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Reactions to the Red Box (UK Budget 2018)

I’ve noticed that there has ended up being a string of primarily financial posts. This was not intentional, but there happened to be lots of interesting material related to finance that has come up over the past few weeks. Also, a disclaimer: I am not a financial advisor and am not offering professional financial advice. Conduct your own due diligence or seek an advisor if necessary.

The UK government announced its Budget for 2018/2019, though with the caveat that it might be subject to change in the event of a no-deal Brexit (which looks a bit more of a risk each day). I’m a UK taxpayer, and thus changes in relation to tax and relevant allowances interests me; tax is my largest expense every year. As an expatriate I don’t have recourse to public funds, so I’m less aware of the changes pertaining to benefits and universal credit. The list below is far from exhaustive; readers should consult a more detailed guide like MoneySavingExpert or even the Budget itself if they want more details, or this Which? article if they’re considering optimising their tax affairs.

Income and Take-Home Pay

  • Personal allowance has increased from £11,600 to £12,500 and the higher rate (40%) band has increased from £46,350 to £50,000.
  • National insurance thresholds have risen; the start of the 12% band has increased from £8,424 to £8,632 (by £208), while its end has increased from £46,834 to £50,024 (by £3,190).

I was aware that the Conservative manifesto had pledged to bump the personal allowance and higher rate thresholds to these levels by 2020, so this is one year early. These increases seemed fairly generous – although I will be paying more in NI (notice that £2,982 is now taxed an extra 10 percent and £208 is now taxed 2 fewer percent – in other words I’m paying £294 more) the income tax saving looks pretty good, especially in nominal terms. (Whether Brexit wrecks the value of the pound further is another separate concern.)

A separate consequence of this is that the 62% marginal band has extended to £125,000 as well, as there’s more personal allowance to lose. Regardless, the changes are certainly positive.

In general, with inflation being positive, the value of a pound decreases over time. Thus, thresholds should be increased nominally at least in line with inflation if the goal is to implement a ‘neutral’ policy. I haven’t been keeping track of the history of these levels, but the roughly 7.75% bump in the thresholds is certainly well above inflation (and hopefully above two years of inflation – since the thresholds will be frozen next year).

Other Income Sources

  • The Personal Savings Allowance remains at £1,000 for basic rate taxpayers, £500 for higher rate and £0 for additional rate.
  • The Dividend Allowance remains at £2,000 – note that dividends in a pension or ISA do not count against this limit. Dividend tax rates are unchanged.
  • The Trading and Property Allowances remain at £1,000.
  • The Rent-a-Room scheme threshold remains at £7,500.

Most things held pretty steady in nominal terms (which means they’ve gone down slightly in real terms). That said, if interest rates continue to go up the savings allowance thresholds might quickly become relevant to me (obligatory hello to Marcus). I’m considerably further from the dividend allowance threshold, though again that’s something to watch out for if the markets decide to be exuberant. I haven’t been using the other allowances, though if an opportunity comes up that could be a possibility.

Securities and Assets

  • The ISA (tax-advantaged savings account) limit remains at £20,000.
  • The Capital Gains Allowance was increased slightly, from £11,700 to £12,000. Tax on capital gains is unchanged.
  • The Lifetime Allowance for pensions was increased in line with inflation, from £1.03M to £1.055M.

Not too much to say here. The markets haven’t been so friendly so there’s certainly no extravaganza of crystallising significant capital gains this time around. To be fair, much of my gains in the 2016/17 tax year centered around massive pound weakness. ISA allowance being held where it is is a bit of a damp squib as I max it, but to be fair it is still very generous.

Consumption Taxes

  • VAT standard rate remains at 20%.
  • Air Passenger Duty (APD) remains flat for short-haul flights, but rises by RPI for long-haul flights (roughly £2 for Y, £4 for premium cabins).
  • Fuel duty is frozen.
  • Alcohol duty is frozen for beer, “most cider” and spirits. Duty on wine and higher-strength cider increases by RPI.
  • Tobacco duty increases by RPI + 2%. I don’t smoke, so don’t know too much.

Owing to how it’s calculated RPI tends to be higher – and it’s a little frustrating / naughty that most payments coming out of the Treasury (e.g. planned bumps in income tax/pension allowances) seem to be CPI indexed while those going in tend to be RPI indexed. The main reason suggested for the double standards is legacy technical debt, but that doesn’t seem to explain why the inconsistencies seem to consistently resolve in favour of the exchequer.

The APD change garners revenue for the Treasury, though it’s a little sad as APD is already incredibly high compared to aviation duties in other countries. That might actually increase the attractiveness of routing through Zurich or one of the German hubs when I fly the London-Singapore route.

For comparison, long-haul premium cabin APD ex-UK will be £172. Singapore’s duty is about S$47 (about £27); Zurich weighs in at CHF 35 (also about £27) and Munich at EUR 42 (about £37).

I guess I’m mildly affected by the alcohol duty change as I do drink wine, but I don’t drink a lot so the impact is very minimal. I’m not currently affected by the fuel or tobacco duty changes.

50p Coin

  • The Royal Mint will produce a 50p coin to mark Brexit.

