Pictures of Pensions 🖼️

Saving for a pension is rarely anyone’s idea of a great time - but sometimes there are great incentives

With apologies to my pensions actuary friends - saving for a pension is rarely anyone’s idea of a great time.

But sometimes there are great incentives:

• Employers might match your contributions - either because employment laws make them, or else because a good pension package helps to attract and retain talent (or both)
• Governments might provide tax incentives - around the world populations are ageing, and governments should prefer a financially independent retiring population
• Compound returns - though certainly not guaranteed, compound returns can work like magic ✨ over a long pension savings horizon

For as long as I’ve needed to think about pension savings, it’s helped me to draw a picture 🖼️

We want to visualize saving for a pension - with some nice incentives

Let’s suppose you save € 1,000 each year from age 50

For retirement at age 65

In the end you, you’ll have saved € 15,000 🎉

But: we hope your savings will grow with compounding returns

md`Assuming **${d3.format('.1%')(unit_growth_rate_in)} compound returns** each year`

You may also get tax relief on the amounts you save: reducing the effective cost

In Ireland the value of tax relief depends on the amount of tax you pay: which in turn depends on how much you earn

Here I include a tax relief allowance for an individual earning €

// some reactive issue causing trigger to fail? moved @cr-pens to :::{focus-on="cr-pens"} but didn't help !
md`The tax relief is <span class="m">**€ ${/*model.js.empee_contribution_tax_relief({...cursor__1, age_in: 60})*/400}**</span> so that the <span class="cell-hl cost">effective cost</span> of saving <span class="m">**€ 1,000**</span> is just <span class="m">**€ ${/*model.js.empee_contribution_cost({...cursor__1, age_in: 60})*/600}**</span>`

Now let’s suppose your employer matches 100% of your contributions

Then you benefit from more contributions and more compound returns

Now we can see that a little effective cost

Can result in lots more value

Compound returns, tax relief, and employer matching can be extremely valuable for pension savings.

But it’s hopeful to think that money will accumulate, untouched by charges 💸

Suppose there is a 5% charge on contributions

And a management charge of 1% - deducted from the savings balance each year

Now we can interpret the value of our pension savings as the area under inflows 💰 minus the area under outflows 💸

At this level of charges, we can still see a lot of value

🏖️

So far, we assumed saving starts at age 50.

What if saving started earlier? 🤔

Over a longer period, the value of compound returns is more apparent ✨

Here in fact, the value from the first 10 years of saving is more than the value from the following 15 years

✨

//md`**${d3.format('.1%')(unit_growth_rate_in)}**`
//md`**${d3.format(',.0f')(salary_0_in)}** salary`

// check_cfs_vs_fund_value is weakened as a check
viz = embed('#viz',spec, {renderer: 'svg', actions:false, tooltip:false});

progress = crTriggerIndex+crTriggerProgress-(crTriggerProgress>0.999999?1:0)+(crTriggerProgress<0.000001?1:0)

o0 = 1

age_1_in_scale = d3.scaleLinear().domain([o0+.5, o0+1.5]).range([51, 70]).clamp(true)
age_1_in = Math.round(age_1_in_scale(progress))

o1 = 4
unit_growth_rate_in_scale = d3.scaleLinear().domain([o1+.4, o1+1.5]).range([0, 0.06]).clamp(true)
unit_growth_rate_in = unit_growth_rate_in_scale(progress)

o2 = 7
salary_0_in_scale = d3.scaleLinear().domain([o2+.8, o2+1.5]).range([10000, 50000]).clamp(true)
salary_0_in = salary_0_in_scale(progress)

statey = (progress > 10.4 && progress < 13.5) || progress > 21.5 && progress < 25.3

oflash = 9

flash = d3.scaleLinear().domain([0.2,0]).range([0,1]).clamp(true)(Math.abs(progress-9.7)) + d3.scaleLinear().domain([0.2,0]).range([0,1]).clamp(true)(Math.abs(progress-14.7)) 


flashall = d3.scaleLinear().domain([0.2,0]).range([0,1]).clamp(true)(Math.abs(progress-15.7)) + d3.scaleLinear().domain([0.9,0]).range([0,2]).clamp(true)(Math.abs(progress-20.3)) + d3.scaleLinear().domain([0.6,0]).range([0,1]).clamp(true)(Math.abs(progress-26.8)) + (progress > 26.8 ? 10 : 0)

outflows_opacity = d3.scaleLinear().domain([16.5,17]).range([0,1]).clamp(true)(progress)

