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Robot angels: Automated seed investing on the Seedrs crowdfunding platform post image

Note: I’m a shareholder in Seedrs. Also, if you follow my links to Seedrs and subsequently invest on that platform, you can get £50 for free towards an investment and I may receive a small marketing bonus.

Like dating a soap star, putting money into venture capital might seem fun, sexy and potentially rewarding – but it can be expensive, unpredictable, tricky to get into, and hard to get out of.

My previous article on the pros and cons of venture capital explained why. I also looked at how you might get started – via funds, VCTs, angel investing, EIS, and more – and the downsides that could put you off.

Passive investors in particular will find venture capital (VC) tricky.

VC usually involves expensive funds run by active managers, or else doing the time-consuming work for yourself via angel investing or crowdfunding – and probably having even less confidence in your returns.

I’m not about to reveal a VC index tracker that charges you pennies a year and makes these problems go away.1

However one of the leading crowdfunding platforms, Seedrs, has launched two halfway house solutions.

Or perhaps quarter-way house solutions.

Or maybe eighth-way! You get my drift.

These new approaches from Seedrs aren’t a panacea for would-be passive dragons.

But I applaud the experimentation, and I think they may be appropriate for some sophisticated and adventurous private investors who already have the important financial bases covered.

Wealth warning: Venture capital is a risky asset class. Crowdfunding is a new way of accessing it. The offerings I discuss below are only a few months old. Faced with this triple-threat I hope you can see you should only risk money you can afford to lose here – and first do your own deep research. This article is just a heads-up, and certainly not a recommendation for what you should do.

Automatic for the people

Quick recap: Crowdfunding on a platform like Seedrs or Crowdcube is easy-access angel or seed investing.

Crowdfunding enables you to buy shares in unlisted companies, but with far smaller amounts of money than would be deployed by a typical high-rolling angel – perhaps as little as £10.

You can invest far more if you want to. High net worth individuals regularly put five or even six-figure sums into crowdfunding companies.

But the big attraction is the low minimum investment. In theory, it could make grabbing a sliver of the next Facebook or Tesla or Starbucks accessible to everyone. That might seem far-fetched, but a handful of already highly-valued British firms did get their start with crowdfunding, including Brewdog, Revolut, and Monzo.

In addition there are often generous EIS or SEIS tax reliefs, depending on the firm. And sometimes crowd investors are also offered perks, such as free samples, subscriptions, or discounts. (Fun as a treat, but never a reason to invest.)

The bad news is that companies pursuing crowdfunding are usually startups. This means many (perhaps most) will eventually fail or be acquired for a pittance. This is high risk investing.

As I discussed in my last VC article, there are other issues, too.

There are plenty of flimsy companies raising money on these platforms. Sometimes you suspect they’re going to the crowd because no professional VC would touch them.2

Valuations can be pie in the sky, too.

With a stock market, at least you know the constant buying and selling activity of thousands of investors normally results in some sort of efficient pricing.

In contrast, crowdfunding companies usually seem to raise as much as they can at the highest valuation they can get away with – and there may not be much ‘adult supervision’ keeping the prices sane.3

Finally, just like with all seed/angel investing, crowdfunding unlisted companies typically locks your money away until there’s an ‘exit’, such as a trade sale or public flotation.

(Seedrs is pioneering a secondary market, and Crowdcube staff have told me they’re exploring the same. But unless and until such markets become more liquid, it’s best to assume your money is tied up until an exit.)

Automatic for the people

So – high-risk companies bleeding money, most of which will amount to nothing, some of which are borderline frauds, and perhaps one or two of which will hit the fabled ‘unicorn’ status of $1 billion.

Do you feel lucky punk?

Diversification is vital to try to improve the odds in your favour. That means little old you has to read realms of marketing material and ideally meet management – and still reject 10 or 20 companies for each one you invest in.

And then it will probably go bust, anyway.

For active investing junkies like me, seed investing like this is manna. I read a dozen start-up business plans a month, attend a pitch night every two or three weeks, and enjoy picking the brains of management. Building up a portfolio of more than 30 unlisted firms has been fun, and I’m looking forward to reaching 50.

But most normal people will feel different, and this is where Seedrs hopes its two new services will come in:

  • Auto Invest
  • EIS100 fund

Both do a similar thing – but they’re implemented in very different ways:

Auto invest

This enables you to invest automatically in firms raising money on Seedrs that meet your predefined criteria. You choose how much you want it to invest in the matching opportunities, and you can cancel an investment if on inspection you don’t like what Auto Invest has put your money into – before that firm’s crowdfunding campaign closes, and for up to seven days after.

Basically Auto Invest expedites the process of investing on Seedrs. The actual investments it makes are just the same as if you’d done it manually by yourself (which means you still get EIS or SEIS tax relief if applicable, of course.)

Seedrs EIS100 fund

Seedrs says “…the EIS100 Fund offers investors passive exposure to the venture capital asset class at scale.”

Yes, they used the word ‘passive’ – but hold your horses, as this is not the same thing as a fire-and-forget Vanguard index fund.

In fact, it’s not really a fund – it’s more like Auto Invest on steroids.