I’m somewhat of a Brexit bear and remain one (pun not intended). Taken at face value, the inscription (“peace, prosperity and friendship with all nations”) is at least one way in which I could see it possibly having a shot at working out – and assuming Brexit does go ahead is what I hope the government will do.

However, the quote is adapted from Thomas Jefferson’s inauguration speech as US President. The continuation is “entangling alliances with none”, which is in some ways apt if the UK is concerned with the EU’s ever closer union – though I’d think the US and UK in a modern-day context certainly are allies!

Conclusion

In terms of personal impact, the Budget felt very much like a constructive or at least benign continuation of previous Budgets. That said, I realise I say that from a point of privilege in that I view the status quo as manageable. I’m aware that there have been changes to benefits (notably, universal credit) which have made some worse off.

The Problem of the Golden Basket

Somewhat related to the previous post on paydays, I had lunch and then coffee with another friend, and for some reason our discussion turned to personal finance as well. Unlike the last time, I was the one starting with the view that deviates from conventional theory this time.

Suppose you have a choice between two savings accounts. One account pays 2% AER and the other pays 1% AER – so £10000 invested for a year would earn £200 in the first account but only £100 in the second. Should you allocate 100% of your savings to the account that pays 2% AER?

In general, if all other things were held equal, there probably isn’t much of a reason not to allocate everything to the 2% account. However, the standard for all other things has to be high. In practice, I can see quite a few scenarios where there may be legitimate reasons to allocate some money to the 1% account.

One possible reason could be terms of access. Clearly, if the 2% account is a fixed rate bond only allowing access to the money after some amount of time while the 1% is an easy-access account, that provides a clear reason. If one wishes to maintain an emergency fund, for example, the fixed rate bond is probably best avoided even if it pays higher interest. Some savings accounts, while not having a fixed term, place restrictions on withdrawals in terms of frequency or advance notice in exchange for higher rates – again, be careful about using these accounts to park an emergency fund.

Another reason could involve how the accounts compound. The annual equivalent rate (AER) refers to how much money one will have after a year. However, if one wants the funds together with some interest before one full year, then precisely how the accounts pay interest becomes significant. If the 1% account compounds monthly while the 2% account compounds annually only, then between one month and one year after the start date the 1% account has more withdrawable interest. This is a variant of the access problem, though this focuses on access to interest as opposed to the principal. This may seem a little short-term minded, but could be interesting if one is engaging in stoozing or has other pressing financial commitments.

The amount of money one has is also relevant. Financial institutions can fail; in this case, the UK’s Financial Services Compensation Scheme (FSCS) guarantees up to £85,000 per depositor per authorised bank/building society. There is thus certainly a case for keeping not more than that amount with each bank; if one was fortunate enough for one’s savings to exceed £170,000, finding a third bank seems reasonable. I’ve never seen cash as doing the heavy lifting as far as growing my portfolio was concerned. I’d collect interest as available, but would prioritise safety. If the accounts were held with the same provider, of course, then this argument falls down – even if one has multiple accounts, the FSCS limit is on a per-bank basis. In fact, one has to be careful as some bank brands do share authorisations – meaning that an individual will only get the protection once even if several of these banks fail.

In general, the inconvenience that might be caused by failures is something worth considering as well. The FSCS compensation only applies if the bank is suitably authorised; even if one’s balance is fully covered by the FSCS, claims can take one to four weeks to process. I think I’d be much more comfortable having at least a nontrivial amount in a separate account (two to three months’ expenses, ideally) if possible.

Customer service is another factor. I’d probably prioritise that more significantly for more complex products – however, for a savings account it would still be useful.

Furthermore, there are other principles which individuals might find important. MoneySavingExpert on its savings account best buy tables has a section for highly-rated ‘ethical savings accounts’. The criteria Ethical Consumer (which MSE works with) include concerns like tax avoidance and funding of climate change, though I don’t necessarily agree with all of them (“excessive director’s remuneration”, in particular – if someone is that valuable it seems unethical to me to artificially depress their salary). Similarly, Islamic banking is necessary for adherents, since interest is forbidden in Islam.

To conclude, there are quite a number of reasons why one might not actually want to put 100% in the higher interest bearing account. Of course it makes sense ceteris paribus (if all other things were held equal), but that seems unlikely in practice. The standard for all other things being held equal here is high – the access conditions, compounding conventions and bank account provider all need to match (and that isn’t even an exhaustive list).

Moving Cash Flows

I met a friend for a meal on the weekend, and among other things my friend mentioned that at his company, there was an internal debate over whether payday should be moved forward. This wasn’t a debate on the financial ability or willingness of the company to do this, but was instead focused on individual workers’ preferences.

My initial reaction was a bit of surprise. I wondered why this was even a debate, as I believed the answer should almost always be yes. This reminded me of the standard time-value-of-money question that I wrote about just over a year ago; being paid the same amount of money slightly earlier, mathematically, seems like an outright win. The UK hasn’t had negative interest rates yet – and even in a place like Switzerland where bank rate is negative, this isn’t typically passed on to most depositors.

Cash flow might be a problem if one considers the dollar-today-or-more-tomorrow question; however, this shouldn’t be an issue in this set-up. Valid cash-flow scenarios remain valid even if payday is brought forward. In a sense, an early payday creates additional options; it shouldn’t invalidate any existing ones.