{
if (progress > 12) {
  viz.view.signal('ydomain_x', (progress < 20 ? progress-12 : progress - 23.9)).resize().run();
//viz.view.signal('ydomain_override', [0,5000]).resize().run();
//console.log(viz.view.signal('ydomain'))
}
}

viz.view.signal('outflows_opacity', outflows_opacity)

viz.view.signal('flash', flash)

viz.view.signal('flashall', flashall).run();

o3 = 10
emper_matching_rate_in_scale = d3.scaleLinear().domain([o3+.5, o3+1.5]).range([0, 1]).clamp(true)
emper_matching_rate_in = emper_matching_rate_in_scale(progress)


o4 = 17
contribution_charge_rate_in = d3.scaleLinear().domain([o4+.5, o4+1.5]).range([0, 0.05]).clamp(true)(progress)
management_charge_rate_in = d3.scaleLinear().domain([o4+1.5, o4+2]).range([0, 0.01]).clamp(true)(progress)
o5 = 21
age_0_in = Math.round(d3.scaleLinear().domain([o5+0.7, o5+1.5]).range([50,40]).clamp(true)(progress))

Health Warnings ⚠️

• This illustrated pension savings projection includes features that may be valuable, but they are not applicable to everyone

• I used a 6% compound returns assumption, but there’s no such thing as guaranteed outcomes at rates such as 6%.
  In a separate post: Visualizing Risk, I illustrate a wider set of outcomes.

• Even when there is tax relief to save for a pension, this doesn’t mean that there aren’t taxes on pension income after retirement¹

• There are usually additional rules about how pension savings can be used after retirement

In other words: for help to understand pensions-related issues you should speak to a financial advisor who can understand your particular circumstances and communicate suitable choices. This blog post isn’t financial advice ⚠️

formulas and custom projections 🔍

I use calculang: a language for calculations, to describe the pensions calculator and income tax calculations used here.

You can explore more visual pension savings projections - and their formulas, using the draft pension calculator example on calculang.dev

This blog post and others are an exploration applying many tools available to understand, interpret and communicate about models and numbers: tools including visualization, interaction, animated transitions, and guided scroll-based interaction.

md`Active sticky: ${crActiveSticky}`

md`Active trigger: ${crTriggerIndex}`

md`Trigger progress: ${(crTriggerProgress * 100).toFixed(1)}%`

md`Scroll direction: ${crDirection}`

md`Progress Block progress: ${(crProgressBlock * 100).toFixed(1)}%`

md`-----`

md`sallary_0 ${salary_0_in}`

appendix

import {spec as spec_} from './spec.js'

spec = spec_(width, y)

viz.view.data('data', [...data]).resize().run();

window.dispatchEvent(new Event('resize')); // without this, my own focus-on blocks don't get triggered (for some reason only my ones - OJS Variables ones work)
// They work when I resize. So triggering this programmatically.