In brief, here’s how it works.

To begin, Seedrs is raising a set amount of capital for EIS100 from its investor base, with a minimum individual investment of £1,000. Once the round closes, the EIS100 fund will start deploying chunks of the money raised into new pitches that fit its predefined criteria.

To be eligible for EIS100 investment, a pitch must already have hit at least 70% of its funding target, it must qualify for EIS relief, and it must have at least 100 unique investors. Like this, the fund presumably aims to benefit from the wisdom of the Seedrs crowd in pre-filtering opportunities.

There are also a few rules as to how much money the EIS100 will put into any particular raise.

The aim is for the fund to invest its money into 100 companies over 12 months across many sectors, though the small print sensibly warns this will depend on what exactly comes to the platform and is eligible.

There will be a 0.25% platform fee, calculated over eight years but collected as an upfront 2% charge. There are no other recurring charges. However on any successful exits by companies EIS100 invests in, Seedrs will charge its usual 7.5% carry fee on the profits – and this is the clue that it’s not really a fund, but as I say more Auto Invest operating at scale.

You won’t see a fund in your Seedrs account. Rather you’ll (ultimately) see 100 or so nominee holdings, as if you’d made all the investments yourself.

This does mean that any exits should involve you getting your profits returned as and when they occur (rather than being rolled up as in a fund, to be invested or distributed at the managers’ discretion).

Similarly you might also be able to sell your individual ‘fund’ holdings via the Seedrs secondary market.

This graphic illustrates how the structure pans out:

Source: Seedrs

Note that in the EIS100 FAQ, Seedrs says it’s not actually a fund. Which makes one wonder why it calls it a fund?

I can see ‘fund’ is easier to market than say my ‘Auto Invest On Steroids’ description.

But I wonder if it will cause confusion, or problems down the line?

Anyway please do see that FAQ for more details – and also read the extensive investment memorandum – and note that the EIS100 round is already over-funding, so head to Seedrs if you think – after the caveats above and to come below – that it might be right for you, to start your research.

Incidentally if more EIS100 funds are launched in subsequent years, then we’ll eventually get annual ‘vintages’ like you see with traditional VC.

What I like about these automated solutions

While the ‘passive deployment’ – as Seedrs puts it – that’s offered by these two services is far from passive investing as we know it, they could make life a bit easier and address a few issues.

  • Diversification – Both Auto Invest and EIS100 should see investors who use them end up with VC portfolios spread across a lot of investments. Okay, so it’s possible to override any particular investment with Auto Invest, but at least it’s encouraging widespread deployment. With EIS100, wide diversification should happen automatically. Placing a lot of bets like this is important with VC investing. You need to hit a few big winners!
  • More easily capture returns from (the Seedrs tranche of) the VC asset classSeedrs says it expects to engage with 15,000 firms over the next year. The vast majority of these won’t make it onto the platform, as they will be rejected at some stage of its own due diligence. Of the 500 or so that do get through its filters, it expects about 260 to achieve their funding target. EIS100 would put money into a selected 100 of these. Seedrs claims a platform-wide annualised internal rate of return (IRR) of just over 12% to-date – a figure that jumps to 26% when tax reliefs are taken into account. Now, we could spend hours debating how much of your hat to hang on these figures. Crowdfunding hasn’t been going for very long and few businesses have exited, so this attractive figure must be largely based on subsequent funding round valuations – and no doubt a few out-sized winners. But with that said, it does suggest the Seedrs ‘funnel’ is doing something right. These solutions could help one harvest that IRR.
  • Less work for investors – If you believe the IRR figure just mentioned is vaguely credible, then it would be an attractive bolt-on to many portfolio mixes – and even more so with the tax relief. However given all the work involved in traditional seed investing, you might argue it’s still not enough to compensate you for many hours of reading flowery business pitches and so on! These passive deployment approaches do offer to get rid of all that. So you don’t have to (notionally) bill your time against any returns you make.
  • Easier access to EIS tax relief – As above, basically. If you want to get EIS tax relief while investing in lottery tickets start-ups, both Auto Invest and the EIS100 could make the process easier (but see the downside section below.)
  • A dispassionate robot might be a better investor than you – Studies of mainstream investors have taught us the average person is better off agonizing over the menu at Pizza Express than trying to decide on good individual investments. I wouldn’t be surprised if a rules-based approach to VC does do better than many individual investors who bring their own behavioral quirks and biases to the process. For example, I see far-fetched technical inventions getting funding on these platforms, and I’d bet my bottom dollar they’ve been backed by high IQ engineers, who as I’ve mentioned before in my experience can be among the worst investors. (No offence engineers, you’re incredibly useful for the other stuff you do!) Perhaps a robot would be savvier? I’ve even heard ‘scattergun’ VCs say it’s not worth spending too much time looking out for frauds, because they’re rare and trying to avoid them will only gum up your odds. Maybe Seedrs will prove that just spreading your bets widely can match or beat traditional active VC investing?

Downsides to automatic angel investing

Hopefully that’s given you a flavour of the potential attractions of these new approaches to crowdfunding.

I do see clouds though, too, which I’ll briefly run through.