With a bit more discussion and thought, though, we found that there were indeed valid reasons as to why one might not want payday to be shifted forward.

First, although the mathematical argument makes sense, there are some edge cases around tax liability. If one’s salary is close to a marginal rate change and a payment is pushed across a tax year boundary, the amount of tax one pays might change (and can increase). 

Also, although we speak of interest as an upside, how much benefit an individual can actually realise may be significantly limited. Some bank accounts pay interest based on the lowest balance on any day in the month, meaning that being paid a few days early yields no benefit. Even if interest is based on the average daily balance, the upside is also in most cases small. For a concrete example, 2017 median UK post-tax earnings would be about £1,884.60 per month. If one was getting paid three days early and storing that into a high-interest current account yielding 5% APR, the additional interest wouldn’t be more than about 30 pence.

Moving away from purely numerical considerations, there are many other plausible reasons too. Clearly, departing from an existing routine may affect one’s own financial tracking. I find this alone to be a little flimsy (surely one’s tracker should be adaptable to variations arising from December and/or weekends?). That said, if one is unlikely to derive much benefit from the money coming early (and it seems like in most cases there indeed wouldn’t be much benefit), the change would likely seem unnecessary.

Another scenario could be if one has many bills or other payments paid by direct debit, and cannot or does not want to pay all of them. In that case, deciding precisely where the money goes could be significant – for example, if one is faced with a decision to lose fuel or premium TV in winter. This is probably not the right system to handle a situation like that, but if one wishes to only make some payments then an unexpected early payday could mess the schedule up. Somewhat related might be joint accounts in households where there are financial disputes.

Taking advantage of an early payday also requires self-control. Consider that if one is living paycheck-to-paycheck, while an early payday might ease financial pressure, it also means that the time to the next paycheck is longer than normal (unless that is also shifted forward). This needs to be dealt with accordingly.

If you’d ask me whether I’d like payday to be shifted forward, I’d almost certainly say yes. Our discussion went to a further hypothetical – would you take a 1% pay cut to have your entire salary for the year paid on January 1st?

From a mathematical point of view, you would be comparing a lump sum of 0.99N dollars paid now, or (for simplicity) twelve payments of N/12 dollars paid 1/12, 2/12, \ldots, 12/12=1 years from now. Assuming that you can earn interest of r% per month and using monthly compounding, after one year we have

Value_{\text{LumpSum}} = 0.99N (1+r)^{12}

Value_{\text{Normal}} = \sum_{i=1}^{12} \left( \frac{N}{12} (1+r)^{12 - i} \right)

If we set these two to be equal and solve for r, we get a break even point of r = 0.00155. This computes out to an APR of about 1.87\%. This is higher than best-buy easy access accounts at time of writing (MoneySavingExpert identifies Marcus at 1.5%). You can beat this with fixed-rate deposits, and probably beat this through P2P loans, REITs and equities – though more risk is involved.

I think I could see that being a yes for me, though I’m not entirely sure I’d have the self control required to manage it properly!

Retirement by 40?

I overheard a conversation a few days ago on the near-impossibility of retiring by forty. It is understandable (consider 40 in relation to standard benchmarks for retirement – a private pension can be withdrawn at 55 and the state pension is given at 65, and these numbers are trending upwards). I’m not sure I agree, though; there exist quite a number of examples of people that have done this [1, 2]. Meta-analyses disagree (against: [3], in favour: [4]). It’s true that internet and media sources may perhaps not be reliable, but in any case one can perform the relevant analysis.

Even given the option, I’m not certain I would take it. It’s arguable that I had a taste of retirement for the two-odd months in between submitting my Masters thesis at Imperial and starting full-time at Palantir, and I didn’t find it that easy to fill my time after a while. I’d probably stand a better chance now, having reignited a couple of interests in things apart from computer science.

Anyway, let’s get to analysis. One simple way of decomposing this problem can involve

  1. Figuring out the amount required before retirement is feasible, and
  2. Figuring out the required savings rate to reach the result obtained in step 1.

For the first point, there is a well-known 4% rule. Suppose you withdraw 4% of your portfolio in the year when you retire, and then adjust your withdrawals for inflation every year. Then, your portfolio will last for at least 30 years in 96% of historical scenarios. I have some issues with this, biasing in both directions.

I think 4% seems lower than is reasonable, for several reasons:

  • The idea that one blindly draws the stipulated salary even when the market is down seems absurd. Really, one should factor in market returns when making one’s decisions about income, as in [5 – note, technical!].
  • The study assumes that the portfolio alone supports the retiree; yet, a side hustle of some kind may be relevant, and at least in the UK the state pension could kick in once the retiree reaches 65 (or whatever the age is at that time).

Yet, there are certain reasons to adjust the figure upwards too:

  • The life expectancy of someone who’s 40 is probably higher than 30 more years (especially one who’s considering retirement at 40!), hence that’s not enough as a baseline.
  • The study used the US markets, which have been performing very well. Of course, one can decide to use exclusively the US markets, but that tends to introduce currency risks too.
  • The study in question does not account for fund and platform fees. These can be kept quite low (I estimate my own portfolio operates at about 0.22%, and some of this is by choice because I hold some active and smart-beta funds, along with indices that are a bit more exotic) but invariably chew into returns.