embed_ = require("vega-embed")

embed = (a,b,options) => embed_(a,b, {renderer:'svg', /*theme:'carbong10',*/ actions, ...options});

viewof actions = Inputs.toggle({label:'vega-embed actions?', value: false})

helpers = import(
  "https://cdn.jsdelivr.net/gh/declann/calculang-js-browser-dev@main/helpers.js"
)

calculang = import(
  "https://cdn.jsdelivr.net/gh/calculang/calculang@dev/packages/standalone/index.js"
)

fs = ({
  "entrypoint.cul.js": await FileAttachment('./cul/pension-calculator-overrides.cul.js').text(),
  "./pension-calculator.cul.js": await (await fetch('https://calculang.dev/models/taxes-pensions/pension-calculator.cul.js')).text(),
  "./simple-incometax.cul": await (await fetch('https://calculang.dev/models/taxes-pensions/simple-incometax.cul.js')).text()
})

model = await calculang.compile({entrypoint: 'entrypoint.cul.js', fs})//require(`https://calculang.dev/models/taxes-pensions/pension-calculator.js`)



formulae = ['empee_contribution_tax_relief', 'empee_contribution_cost', 'emper_contribution', 'fund_growth', 'contribution_charge', 'management_charge']


cursor_0 = ({age_0_in, fund_value_0_in:0, unit_growth_rate_in:0, retirement_age_in:65, missed_contribution_age_in:15, salary_age_0_in:50, salary_0_in, salary_inflation_rate_in:0, /*empee_contribution_rate_in:.1 Moved to fixed contribution amount */emper_matching_rate_in, contribution_charge_rate_in, management_charge_rate_in, age_1_in})

cursor = cursor_0

cursor_1 = ({...cursor, unit_growth_rate_in})
//cursor_2 = ({...cursor_1, emper_matching_rate_in})

viz.view.signal('statey', statey).run()

cursor__0 = {
  if (progress < 17) return ({...cursor_1,emper_matching_rate_in:0})
  else if (progress < 21) return ({...cursor_1, management_charge_rate_in:0, contribution_charge_rate_in:0})
  else return ({...cursor_1, age_0_in:50})
}

cursor__1 = {
  return cursor_1
}

data = helpers.calcudata({
  models: [model.js],
  input_domains: {age_in: _.range(cursor.age_0_in,cursor.retirement_age_in)},
  input_cursors: [cursor__0, cursor__1],
  outputs: [...formulae, 'check_cfs_vs_fund_value'],
  pivot: false
})

viewof shared_y_scale = Inputs.toggle({label: 'shared y scale?', value: true})


y = shared_y_scale ? 'y_shared' : 'y'

f = d3.format(',.2f')

// I need ojs blocks to be inside focus-on blocks, or they break a trigger
e = d3.sum(data.filter(d => d.input_cursor_id == 1 && d.formula =="empee_contribution_cost"), d => d.value)

{
for (const el of document.getElementsByClassName('cr-column-screen')) {
  el.classList.remove('cr-column-screen')
}
}

mutable progress5 = false;
  mutable progress10 = false;
  mutable progress15 = false;
  mutable progress20 = false;
  mutable progress25 = false;
  mutable progress30 = false;

{
  if (window.plausible) {
    if (progress > 5 && !progress5) {
      mutable progress5 = true;
      console.log('hit 5')
      window.plausible('pictures-pensions progress', { props: {index: 5}})
    }
    if (progress > 10 && !progress10) {
      mutable progress10 = true;
      console.log('hit 10')
      window.plausible('pictures-pensions progress', { props: {index: 10}})

    }
    if (progress > 15 && !progress15) {
      mutable progress15 = true;
      console.log('hit 15')
      window.plausible('pictures-pensions progress', { props: {index: 15}})

    }
    if (progress > 20 && !progress20) {
      mutable progress20 = true;
      console.log('hit 20')
      window.plausible('pictures-pensions progress', { props: {index: 20}})

    }
    if (progress > 25 && !progress25) {
      mutable progress25 = true;
      console.log('hit 25')
      window.plausible('pictures-pensions progress', { props: {index: 25}})

    }
    if (progress > 30 && !progress30) {
      mutable progress30 = true;
      console.log('hit 30') // not used
      window.plausible('pictures-pensions progress', { props: {index: 30}})

    }
  }
}

Footnotes

1. often there are taxes on pension income - so that it might be better to say that tax is deferred rather than relieved whenever we save