  • Lack of individual scrutiny/diligence – For some in the VC community, the idea of amateur investors piling money into unlisted start-ups is already a crazy proposition. Where is the 100-man years of experience, the MBAs, the legal backup, the broad networks to tap for background information? Crowdfunding fans would dispute those complaints, of course, but they’re not utterly unreasonable. Now add in semi/fully automated investment (albeit via the filters and checks I’ve mentioned) and you are a very long way from traditional VC investing. Too far? Time will tell.
  • Funding targets are a moveable feast – Platforms and the firms seeking funding might dispute this, but my observation is companies may set low targets with the aim of achieving a successful raise, and then gathering much more money in during so-called ‘over-funding’. I see this pattern a lot. It’s a debate for another day, but anyway selection filters based around firms achieving a certain proportion of what might be an arbitrarily low funding target will perhaps not prove as robust at weeding out unpopular/unloved ideas as you might hope – especially if the auto-solutions then tip weak ideas into over-funding, which could increase the incentive for a pitch to set a low target.
  • Potential Heisenberg-ian issues – To mangle the go-to quantum physics metaphor, Seedrs‘ faith in its filtering and IRR to-date is predicated on data covering funding before either Auto Invest or the EIS100 got going. These new services could distort future returns, for good or ill. While the EIS100 includes a few safeguards to presumably try to avoid it distorting the market (from maximum investment percentages to maximum total money invested) it’s hard to escape the thought that if they take off they could eventually change outcomes on the platform. (The EIS100 has only raised £1.2m so far of the £1 to £5m Seedrs originally expected, so currently this is moot.) Similarly, Auto Invest could negate the ‘wisdom of the crowd’ by automating ‘pile on’ investing. If these solutions became big features of the platform, firms seeking investment might even somehow game for them. Seedrs will need to be alert and adaptive to this potential.
  • Lots of detail to tell HMRC to get EIS tax reliefSeedrs says its platform makes claiming EIS reliefs easier – with digital tax certificates accessible on-site – but you will still end up with 100-odd items to declare to HMRC with the EIS100. In my experience, for each qualifying investment you have to open a form, get certain details off it, and put them on a tax return. I do 5-15 a year, and it’s fiddly. You’ll want to set aside some time to do a hundred! (That said, depending on how much you invest it’ll probably be well worth it on an hourly rate…)
  • No chance to discover you’re a good VC investor, or to have fun! – As I’ve said before, I was drawn to seed investing because I wanted to expand my investing and business knowledge. If I was worth £20m I’d be doing it via traditional angel investing but I’m not, so I’ve chosen to explore crowdfunding – warts and all – with 3-5% of my portfolio. For me, the learning is a huge part of why I went down this route. If I wanted to outsource VC investing I’d probably look to traditional funds, or even VCTs for the tax reliefs (though the high charges are off-putting).
  • Why isn’t Seedrs running its own VC funds?Seedrs is putting a lot of store on its own due diligence and pre-filters as to why these solutions could be successful. Indeed if that 12% IRR it claims to-date across all successful fundraising on the platform holds up over the long-term, I think it will be a remarkable and impressive figure. So much so, that you wonder why Seedrs hasn’t put its smarts into creating a conventional VC fund? The FAQ cited above claims it wants to give investors in the EIS100 liquidity opportunities as individual firms exit, hence it avoided the traditional fund route, but that’s never been a concern for traditional VC houses. Such funds charge a lot more than 25 basis points a year, too! I suppose Seedrs might argue the crowdfunding platform – and even the crowd of individual investors it attracts, who may go on to promote the funded companies and so on – is part of the secret sauce, and that it wouldn’t expect to see 12% IRR without it. Still any cynic would ask this question, and it often pays to be a cynic in active investing.

Do androids dream of electric exits?

I started this article vowing to write no more than 1,200 words, and here we are with another 3,000 word-sized monster!

No doubt some Seedrs insiders might still think I’ve skimped over aspects of their offerings, or been too glib in my pros and cons. The investment memorandum you can download from the EIS100 pitch page is 78 pages long, by way of comparison. (And I’d urge you to read it if you’re thinking of investing.)

Similarly, I’m sure some of you believe even writing about all this (rather than a 97th article about global tracker funds) is a dereliction of duty.

So I’ll just conclude by saying the answer is to go and do your own research on Seedrs if your interest is piqued, take this simply as an introduction, and maybe continue the conversation (constructively, please) in the comments below.

I’m fascinated by the evolution of this market, but it’s very early days.

Remember, if you follow my link to Seedrs and subsequently invest then you may qualify for a free £50 credit to your account – and I may get a bonus, too. But please don’t consider investing just for this cash! Again, this is high-risk investing where outcomes vary wildly. Do a lot of research before considering investing more than fun money. I also suggest you read Angel by Jason Calacanis for a blunt introduction to seed-style investing.

  1. It’s not impossible we could eventually see something – an investment bank could decide to offer some sort of synthetic note that tracks a VC index, for example. But it’d still be a complicated product. []
  2. This is called ‘adverse selection’. []
  3. With that said, traditional stock pickers need to learn new methods to value early-stage firms. I often see people talking about P/E ratios or even asking for dividends when talking to start-ups about valuations. That won’t get you far in valuing new companies. []
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The Gordon Equation gives a glimpse of the future

The Gordon Equation1 is a popular rule of thumb for gauging expected equity returns.