It seems like it’s a reasonable rule of thumb, though I wouldn’t treat the figure as authoritative.

One needs to estimate asset returns and inflation for both parts 1 and 2; this can be partially simplified by working everything in real terms, though there is a risk that owing to high inflation increasing one’s savings in line with inflation can prove untenable. Typically, one relies on historical data; for instance, UK stocks have returned about a CAGR of 5.2% from 1900 to 2011 [6]. Post-retirement sequence of returns risk can prove troublesome, although the variance might indeed be smoothed out over a longer period.

Notice that assuming one starts from zero and using the 4% or any constant-percentage model, the only factor after the asset returns and inflation rate have been factored in would be your savings rate – the level of expenditure needed is a function of this. I guess one could introduce another factor for decreased spending upon retirement! An example of a concrete calculation (inclusive of a link to a spreadsheet) can be found in [7]. Using the examples there (5% real returns, 4% withdrawal rate) and bearing in mind that I have 14 years till I’m 40, that clocks in at a smidge above 55 percent.

For an individual, though, there’s probably a somewhat easier method to determine if a retirement by 40 or early retirement is feasible:

  1. As above – figure out the amount required.
  2. Given one’s past saving and investment patterns, estimate the amount one is likely to have at 40 if one continues to behave in the same way.

Of course, we need to make the same assumptions involved in figuring out the value computed in step 1. We also still can’t get away from estimating inflation or market returns in step 2. However, the previous calculation for step 2 assumes a constant savings rate; with this method it is a lot simpler to adjust the model to account for events peculiar to one’s own situation (such as long CDs maturing, stock options, vesting of bonuses, known large expenses etc.).

We then compare the figures in steps 1 and 2; there is of course some wiggle room. I think there’s a distinction to be drawn between deciding that one is financially independent and pulling the retirement trigger, though that’s perhaps a separate discussion topic. [8] I certainly would be interested in the first, but not the second at this time (and, hopefully, even at 40).

One can even switch the method up a bit further:

  1. Figure out the amount one is likely to have at 40 (step 2 above)
  2. Figure out the withdrawal amount one can derive from that. Decide if that’s feasible.

Again, we don’t get away from assumptions concerning inflation or market returns. Deriving values in step 2 gets tricky; one can always use the 4% rule or assume some other constant factor. It’s worth saying (for all of the methods) that building in fudge factors to leave some leeway for underwhelming market returns is probably a good idea, since getting back into the workforce after a long spell of early retirement might prove difficult.

Personally I’m very fortunate that this should be possible if I decide to push hard on it. It’s difficult to say though – past performance is not an indicator of future performance, and I’m at a point where I’d say my past spending is also not an indicator of future spending. I think I’m pretty frugal, but don’t entirely fancy maintaining the same degree of strictness I’ve been running with in my university years throughout. It’s certainly possible, but also definitely not easy, and I’m not sure it’s what I’d want to do.

Inflation and the Substitution Effect

I sometimes pick up my groceries at Iceland (the supermarket, not the country). When I was there today, I noticed a bunch of frozen pizzas which were typically on sale at £1 now on sale at 2 for £2.50. I thus bought zero of them, opting for a substitute (that turned out to be pretty good!). This is one example of a shortcoming of the generally accepted way of measuring inflation (via a consumer price index).

Inflation refers to an increase in general prices of goods and services (in numerical terms). With the devaluation of the pound after the Brexit vote, I’ve experienced imported inflation (because a pound buys fewer dollars/yen etc., and overseas suppliers of goods want to be paid in their currency).

Of course, one problem is how one measures “general prices of goods and services”. Typically, inflation is measured via changes in a consumer price index. This is an aggregate of the prices of a supposedly representative basket of goods and services. The basket is reviewed periodically, as some goods become more (or less) frequently consumed. For example, in the UK, this is managed by the Office for National Statistics. The 2016 basket is listed here, and changes included the addition of video game downloads and removal of nightclub entry.

Of course, individuals’ spending patterns can be very different from the “average”. One can imagine a personal inflation rate that could be very different from CPI. For example, I don’t drive, so a significant increase in the price of cars might not affect me very much. (There could be some knock-on effects, e.g. if the cost of minicab rides increases.) Similarly, an increase in the cost of recreational boats (which are part of the basket) would have little impact on me. Conversely, I consume a fair amount of potatoes, so a cost increase there could have an outsize impact on me…

It probably won’t, actually. If potatoes become expensive, I will eat fewer potatoes and more rice or noodles.

Something similar actually happened after the Brexit vote. I used to enjoy an occasional instant ramen treat from the Japan Centre in London. However, with the pound falling almost 20 percent against the yen in the wake of Brexit (from 160 to about 130), prices were increased significantly. In many cases, this exceeded the 25% cost increase, perhaps because they wanted to avoid further increases if the pound fell further. GBPJPY is now about 149, but the GBP prices haven’t moved, possibly for the same reason. In any case, I’ve switched to eating more of other forms of carbohydrates.

Note that the above doesn’t always work as goods actually need to have a reasonable substitute. Medical services, (possibly imputed) rent and education come to mind. There are opportunities for geographic arbitrage here (e.g. travelling to Brazil as a medical tourist, living in an RV or attending university in continental Europe respectively), but these tend to have higher barriers to entry.

