What caught my eye this week.

War pioneer and on/off conqueror of Europe, Napoleon Bonaparte, supposedly said he’d pick a lucky general over a good one.

Investors might take the same deal.

Alas, there’s apparently no evidence that Napoleon stated the preference that’s famously ascribed to him.

Which is a shame. Trying to invade Russia in winter seems hubristic. It’d be nice to think there was some offsetting humility and self-awareness in the mix. A little balance to the man.

Of course, bloody and chaotic 19th Century battles and trading stocks at your online broker might not seem to have much in common. And that’s because they don’t.

But one thing they do share is that fortune plays a big role – especially in the short-term.

(If your experience of investing is any closer than that to getting shot at close-quarters with a musket, you might want to consider switching platforms).

Sympathy for the Devil

Indeed for some academics the jury is still out as to whether even a long-term record of out-performance can better be chalked up to luck.

Warren Buffett, they say, is just the same kind of statistical anomaly you’d expect to see if you asked a few hundred million people to flip coins and someone did a thousand heads in a row.

I don’t believe this myself. But I do accept we’ve not got much evidence to go on.

Investing in securities as we recognize it today has only been going on for a few lifetimes, and only over a limited number of economic cycles, with a very quirky sequence of returns (e.g. World War 2), and with technology and society broadly headed in a particular direction.

Would we know the name Buffett in a parallel universe where the Nazis conquered London or the semi-conductor was invented 20 years earlier?

We cannot know. But it seems unlikely.

Gimme shelter

For a less existentially taxing case study of luck at play, consider my history with Amazon shares.

As a former Amazon shareholder – and keen watcher of the technology sector – I gasped with everyone else when Amazon shares fell more than 10% on Friday.

Amazon’s market cap is over $1 trillion. Ten percent of that is real money, even for Buffett.

The stock eventually pared its losses as the day progressed and the market ripped higher, but still I couldn’t help thinking about my lucky escape. (And thanking the investing gods!)

Long-time readers may recall I sold my large – un-sheltered –  Amazon holding back in February 2021.

Around that time I also disposed of a big position in a technology trust that I’d been holding forever, again outside of an ISA or a SIPP.

Why were they unsheltered, I hear you rightly ask?

Well that was a legacy of getting religion about ISAs only several years into my journey (and of pensions being unattractive alternatives, prior to the reforms).

I spent many subsequent years trying to manage down these positions, given the limited annual ISA and pension contribution allowances.

Which is why I have always been strident that you shouldn’t be as dumb as me and instead fill your ISAs to the max.

And also how I learned so much about defusing capital gains tax, despite not owning a boat.

Start me up

Anyway, by early 2021 I had it down to just the tech trust and the Amazon shares outside of my shelters.

These two now-huge-for-me positions lasted longest for two reasons.

Firstly they paid no dividend. Rightly or (as it turned out, given the capital gains, probably) wrongly I had prioritized dealing with un-sheltered income payers first. Not least because I hated the self-assessment paperwork.

But secondly, as time went on I knew I faced a capital gains tax bill of many tens of thousands of pounds when I did tackle them.

I’d diligently used my CGT allowances to defuse down those other holdings. So there was nothing to spare in any given year, which meant I faced the high-quality problem of ever-larger gains and a bigger nailed-on future tax bill.

After all, my Amazon stock had more than ten-bagged1 since I bought it.

Paying taxes on investment gains savages your returns. It also feels rotten – like you took all the risk and Joe Spender down the road gets some of your gains.

Still by early 2021 the size of the position and the fact it was unsheltered was doing my head in.

So I sold: at $3,328 in old money, or $166.40 today.2

Time is on my side

Amazon shares fell below $100 on Friday, so you can imagine my feelings. I’d dodged a more than 40% loss by dumping my shares very close to the top. I was well ahead, even after the tax bill.

Yet more evidence I’m an investing genius!

Indeed if I was another kind of commentator I’d get a dozen TikTok videos out of all this.

Alas, the real story is more edifying.

For one thing, while I was certainly worried about the frothiness in markets in early 2021, I was more focused when it came to my Amazon position on UK politics and the state of the nation’s finances.

Because while it didn’t seem like State borrowing would be a problem so long as low rates prevailed, the new Covid-era chancellor Rishi Sunak had made plain he wanted to make down-payments on the national debt.

The talk was that capital gains tax would rise.

