24 Oct 2015, 3:28pm
personal finance
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  • Compound Interest – quantitative takedown

    I keep getting flack for being cynical on compound interest. I was an engineer in a previous life, and this is amenable to quantitative analysis, here are the charts on why compound interest won’t help you that much to retire early. It will help you a bit. but if you want it to do the lion’s share then be prepared for a nice 40 or 50 year working life.

    You know the story of Alice in a Wonderland of Compound Interest. Astute Alice saves £1000 a year from 18 to 38. She then stops work to have children, never saves any more in her pension and retires at 68 on £1M. Lovely jubbly. Cat-brained Camilla jumps to it at 38, and saves £1000 for 30 years until 68 but lives on cat food and baked beans for the rest of her life.

    Let’s test this for Sensible Susan who works for 40 years from 21 to 61. Nobody in the personal finance field wants to work for 50 years like Alice 🙂 Warren Buffett tells us that she should expect an annual real return of about 5%. She works in the public sector and never gets any real career progression. To normalise everything I have her saving one unit of real money every year, all these entities live in an inflationless world where their nominal rate of return on capital is deflated by inflation to get the real return. At the end of her career she looks back at how much each tenth of her working life has contributed to her pension. Compound interest sees to it that the early years contribute more, that much is clear, and of the total amount of 120 units accumulated, 67% is compound interest – it triples her money.

    Amount each tenth of her career (four years to a pie slice) steady savings contribute to Susan’s pension, saving exactly the same amount in real terms for 40 years and at 5% p.a. real return

    She observes that the savings in the first third of her working life contribute half her pension capital, she goes out and tells all the young pups that the first 12 years of savings are the most critical, if she had started at 35 she would be on cat food and beans. Quod erat demonstrandum.

    Let’s cast a beady eye at how this compares with the real world:

    Susan got no career progression. Let us hear it from the people at the ONS on this subject. The downturn is because everyone took the earnings sucker punch from the financial crisis, I correspond roughly to line 2. Look at how the career paths of people 10 years younger than me leave my cohort for dust 1 😉

    career progression is much faster now

    I got roughly three times real terms career progression over 30 years, this happens faster now though it may peak earlier, and I did better than the ONS average. It’s not unreasonable to expect someone to save to a pension as a constant proportion of their gross salary. Let’s say Susan got 2 times real terms career progression over 40 years – compound interest still more than doubles her money, it’s 63% of the total of 164 units

    Susan saves a steady segment of salary as it doubles in real terms

    Susan saves a steady segment of salary as it doubles in real terms

    Just for the record, this is what this would have looked like for me, getting 3x career progression although that was in 30, not 40 years so I have just taken eight of Susan’s four-year segments, getting 3x career progression over that 32 year time. 52% of my total of 134 units comes from compound interest – it’s doing a hell of a lot less of the lifting than for flatline Susan. But I end up with more 😉

    three times career progression in 32 simulated years - the pies are eighths, not tenths in this chart

    three times career progression in 32 simulated years – the pies are eighths, not tenths in this chart. The pies are more even than Susan’s

    It is the combination of career progression and the shortened working life of FI/RE types that makes compounding a lot less relevant in the real world. I’m not even particularly exceptional here – a 30 year working life is early retirement, not the extreme early retirement, and I dramatically lacked ambition compared to what people like RIT or The Escape Artist were prepared to do to retire early. I would imagine they got more than three times real terms career progression.

    Even that’s not realistic, though. There is a problem in humans called hyperbolic discounting, which means when we are closer to something delivering it gets much more interesting. The young Ermine didn’t really bother about pensions, though of course I signed up the The Firm’s scheme – companies were more paternalistic in those days and told you what was good for you. As the concept of retirement hove into view and I got within ten years of NRA I started to divide the tax privilege of 40% by the number of years (10) and saw I would struggle to get that sort of return on cash, and all of a sudden AVCs (a DC type of pension saving) became interesting, so I set to it. Tax savings mean a HRT taxpayer gets a 66% return on net income foregone, compared to the 25% for a basic rate taxpayer. I was lucky enough to be able to save to AVCs by salary sacrifice, so I took some basic rate tax + NI savings which still worked out to about a 50% ROI. The whole thing gets a hell of a lot more interesting. I don’t know about you, but it really, seriously, pissed me right off to be working two days a week for the taxman to I tried everything legit as I started running into HRT – first employee share incentive plan shares, and then somebody introduced me to AVCs and life was sweet. Life is too short to work nearly half for the government 2, a third is okay, more than that, sod that.

    I tried to simulate the effect of that by increasing the Ermine’s later savings by 1.3 times, which reflects the better return on net earnings lost that a HRT taxpayer gets. It somewhat underestimates my later savings, I was simply not prepared to pay 40% tax at all after a bit, so any bonuses and pay increases were salary sacrificed to AVCs and in the very last two years I hit AVCs harder driving my pay well below the HRT threshold. But ignoring that and simulating my boosted contributions from HRT alone, the contribution to my savings if I had saved steadily as a proportion of net income is much more even across the eighths of my career –

    Add HRT boosts into the mix a way into the career plus career progression and compound interest is beaten out by bigger contributions later

    Add HRT boosts into the mix a way into the career plus career progression and compound interest is beaten out by bigger contributions later

    Compound interest is about half the total 145 units. Unlike for the slow savers it just doesn’t do much for aggressive savers, and I was never a particularly aggressive saver compared to the people who want to retire in their forties!

    There’s a takeaway from this all – yes, compound interest will help you triple your savings to FI, if you are unambitious and you want to work 40 or 50 years. It will roughly double the savings of the typical FI/RE saver. Where it really starts to show up is once you have FI and your aggregate savings are significant. Some anonymous dude called Cumulative Dividends has put more money into my ISA 3 than I have this year. He appears to be gathering speed with time – in the last tax year he contributed nearly a fifth of what I did. He is one aspect of compounding, there is a similar but volatile and flighty bastard called Capital Appreciation that is the other.

    I will not be drawing down my ISA savings for probably another 10-15 years until my final salary pension starts to be eroded relative to other people’s earnings (earnings inflation is usually higher than price inflation) and then I will start to use the tax-free ISA income to top my pension up, and finally start to run the capital down or part-buy an annuity in 20 years’ time. Who knows. Compound interest helps people with capital, but it doesn’t help ambitious early retirement savers to build capital that much, though it roughly doubles the money. As for Alice in compound interest wonderland, well that is Alice in Wonderland – the weakness of that is the unrealistic 10% annual real return. Alice may get that in Wonderland, but you ain’t gonna get that in the real world. Put the work in or put the time in.

    You shouldn’t take away from this that you don’t need to start saving to a pension early, all the parts of the pie matter, but you shouldn’t take it as totally devastating if you didn’t start early. If you have any ambition to early retirement at all, the myth of compound interest and the trickle of free money from Time isn’t going to do the heavy lifting for you in the accumulation phase.

     

     

    Notes:

    1. I acknowledge they need that better career progression, to be able to pay for student loans if applicable and housing which is dearer in real terms than back in the day. It’s still an impressive feat and I tip my hat to their superior industry or negotiating power, at least up until ’09
    2. I know, indirect taxes and Tax Freedom Day and all that, you can reduce indirect taxes by not buying loads of Consumer Shit
    3. over its ~six year existence
     
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