This is the key intuition behind chained CPI; it aims to account for people consuming different goods and services as prices change. This is currently being considered in the US as part of Trump’s tax reform (and would, in the future, save the government money by reducing tax bracket adjustments – chained CPI would be lower than CPI).

Of course, computing chained CPI is a hard problem. For example, there was a parasite problem in salmon farms in early 2017, causing supply to fall. (Again, this was another instance where my consumption habits changed.) Is trout an acceptable substitute? Cod? Chicken? Tofu? Any kind of food? I’d answer yes to the first and kind-of to the second. For the last three, that would probably only be the case in emergency circumstances. There were similar problems with an iceberg lettuce shortage in early 2017, and yet people continued to buy them in spite of prices almost tripling.

Furthermore, one typically only gets to witness substitution effects after the fact. If the price of lettuce triples, it’s difficult to predict how many people would switch or partially switch to substitutes. In practice, statistical offices usually come up with a preliminary estimate and then revise it when they have more data available.

As an individual who has responded to the substitution effect quite a few times, especially since I moved to the UK, I think chained CPI makes sense. For me at least, the substitution effect is real and powerful. It hasn’t received the friendliest of receptions in the US, at least in part for political reasons (it hits the poor and elderly hard, for various reasons). It does make sense to have a different metric to use for benefits or the state pension, perhaps more tailored to the relevant populations (should video game downloads, generally speaking, really go into an elderly CPI?). However, in general the chained CPI seems more accurate and I see no reason not to use it.

The Time Value of Money

There is an apocryphal interview question I’ve come across several times:

Would you prefer to have a dollar today or a dollar one year from now?

I do technical interviews for software engineers. Hence, this isn’t a question I would typically ask candidates (even if at times I wish it was – it could be interesting to see how candidates react!). Although it naturally seems like it would fit in a financial context, it seems too easy to be used as a serious question.

Anyway, the answer I’d go for is “today”, because I could take the dollar and put it in the bank to earn interest. In practice, I’d invest the dollar. Furthermore, inflation is more likely to be positive than not, and this eats away at the value of the dollar. The idea that getting the dollar now is better is known as the time value of money. That said, I can also see legitimate cases why one might argue for “one year from now” – mainly centering around the idea that custody of the dollar is taken care of (assuming we allow this to be assumed!).

Conversely, if you asked me a slightly different question:

Would you prefer to have a dollar today or $100 one year from now?

I would probably go for the hundred dollars, because my investments are very unlikely to increase hundred-fold (unless we have hyperinflation) in a year. As before, there are legitimate cases why one might go against the grain of financial theory – cash flow issues, in particular.

If the amount is reduced a fair bit, such as to $1.09 (for me at least), then the decision gets more difficult. Using some kind of intermediate value theorem, there should be some value of r for which I’m indifferent to this question:

Would you prefer to have a dollar today or $(1 + r) of today’s dollars one year from now?

The conventional theory here is that if I got the dollar today, invested it for a year, and then have (1 + r) of today’s dollars, then I should be indifferent. I’m not sure I agree in practice. This is mainly because of the aforementioned cash flow issues. If 6 months on I find that I need the dollar, I can take it out and still keep the partial returns. You would need to give me an illiquidity premium. (Of course, I’ve assumed here that I invest in liquid securities.)

There is also another shortcoming of this question. The size of the capital relative to my net worth would also affect my answer. Rather interestingly, I think I would take the money early for small or large amounts, but consider waiting for medium-sized ones.

For small amounts, I would need to remember that a capital inflow is coming in a year’s time. The cost of tracking this could exceed the “premium” I derive from waiting. Conversely, for massive amounts, we start delving into the realm of diminishing marginal utility – if I could pick between $1 trillion today and $1.1 trillion this time next year, I’m pretty sure I’d pick the former.

Up to this point, we’ve also avoided what’s known as counterparty risk. The person offering the money might become insolvent within the year. This would bias people towards taking the money now, and is reminiscent of a well-known proverb (“a bird in the hand is worth two in the bush”).

Nonetheless, this practice of time discounting is useful when trying to assess the value of investments or securities, such as annuities or structured products. It is also frequently used in discounted cash-flow analyses, which are useful for determining if business ventures are likely to be profitable. I have not had to put this skill into practice yet, though (well, apart from the Computational Finance exam I did at Imperial).

In theory, these concepts should be applicable to other resources or assets which (1) appreciate over time, and (2) can accumulate in value without substantial effort. That said, I’ve struggled to think of assets outside of the standard “investment” universe (stocks, bonds, real-estate, commodities, private equity, collectibles?) that satisfy both criteria.

I did think of social capital (i.e. friendships, reputations) and human capital (for me, software development and other skills). They don’t seem to satisfy (2), though it could be argued that (2) is too strict. For example, by going about my daily routine, I already (hopefully) absorb more and better dev practices. Similarly, one needs to (well, should) do one’s homework regarding asset allocation and understanding one’s investments. Also, in practice to maintain one’s asset allocation one needs to rebalance a portfolio.