It’s been used by investing luminaries such as the late great John Bogle, Bill Bernstein and others to get a sense of what the future could hold for our investments in the long term.

All good investment plans rely on having some idea of your investments’ growth prospects. Using average historical return data is one way of estimating your chances, but it’s not necessarily the best.

The Gordon Equation is arguably a better signal because it bundles current valuations and long-term trend data into one simple formula – one which anyone can calculate.

I’ll take you through it now, and explain how it works.

I’ll also deliver the customary caveats and misuse warnings. (Now that you could have predicted!)

The Gordon Equation formula

The Gordon formula can be applied to any broad equity market index, such as the MSCI World or FTSE All-Share.

It looks like this:

Expected real return from equities = Current dividend yield + Real earnings growth

Let’s try plugging in some numbers:

Expected return FTSE All-Share = 4 + 1.4 = 5.4% (annualised2)

Expected return MSCI World = 1.7 + 1.4 = 3.1% (annualised)

That’s it. The Gordon Equation tells us that prospects for the UK over the next couple of decades are pretty cheery overall, while it douses our flame for global developed markets.

So where did I get those plug-in numbers from?

Current dividend yield

The dividend yield is the percentage return paid by your holdings as dividend income.

For a tracker fund, the dividend yield is the total dividend payments (over the last 12-months, typically) divided by the Net Asset Value (NAV).3

Grab the dividend yield from an index tracker that follows the market you care about, and you’ve got the first half of the Gordon Equation.

I got the 1.7% above from the current yield of the iShares MSCI World ETF.

The 4% came courtesy of the Vanguard FTSE All-Share Index Trust.

Expect the numbers quoted to vary a little, depending on your source. For example, Vanguard’s FTSE 100 ETF has a slightly different yield to its index fund (which varies again by Inc or Acc version.)

Don’t stress it – expected returns have all the accuracy of nerf gun darts. They are not laser-guided munitions and can only get us into the splash zone.

Real earnings growth

For the second number, we’re talking about the expected annualised growth rate of earnings per share. Yes, we are!

By earnings I mean corporate profits and by real I mean after inflation is stripped out.

Some versions of the Gordon Equation refer to real dividend growth instead. In the long-term it’s all the same hamburger, as rising profits and dividends usually go together like early marriage and divorce.

We’re looking for a long-term trend rate and we’re looking for a credible source to give it to us.

Here’s a few taken down from the Credible Source Shelf:

  • Investing sage Bill Bernstein recommended a 1.32% real dividend growth rate for the US in his excellent book, The Investor’s Manifesto.
  • That’s similar to the 1.4% real earnings growth forecast by fund provider Research Affiliates for global developed markets.
  • Then there’s the 1.5% real earnings growth for developed markets calculated by AQR, another fund provider with a great track record in research. AQR also proposes a 2% figure for emerging markets.

In my examples I plumped for the middle ground of 1.4%. Different practioners use different assumptions, so pick your poison and don’t drop into the bookies on the way home.

Incidentally, these three sources all adjust their aim to take into account the increasing use of share buybacks.

Handle me with care

As I’ve hinted, the Gordon Equation isn’t a trip to the future in a Delorean, but neither is it a crackpot prophecy.

The equation has a decent track record of guiding expectations into the right ballpark, over the long-term.

If you consult Gordon everyday like a Magic 8 ball then you’ll constantly get a different answer, because the dividend yield varies in tune to the rise and fall of market P/E ratios.

I suggest you use it annually to keep your plan on track. Combine it with our piece on estimating your overall portfolio expected return to keep a grip on the bigger picture.

Take it steady,

The Accumulator

  1. Finance professor Myron Gordon of the University of Toronto created the Gordon Equation. []
  2. i.e. The expected average annual return. Note annual returns will not be smooth in practice! []
  3. Technically the yield you’ll receive as an investor is the total dividend divided by the market price, but for trackers price and NAV are usually the same. []
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Weekend reading: Actively able

Weekend reading logo

What caught my eye this week.

I don’t write much about active investing on the blog these days – but I remain the same investing junkie who was buying housebuilders in 2011 and getting gold miners wrong in 2013.

I was therefore thrilled this week to meet a fund manager I’ve admired for well over a decade – Nick Train, who runs the Finsbury Growth & Income and Lindsell Train Investment trusts, among other things.

Train’s writings on the Lindsell Train website have been must-reads for me for years. But I was still steeled for disappointment on meeting the man in the flesh.

A lifetime ago I used to interview bands, and it was almost always underwhelming. The one time I did interview a band who truly lived up to my youthful notions of rock-and-roll1 I sheepishly retired from band-interviewing! I’m much older, a tad wiser, and have fewer delusions about people these days.

The funny thing is I don’t even invest the way Train does. I think it’d be great to identify and hold the best companies forever, Train-style, but experience has taught me I can’t do it.

