to his mates before he left.

    If Bush could have he would have turned people on social security into slaves so he could give them all away to his mates.

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