On Paying Oneself First

The expression “pay yourself first” is one very frequently put forth in personal finance circles. In practice, this often involves automatically rerouting some amount of money into a separate savings or investment account whenever a paycheck comes in. Besides the mathematical benefits (compounding; to some extent, risk mitigation via cost averaging if one’s investing), I can see how the approach could be useful psychologically (in that it reflects a shift in one’s mindset concerning money, as well as a conscious prioritization of savings and capital growth). I’ve personally been following this, though I’ve been investing the money into a portfolio of equity trusts and index funds (I’d recommend having an emergency pot to sustain a few months’ expenses first, though).

I see no reason why this can’t be generalized beyond money, though, especially since we do have to manage far more important scarce resources. In particular, I’m looking at time. I’ve received feedback that I tend to slant towards being outcome-oriented, and this does mean that if an important project is lagging but I see a way to recover, I’ll tend to vigorously pursue it – it’s thus not too difficult for me to end up spending 70 or even more hours a week on said project (or even 90-plus, as I did in second year at Imperial). I’ve learned that this is unsustainable, but for me it’s still not the easiest decision to drop something (to the point where a friend commended me for actually using some of my leave during the industrial placement!).

If we look at time in the same way, we get 24 hours a day, or 168 a week; things like sleep are of course important, but I tend to see them more as bills or taxes that need to be paid (not paying them tends to lead to interest!). So paying myself first would involve reserving some time for something else; I’d propose personal learning and development as a good candidate for this.

This is perhaps unsurprising; I suspect that if I polled people as to what “investing in oneself” entails, many answers concerning education would be forthcoming. Like bonds and equities (hopefully), developing one’s skills can lead to future payoffs. I do tend to partition this time into roughly three different domains:

  1. Technical development – e.g. paper reading, programming contests, code katas. These are likely to feed back in to my software engineering work. I’d probably consider these similar to equity income mutual funds; they (ideally) grow in value reasonably steadily and generate nice payoffs along the way too.
  2. General professional development – e.g. writing, finance, tax. Useful for both software engineering work (from what I can recall, I’ve written a lot of docs) and also for managing my own professional matters. Again, these are generally useful; perhaps they have smaller immediate payoffs than technical development, though I tend to think of them as also very important in the long run. Perhaps these would be more similar to a growth-focused fund then? Or even BRK-B (or BRK-A; we’ll get to that but I don’t have a quarter of a million quite yet!)
  3. Random development – singing, photography, etc. These are generally quite fun (I do also enjoy software engineering, writing and finance, but they like all other domains tend to have diminishing marginal returns), and might suddenly explode into usefulness or value given the right conditions. Perhaps these are like emerging market equity funds that are focused on a specific country. There’s certainly a fair bit of variance, but the returns can sometimes be impressive. (If one wishes to take the metaphor even further, deeply out of the money options could be more accurate; they certainly add a bit of fun to a portfolio, too! That said, I have no direct experience with option trading.)

Of course, money and finances are an important thing to manage, and I believe that paying oneself first is a good strategy there. However, it does feel to me that time is even more important. My admittedly equity-heavy portfolio lost around 6 percent during the US election jitters, and this is a portfolio which I’ve built up over the course of about a year and a half now – yet I didn’t feel much (I was expecting a further fall post-Trump win, though in the end the markets rallied). I’m the kind of person who can get annoyed if I find that a day was wasted – let’s not even get started on my reaction to 6% of 18 months (just over a month; 32.87 days). Of course, we have to be careful about jumping to conclusions about what constitutes waste or loss, but I think the point that I find loss of time more painful than loss of money (at least at a small-percentage scale) still holds.

An Unexpected Economic Computation

Here’s a calculation that I found pretty surprising. Have a guess as to its meaning:

 \dfrac{\left( \dfrac{60}{(24-15)} \times 2.40 \right)}{1 - (0.4 + 0.02)} \approx 27.59

If you guessed something relating to savings, you’d be on the right track; the denominator would probably have clued you in to something along those lines, since the 0.4 + 0.02 is the marginal tax that higher rate earners in the UK would face (as of the 2016/17 tax year). You might have figured out then, that the fraction on top probably refers to some form of a time savings expressed in minutes. The 2.40 is probably a bit more puzzling especially if you’re not from London; from the previous observations it’s the cost of taking some convenience that saves nine minutes. That’s right; you might recognise that as the price of a single-trip Tube fare.

Putting that together, that computation is actually the effective hourly gross rate I’m being paid to walk to my office as opposed to taking the Tube. Specifically, I’m comparing (a) taking the Tube, which takes about 15 minutes plus a single trip fare of 2.40, and (b) walking, which takes 24 minutes. We’re thus looking at a net rate of 2.40/9 minutes. Of course, I pay for the Tube using post tax money, so we need to factor that in, and to get an hourly rate we scale that linearly.

Now of course this doesn’t mean I’ll never take the Tube to work again, or even that I’ll take it much less often – the 9 minute difference can be important (say there’s a high priority issue going on, or I’m about to be late for a meeting), and walking can be pretty unpleasant (if I’m very tired, it’s late, or it’s too cold; that said, I’ve done this in the current ~0 degree weather and found it fine, at least). Probably, doing this in the mornings would generally be more reasonable and sustainable as I’m pretty tired by the end of the day. Saving one trip even occasionally is enough of a win, I’d say, and getting some time to clear my head in the mornings is probably not too bad as well.