I can’t even buy and hold Train’s funds! Although I do own a little FGT right now.2

So in some respects this was simple investor-groupie-ism.

Anyway, Train did not disappoint. He seemed about as level-headed as one of the best fund managers of his generation could be expected to be – and winningly paranoid about what the world and the market could yet do to his portfolio. He even warned against applying the word brilliant to anyone who owes their fortune and livelihood to something as capricious as the stock market, and to Lady Luck.

Fund managers get a rough ride these days, and understandably so. Academia – and common sense – has shown active investing is a zero-sum game – and a weight of evidence has demonstrated that after costs, most active funds lose to the market.

Nearly everyone reading this will be better off using tracker funds than active ones – let alone doing what I do, which is pick stocks.

But as I’ve said before – to some criticism from the passive purists among you – every fund manager (as distinct from wealth manager or banker, where this definitely does not apply) that I’ve met has been really interesting to talk to, and most have made me a little jealous of their day jobs.

Obviously it helps that we have a passion in common – but that’s my point. Criticize these guys for cognitive dissonance if you like, but don’t think the best don’t live and breathe investing. They fail to beat the market because it’s incredibly difficult to do so, not because they’re out playing golf.

The era of the star fund manager is long gone. I expect most readers under-30 can’t name a famous investor besides Warren Buffett, and amen to that.

But I don’t mind admitting I’m from another era, and a little weird.

And that I was a little bit starstruck – and a little envious – of Nick Train!

[continue reading…]

  1. Mercury Rev, if there are any indie musos out there. []
  2. I never invest in open-ended funds, and only occasionally in investment trusts. The fun for me in active investing is finding great companies, not great fund managers. []
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Simple maths for investors

A teacher points at a blackboard covered in his simple investor maths.

Maths is not my strong suit, but it doesn’t half1 come in handy for keeping a grip on your investments.

In this post we’ll look at a few simple investing maths techniques to help you stay on top of your financial life.

Apologies in advance if you find it all too simple, or too hard, or too clumsy. When it comes to maths, I’m like a foreigner with an amusing accent.

Percentages

To do percentages on your phone calculator, first divide the percentage by 100 and forget the % sign. So:

10% / 100 = 0.1
1% / 100 = 0.01
0.1% / 100 = 0.001

Now you have the percentage as a decimal figure you can multiply with other numbers in your life to find percentage values.

For example, let’s say you hold £10,000 in a global index tracker that sports an Ongoing Charge Figure (OCF) of 0.1% and you want to know the cost in £££s.

Take the percentage figure, 0.1%, and divide by 100:

0.1% / 100 = 0.001 (the percentage as a decimal figure)

Multiply the decimal by your holding:

£10,000 x 0.001 = £10 (the OCF’s cost per year)

From there, you can decide if a 0.09% global tracker is worth switching to. First, find the percentage saving between the two trackers as a decimal figure:

0.1% – 0.09% = 0.01%

0.01% / 100 = 0.0001

How much does that save us on our £10,000 holding?

£10,000 x 0.0001 = £1 (saved per year)

Quick, call Martin Lewis!

To convert fractions to decimals: divide the top by the bottom. That is, divide the numerator by the denominator.

¼ = 0.25

⅔ = 0.667

Multiply the decimal by 100 to get the percentage:

0.25 x 100 = 25%

0.667 x 100 = 66.7%

Also handy:

x% of y = y% of x

So:

8% of 50 = 50% of 8

50% of 8 = 4

8% of 50 = 4

Gains

How much is a 20% gain worth to you?

First add your percentage gain to 100 then divide by 100.

So:

(20 + 100) / 100 = 1.2

Multiply this number by your holding:

£100 x 1.2 = £120 (your holding after a 20% gain on £100)

Losses

Losing money is not so much fun. Maybe the market has plunged 20%. Or the taxman is after you.

How much are you out of pocket?

Divide your loss by 100 to get the decimal: 20% / 100 = 0.2

£100 x 0.2 = £20 (loss)

Or you might wonder: What have I got left after the taxman takes his 20%?

Well, after a 20% loss you’ve got 80% left:

£100 x 0.8 = £80 (remaining)

Regaining losses

What gain do you need to recover from a 20% loss?

20% / 80% x 100 = 25% (gain needed to make good the loss)

Where 20 is the percentage lost, 80 is the percentage left after the loss, and 25% is the gain needed to breakeven.

Here’s the proof:

£80 x 1.25 = £100 (the amount we had before the 20% loss)

You can also use these calculations to work out how much tax relief you’re due. For example, a 20% tax-payer should get 25% of their net contribution returned to their SIPP in tax relief.

Play around with the numbers and you’ll see very big losses can be hard to recover from.

Picture a 75% loss:

75% / 25% x 100 = 300%

You need a 300% cumulative gain to climb back out of the hole. *shudder*

Compounding gains and losses

We rarely make a single gain or loss and that’s the end of it. Our portfolios are advancing and retreating every year, every day – every nanosecond if you check too often.

You can string a sequence of returns together like this:

£100 x 1.05 x 0.9 x 0.85 x 1.11 x 1.32 = £118

…where the returns are 5%, -10%, -15%, 11%, 32%.