A question could be why I don’t use a Travelcard for the computations instead. The weekly one for zones 1-2 costs 33 and since I largely stay within zone 1 and 2 we can assume that that’s all I’ll need (I’ll ignore the odd trip to Heathrow). I think 16 or 17 is probably about the number of rides I’d take in a week if I used it aggressively (two a day, maybe three or four on the weekends). We can re-run the numbers with \frac{33}{16.5}, which means a trip costs 2.00. Our final answer is 22.99 which is still pretty solid (if you work 42 hours a week that’s a gross annual income of just over 50,000). Anyway, as it turns out because I use contactless, if I happen to have a week where I do travel a lot I’ll effectively be using one.

Now let’s have a look at the monthly or annual tickets. These cost 126.80 for monthly, or 1,320 for annual. Assuming that we make 2.357 trips a day on average (taking the middle of the estimates above), and a month as 365.25/12 days, with the monthly card the cost of a trip falls to 1.767 and with the annual card it falls to 1.533. The “gross wage” calculations become 20.31 and 17.62, which while not as high are still solid amounts. 17.62 an hour corresponds to about just over 38,000 in gross income assuming a 42 hour week, which would put you in about the 78th percentile of earners according to the ONS data for 2013-2014. I guess this will probably be a bit lower now, with inflation/wage growth, but still decent.

Assuming usage is high, it seems that the annual card might be the way to go. However, an issue is that I sometimes need to travel overseas for work potentially a fair chunk (let’s say personal plus work travel adds up to two months a year), so the annual one is quite definitely a non-starter. Multiply the price of a trip by 6/5 to factor that in, and you end up with a per-trip figure that’s higher than the monthly card. I have been getting the monthly card in the past, especially when I was a student and it only cost 86.50, partly because walking to Imperial was going to take a very long time (that route yields savings more on the order of 30 minutes). Note that while losing a card is a legitimate concern, you can usually recover the travel passes using the TfL website.

(N.B. This idea was conceived independent of the currently ongoing Tube strike, though in a sense it’s a bit of a bonus that things aren’t affected.)

Navigating Tube Fares

A bit of an additional post for the week, as I’ve had a little bit more spare time! This post is a more fully-fleshed out response to a question my friend Andrea had, about the value of an annual travelcard.

I’ve started doing my preliminary accounts for 2016, and one of the things I examined was my transport expenditure. I typically try to use what’s known as zero-based budgeting (that is, each category and the value assigned to it is justified from fresh assumptions, rather than say raising the previous year’s data by RPI and calling it a day). Of course there’s some flexibility (I’m not going to pass up a social gathering just because of finances, unless it’s insanely expensive – which is unlikely given the background of my friends, or at least the activities we take part in together).

There’s a column of 86.50s, corresponding to a string of monthly zone 1-2 Travelcards purchased on student discount. We then have a crash to two low months as I was in the US and Singapore respectively, a figure just over 100 for November, and December looks to be closing around 50; I didn’t purchase any Travelcards after August. At the time, I made these decisions because I was unsure if going for the annual Travelcard was a reasonable idea, especially given that I would frequently not be in London owing to international travels, both for work and for personal affairs. The total cost for the category for the year was 894.68; this is lower than normal because I didn’t purchase any flights this year. I’ve been a bit cautious having been deployed internationally on quite a few occasions; I didn’t realise that you can refund the remaining value of a Travelcard!

This would have been 924 if I bought an annual zone 1-2 Travelcard (sadly, I’d now need 1,320 as I’m no longer a student); that said, with one I might have travelled more as well. Also, I was out for two months and started occasionally walking to the office in December. You can get refunds on the remaining value of a Travelcard – that said, I’m not sure repeatedly canceling and then repurchasing annual Travelcards is permissible, and it seems like it would certainly be inconvenient. Loss shouldn’t be too major of a concern, as Oyster cards can be registered to an online account which one can use to transfer a season pass away from a lost card. (I’ve done this before, though with a monthly pass.)

I think a question would then be as follows: exactly how frequently (in terms of number of days) do I need to use the Tube to make pay-as-you-go (PAYG)/monthly/annual Travelcards the best choice? We can examine that under a few assumptions:

  • The traveller is an adult.
  • All journeys are within Zone 1.
  • PAYG is implemented through contactless, so weekly caps apply.
  • The year begins on a Monday (this matters for weekly capping computations).
  • 16/7 trips per day (that’s reasonably realistic for me).
  • (Somewhat cheeky) If one travels for N days one travels for the first N days of the year.
  • Journeys on day are made between 0430 of D and 0430 of day D + 1.
  • The “greedy monthly flexible” (GMF) strategy works as follows:
    • It buys monthly travelcards as long as there are full months remaining.
    • For the partial month (if one exists), it uses the cheaper of:
      • a monthly travelcard
      • PAYG (with weekly capping)

Obviously GMF dominates a pure PAYG strategy, because for full months a monthly travelcard always beats PAYG (consider February), and for partial months GMF considers PAYG, so it does at least as well as PAYG. If I’m not wrong GMF is optimal under these contrived conditions: it intuitively seems difficult to recover from burning through February, the shortest month, without buying the monthly travelcard as you’d need four weekly ones. However, in the general case GMF is certainly not optimal (consider the period February 28 – March 31; you can buy the Travelcard on February 28, which expires March 27, and then pay for four days of fares, or pay February 28 and buy the Travelcard on March 1; the optimal strategy saves three days of fares).

The fare if one has to travel for N days is reflected in the graph below; and unsurprisingly the flexible methods are superior for small N but inferior for large N. Our model has a break-even point at about 314-315 days.

The final decision, unsurprisingly, boils down to the level of certainty you can have about your travels. If you don’t expect to be spending more than around 50 days outside of the UK, the annual travelcard seems like an idea worthy of consideration especially if you know when said days lie. That said, we have made two key assumptions, one of which favours the monthly strategy and one of which favours the annual one:

  • An upfront lump-sum payment is needed if you’re using the annual scheme. Our analysis did not account for the time value of money (you would need to discount the monthly payments to today to get a fairer comparison of the two).
  • However with the monthly strategy we’ve assumed that plans are known well in advance (at least a month) and implementation is done perfectly. In practice, there are likely to be some minor errors or plans not aligning neatly on month boundaries that will result in slightly higher fares.

I personally don’t expect to travel more than that, but I won’t be getting an annual card next year, for other reasons. (In particular, that “16/7 trips per day” assumption is unlikely to be valid, but that’s a subject for another post.)

Interest on the Interest

midpoints

I don’t remember the early years of my education that well. I do remember that maths was consistently my favourite subject back in primary school, though I wasn’t particularly good at it.

Anyway, it was around year 4 (so I was about 10 years old) when I started to take a bit more interest in personal finance. I’m not sure why this happened (I don’t remember young Jeremy being very interested in material things, and although the dot-com crash was in 2001 I’m not sure I knew about it at all back then!). I think at the time I viewed the stock market as very speculative (clearly hadn’t heard of mutual funds or ETFs); the childish me probably saw it as an “adult thing” to do as well (to be fair, if manually picking stocks that’s probably a reasonable view). I was thus more focused on what the older me would recognise as fixed-income investments.

However, in any case, I had saved some money from birthdays and the Lunar New Year, and given that I wasn’t going to be using it immediately I thought it would be good to put it to work. I was vaguely aware of how banks worked, at least as far as retail banking was concerned (i.e. the bank takes your deposit at rate x and lends out your money at y > x; the delta is for the service of matching depositors and borrowers). I was also aware of other schemes such as fixed deposits and other types of savings accounts. Interest rates at the time were about 2 to 3 percent, and knowing little else I thought that was not too bad for a start; my account at the time had an annual equivalent rate of 3%.

I remember looking through my bank statements then, and noticing that interest was paid twice a year, at the end of June and December. It didn’t take long for me to figure out that the December figure was bigger, at least partially because it was calculated including the interest from June. I then started wondering what would happen if the interest payments were made monthly, daily … or even billions of times per second. With some research I learned about continuous compounding; even if you were able to do this compounding at 3% infinitely often you’d still “only” get a rate of e^{0.03} - 1 = 0.0305 for your efforts.

However, the figures didn’t tally up with my calculations for a long while. I remember initially wondering why I wasn’t paid exactly 1.5% on each payment. Nevertheless, by then I had some familiarity with exponents, and I realised that 1.015^2 = 1.030025 > 1.03 and really we should be expecting \sqrt{1.03} - 1 = 0.01489 each time, rather than 1.5 percent. Still, this didn’t square up with the figures (it was getting down to cents, but still). I let the matter rest at the time, since it was broadly correct. Also, I noticed that the June payments tended to be a little small, the December payments a little too big – so I thought it averaged out in the end (which it did – that’s the point of an AER!).

Anyway, 15 years later I found the reason why, as part of prep work for a reading group I’m doing with Stan. I’m surprised I didn’t think about it back then especially given the observation about June and December payments (at the time, I made the oversimplifying abstraction that the payments were made “every six months”). The key is that the interest was calculated using what is known as an act/365 daycount which factors in the actual number of days for the period you were earning interest, and the first “half” of the year is shorter than the second “half”! Consider that in a non-leap year:

  • From 1 January to 30 June you have 3 \times 31 + 2 \times 30 + 28 = 181 days, but
  • From 1 July to 31 December you have 365 - 181 = 184 days!

With this, we can calculate how much should actually be paid each time. We need to solve

 \dfrac{181}{365} r + \dfrac{184}{365} r \left( 1 + \dfrac{181}{365} r \right) = 0.03 \leadsto r \approx 0.0297783

And so for the January-June period, on a $1 investment you would expect interest of

 \dfrac{181}{365} r \approx 0.0147668

which is notably less than the 0.01489 figure that we have treating each month to be the same length.

Note that a wide variety of daycount conventions are used, depending on which financial instruments are concerned! There is the 30/360 daycount, where every month is treated as 30 days and the year as having 360 days, which makes month-level abstractions valid but becomes unpleasant when you go below that; you also have the act/360 which like act/365 seems computationally nice. There’s also act/act (used for US treasury debt, notably), which guarantees identical value per day within a period at the expense of dealing annoyingly with leap years and/or the fact that the number of days in a year is odd, and many further variants of what I’ve discussed so far as well including a few particularly nasty ones that scale on business days as opposed to calendar days.