Negative compounding can set you back quickly. Consider how your salary is corroded by annual inflation unmitigated by an offsetting pay rise:

£100 x 0.96 x 0.98 x 0.97 x 0.95 x 0.97 = £84

Now your salary buys 16% less than it did five years ago. Or it’s fallen to 84% of its former value.

You can also use this method to see by how much a tracker is lagging behind its index every year.

Returning to positive territory, those magic compound interest calculators work the same way:

£100 x 1.1 x 1.1 x 1.1 x 1.1 x 1.1 = £161

Where a £100 lump sum accumulates 10% interest once a year for five years.

You can save on typing by multiplying your interest rate by the power of the number of years you’ll compound.

So 1.1 is multiplied by the power of 10 if you’ll earn the 10% interest for 10 years. (This is assuming annual interest payments – if interest is compounded daily or monthly then you’ll need to dive deeper into the formula.)

You can also quickly use this formula – or a compound interest calculator – to check the damage done by expensive funds:

Expensive active fund

£10,000 lump sum invested
£6,000 invested every year
40 years compounding
5% expected return minus 0.75% OCF = 4.25% return p.a.
Future value = £683,497

Cheap tracker fund

£10,000 lump sum invested
£6,000 invested every year
40 years compounding
5% expected return minus 0.1% OCF = 4.9% return p.a.
Future value = £809,781

Using our mad maths skillz:

£809,781 / £683,497 = 1.185
1.185 x 100 = 118.5
118.5% – 100% = 18.5%

You earn 18.5% more by avoiding high fees.

Weighted average

You might want to know how much each asset class contributes to your overall portfolio expected return, or to the overall cost of your portfolio.

Enter weighted averages!

Let’s say your portfolio breaks down like this:

Index fund Allocation (%) OCF (%)
Global index tracker 50 0.2
UK index tracker 10 0.1
UK bond index tracker 40 0.15

The weighted average will tell you the overall OCF of your portfolio, after taking into account how your money is allocated across the differently priced funds.

First, multiply each fund’s allocation by its OCF.

For instance, the global index tracker’s weighted OCF = 0.5 x 0.2 = 0.1%

Then add up each weighted OCF to find your portfolio’s total OCF:

Index fund Allocation (%) OCF (%) Weighted OCF (%)
Global index tracker 50 0.2 0.5 x 0.2
= 0.1
UK index tracker 10 0.1 0.1 x 0.1
= 0.01
UK bond index tracker 40 0.15 0.15 x 0.15
= 0.06
Total portfolio OCF 100 0.17%

Go through the same process to estimate your portfolio’s expected return, but replace the OCFs with each asset class’s expected return figure.

How about if you have two different accounts on two different platforms and want to know your overall return?

Weighted average swings into action again:

Account one is worth £100,000 and returned 7%.

Account two is worth £250,000 and returned 5%.

Overall return = [(£100,000 x 7%) + (£250,000 x 5%)] / (£100,000 + £250,000) = 5.57%

Here’s the slow-motion action replay:

£100,000 x 0.07 = £7,000 (the return from account one)

£250,000 x 0.05 = £12,500 (the return from account two)

Add up your return and divide by your overall account total:

£7,000 + £12,500 = £19,500 (overall return)

£19,500 / £350,000 x 100 = 5.57% (the weighted average return of your accounts)

Pound cost averaging

Pound cost averaging can come off as some kind of witchcraft – shares go into free-fall and somehow you come up smelling of roses. But it’s the average price that counts.

En guarde!

You buy one share at £100
The market tumbles 50%
You buy two more shares at £50 each
You’ve paid £200 paid for three shares

£200 / 3 = £66.67 (average price paid)

When the market share price bounces back above your average share price then you’re in profit:

3 x £66.68 = £200.04 (back in the black)

Profit and loss

How do you calculate a profit or loss as a percentage?

Like this:

(Price sold – Price bought) / (Price bought) x 100 = profit or loss %

For example, the price bought is the amount you originally paid for the investment, say £100, and then we sold at £110:

£110 – £100 = £10 (profit)

£10 / £100 x 100 = 10% (gain)

You probably paid some trading fees along the way and maybe got a dividend, too:

((Price sold – Price bought) + Income gain – Costs) / Price bought x 100

£110 – £100 = £10 (profit as before)

£10 + £4 – £12 = £2 (after adding a £4 dividend and subtracting £12 in trading fees)

£2 / £100 x 100 = 2% gain.

(Welcome to The Investor’s life!)

Financial independence: How much do I need?

The big kahuna – what will it cost you to stick it the man?

First calculate how much annual income you need for financial independence (FI).

Let’s say you can live on £25,000 a year.

Now choose a sustainable withdrawal rate (SWR) that you’ll use to drawdown your wealth when you reach FI.

Let’s say 3%, which is 0.03 in decimal.

£25,000 / 0.03 = £833,333 (the stash you need to accumulate in today’s money to declare FI at a 3% SWR)

The proof:

£833,333 x 0.03 = £25,000
£25,000 / £833,333 x 100 = 3%

Side note: 3% SWR is a more conservative version of the ‘4% rule’ commonly bandied about. Because it’s more conservative, it’s safer. This is not a party political broadcast.

‘Multiply by 25’ is another way of expressing the 4% rule: 1 / 0.04 = 25.

Multiply your annual income target by 25 and you get the same result as dividing by 0.04. Multiplying by 33.333 is the same deal but for a 3% SWR.

The rule of 400 is a quick way of estimating how much capital you’ll need to support a monthly expense in your FI golden age.

Say you spend £40 a month on the gym:

£40 x 400 = £16,000 (the capital to support that spending during FI using a 3% SWR)

Now you can decide whether that gym is really ‘giving you joy’ or not.

You can work out the yield of an annuity using SWR maths, too. If the annuity company wants £833,333 in exchange for an income of £25,000 then they’re offering you a yield of 3%:

£25,000 / £833,333 x 100 = 3% yield.

You can compare that yield to your other investment options.2

Probability: Will you need all that money?

You and your significant other are planning a long and happy retirement. The longer you expect to last, the more conservative your SWR should be.

But you can be too conservative, if you’re not realistic about your survival chances in old age.

It’s easy to be squeamish about this but what are the chances of either of you surviving to, say, 100?

Jill has a 15.4% probability of living to 100 according to the Office For National Statistics (ONS) life expectancy calculator.

Jack has an 11% chance.

What’s the probability they’ll still need an income for two at 100?

0.154 x 0.11 x 100 = 1.7%.

Gosh. I don’t know who the hell Jack and Jill are but I’ve got a lump in my throat.

Quick, let’s get Vulcan on this!

The probability formula that determines our couple’s joint chances is:

p(A and B) = p(A) x p(B)

We need a different formula to figure the chance of Jack OR Jill surviving to 100… [I can’t look! – The Investor]

First, add their individual probabilities together:

0.154 + 0.11 = 0.264

Now multiply their individual probabilities together:

0.154 x 0.11 = 0.01694

Subtract the second number from the first:

0.264 – 0.01694 x 100 = 24.7% the chance of Jack OR Jill surviving to 100.

The or probability formula is:

p(A or B) = p(A) + p(B) – p(A and B)

This formula is used because Jack or Jill’s survival are not mutually exclusive events. They can both survive and that’s OK. They love each other.

When the events are mutually exclusive you’d use:

p(A or B) = p(A) + p(B)

There can be only one!

Chances of Jack and Jill not making it to 100? Just for completeness:

0.846 x 0.89 x 100 = 75.3%

If you’re dying to try this for yourself then the ONS publishes extensive life expectancy data for the UK.

Another side note: Here’s the Monevator take on life expectancy and your retirement plan.

Back in the present, Jack and Jill are planning a 40-year retirement from age 60 with a 3% SWR. They’ve baked in a 10% failure rate.

The failure rate means that in 10% of their scenarios, they’d need to lower their income at some point because of a poor sequence of returns. But for the failure rate to matter, Jack and Jill have to be alive to worry about it at the time.

The probability of that is:

0.1 x 0.247 x 100 = 2.47% (failure rate)

Where there’s a 10% chance of failure within 40 years and – from our sums above – a 24.7% chance of either of our two protagonists living to 100.

The two events are independent of each other3 so we multiply their probabilities together and end up with a 97.5% chance of success!

Of course success could mean that everybody is dead, but let’s set that aside for the moment.

The 10% failure rate only matters 25% of the time, which turns out to be a very small 2.5% probability of both events occurring simultaneously.

Adjusting for inflation

Earlier we calculated an FI target of £833,000 – but inflation is going to weaken the potency of your stash like an intestinal worm. This means every year your target will be less capable of delivering the purchasing power you require.

To maintain purchasing power, you must upweight your target by the inflation rate.

If inflation is 3% this year then multiply your target by 1.03 after 12-months:

£833,333 x 1.03 = £858,333 (adjusted for 3% inflation)

Next year, multiply £858,333 by year two’s inflation number.

Perhaps it’s 2.5%:

£858,333 x 1.025 = £879,791 (FI target after two years of inflation adjustment)

Adjust last year’s target by this year’s inflation rate every year.

If you stick to £833,333 then your portfolio will be like a puffed-up bodybuilder – it will still look good but isn’t really that strong because your returns are nominal. We live in today’s money, and inflation adjustments keep our returns real.

The same upweighting technique applies to your investment contributions and your target income.

The UK’s inflation figures are published by the ONS. Personally, I adjust for Retail Price Index (RPI) inflation because it contains housing costs and Consumer Price index (CPI) inflation does not.

Also RPI is always higher, and I’m a glutton for punishment.

RPI has come in for much official criticism, however, and so now there’s CPIH – the Consumer Prices Index including owner occupiers’ housing costs.

So you could use CPIH if RPI looks depressing and you’re not into government conspiracy theories about how they suppress the true inflation figures to keep us peons in our place.

[Editor’s note: Please don’t comment about inflation conspiracies below, this paragraph was permitted for leavening purposes only.]

Tax costs

Your effective tax rate is the total amount you pay in taxes, divided by your gross income.

Perhaps you earn £75,000 and pay £23,000 in income tax and National Insurance (NI).

£23,000 / £75,000 x 100 = 30.7% (your effective tax rate)

After income tax and NI, each £1 of spending costs you:

£1 / 69.3 x 100 = £1.44

Your marginal rate of tax is the amount you pay on each additional pound of income you earn.

How much will I need to cover tax?

If you need £25,000 income to live on then:

£25,000 – £12,500 tax-free personal allowance = £12,500 (taxed at 20%)

£12,500 / 0.8 = £15,625 (the gross income you need)

The proof:

£15,625 x 0.8 = £12,500 after 20% tax.

I haven’t factored in ISAs and personal savings allowance and so on, but you get the idea.

Platforms: choosing the cheapest

To compare fixed fee Platform A with percentage fee-based Platform B, make the following calculation:

Tot up all the charges you’d incur with the most competitive of the fixed fee platforms you can find on our broker table.

Make sure you count any annual fees, platform fees, dealing charges, and other relevant costs.

Take your fixed fee cost and compare that against the most competitive percentage fee platform.

Total annual fixed fee platform costs divided by percentage fee platform cost = your breakeven point.

Here’s one we made earlier:

Fixed fees at Platform A = £80
Percentage fee at Platform B = 0.25%
£80 / 0.0025 = £32,000 breakeven point.

The breakeven point – £32,000 in this example – refers to your portfolio’s size.

In the example above, we’re better off with platform A if our portfolio is worth more than £32,000. Any less and we should bunk up with platform B.

A few notes:

  • Subtract any fixed fees charged by Platform B from Platform A’s fixed fees before making the calculation.
  • If one platform offers fund discounts, or doesn’t stock exactly the same products, then you can factor that in using the portfolio weighted average OCF technique detailed earlier in this piece. Work out your portfolio’s average return in £££s on both platforms and add to the fixed fees above.
  • Add on entry and exit charges.

Switching platforms can be mucho hassle, and platforms periodically change their charges. Only switch when it’s seriously worth your while.

Withholding tax cost comparison

Okay, so we’re tempted by a tracker with a cheap OCF but which has a high withholding tax rate on dividends. We want to pit it against a higher OCF tracker with a lower withholding tax rate.

Find fund one’s dividend yield e.g. 2%. Then multiply the dividend yield by the withholding tax rate. E.g. 30%.

0.02 x 0.3 = 0.006 (the percentage cost of the withholding tax)

Add this cost to the fund’s OCF. E.g. 0.1%.

0.006 + 0.001 = 0.007 x 100 = 0.7% (OCF and withholding tax cost)

Fund two has the same 2% dividend yield, a lower 15% withholding tax, 0.2% OCF.

Going through the same process:

0.02 x 0.15 = 0.003 (the percentage cost of the withholding tax)

Now add the OCF:

0.003 + 0.002 x 100 = 0.5% (OCF and withholding tax cost)

Fund two is 0.2% cheaper than fund one – despite its higher OCF – because it has a lower withholding tax rate.

Rule of 72

The famed rule of 72 calculates approximately how long it takes to double your money at a given rate of return. Divide 72 by your actual or expected return rate.

For example:

72 / 4% = 18 (years to double your money if you earn 4% p.a.)

Rebalancing your portfolio

For a quick rebalance, multiply your total portfolio value by your target allocation for each asset class.

For example:

Target asset allocation
50% Global equity
50% UK gilts

Total portfolio value = £50,000

0.5 x £50,000 = £25,000 target value for each asset class.

Now subtract the actual value of each fund from the target value (assuming that each fund represents an asset class).

For example:

Global equity tracker
£25,000 – £30,000 = -£5,000
So sell £5,000 of this fund.

UK gilts tracker
£25,000 – £20,000 = +£5,000
Buy £5,000 of this fund.

Preference for lotteries

People love a bet. Long odds and big pay-outs are the stuff of dreams. Next time you’re counseling a relative on that lottery ticket purchase, here’s the math:

£1 ticket price
£1,000,000 jackpot
Odds of a win: 0.00001%

The value of the gamble is:

£1,000,000 x 0.0000001 = £0.1 or 10p. The value of your gamble vs the ticket price is -90p.

What if you have the opportunity to invest £1,000 for a 50% chance of making £1,500 vs a 50% chance of losing the lot?

(0.5 x £1,500) – (0.5 x £1,000) = +£250

That’s a better bet than buying a thousand lottery tickets if you can afford the potential loss.

The final reckoning

Obviously you can use a calculator to do all the work. There’s a Monevator page with a ton of useful financial calculators.

But calculators break. And I think it’s empowering to know how these things work, and to be able to double check the information yourself.

If you have a simpler take on the investor maths above or want to share any other techniques, please tell us in the comments below!

Take it steady,

The Accumulator

  1. Or 50% or ½ or 0.5. Hmm, landing a maths joke is not easy. []
  2. Remembering to take into account the certainty of payment and myriad other factors. []
  3. Sort of, in theory with a constant SWR. In practice if one died the other might spend less of that annual withdrawal / allowance, saving a bit and reducing the chance of failure. []
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