Now, I’ve heard that such taxes are going to rise every year for as long as I’ve been investing. Platforms invariably provide quotes to the financial media every ISA season. This encourages people to put more into tax shelters, and hence increase the platforms’ assets under management.

All good fun, but not something I took very seriously.

But this year was different.

Even by early 2021 lots of people had already forgotten just how generous the State had been in supporting workers and the economy through 2020. But the fact was the bill was enormous, and it had been put on the never-never.

So I could well believe taxes would rise. Why not target investors who’d made an unexpected killing in the lockdown bubble?

I have to be humble then because I sold partly in fear of capital gains tax rises. Doubly humble, given that as things turned out the capital gains tax rise never came.

Strike one off the genius tally.

But secondly and even more candidly, if I’d held Amazon in my ISA then I’m pretty sure I would have sold it years earlier. I would never have been sat on such a big gain in the first place.

Even today I tend to turn over my portfolio fairly frequently as an active investor. (Remember my Tesla car crash?)

In those days I was much worse.

It’s not quite a bad as it might seem. My overall returns are good. Stuff I sell tends to get recycled into other stuff that does well, on average.

But at the same my returns over the years have been juiced by my stellar run with Amazon.

And the reality is that if I’d held Amazon in an ISA – especially ten years ago – I’d probably have banked my profits after the first 100% or so.

Hence leaving maybe 1,000% on the table.

Satisfaction

So there you go. As I watched Amazon tank this week (and Alphabet and Meta too, given the big position in the technology trust I’d sold at the same time) I allowed myself a smile.

Perhaps I even started to tell myself a story about how good an investor I am.

But I’d prefer to tell you something closer to the truth, which is that this time I was definitely a lucky one.

Have a great weekend all!

[continue reading…]

1. That is the shares had gone up more than 900%. Actually it was even more than that – the return clocked in at 1,095%. [↩]
2. The shares were split this year, 20-for-one. [↩]

Disclosure: this article contains affiliate links to Plum. We may be paid a commission if you sign-up. This does not affect the price you pay. Also please note that the owner of Monevator is a shareholder in Plum.

Every one of us walks around with a devil on our shoulder. A little demon prodding us to buy this, splurge on that, and don’t miss out on the other.

Buy me! Buy me!

Of course in the old cartoons, there was always a counter to the tempting voice of un-reason. An opposing angel on the other shoulder, pulling Mickey Mouse back from the beer hall or Donald Duck out of the casino.

Wouldn’t it be great to have a money-conscious sidekick in real-life who also had your back? Encouraging you to save more and invest more?

Making budgeting easy?

A Plum job

Happily technology has come if not to the rescue then to the clean-up job to tackle the mindless consumerism it makes so easy.

Plum is one of several automated savings and investing apps that connect with your existing bank account. It helps you to automatically set money aside without you needing to remember, by evaluating your income and expenditure and tucking money away for you.

The Plum app boasts other features, too, including investing capabilities that even run to ISAs and pensions.

Plum also gives you an overview of all of your bank accounts – not just your main account. That’s a plus point for those of us with multiple banks to keep tabs on.

There are both free and subscription options. But the no-cost option is actually pretty capable, and the fees for the premium versions aren’t too bad at all if you’re taken with what they offer.

More than 1.4 million people already use Plum. Should you join them?

In the rest of this article I’ll look more at what Plum offers, the pros and cons, and suggest the kind of person who Plum would suit best.

Plum summary review

To cut to the chase:

Strengths

• Plum is a simple-to-use savings app that’s easy on the eye
• Automatically helps you to set aside money and invest
• Great for beginners and those who struggle to get started with saving

Weaknesses

• Interest rates are not market-leading
• Monthly payment is charged for premium features
• Investing fees aren’t the lowest

Plum’s fees

Savings account fees

There are no fees for Plum’s basic account.

Plum ‘Pro’ is £2.99/month, ‘Ultra’ is £4.99/month, and ‘Premium’ is £9.99/month.

All of Plum’s non-basic accounts give access to a higher interest rate for your savings.

Investing account fees

There’s a flat 45 basis points (bps) currency conversion charge for share purchases in an overseas currency, plus possible regulatory fees imposed by the SEC or FINRA.

In addition the following fees also apply:

• £1/month for access to Plum’s investments, plus a 0.15% annual management fee
• 0.13% – 0.88% ongoing charge fees (depending on the fund)
• £25 in-specie transfer charge to another provider

Illustrations from Plum:

SIPP fees

There’s a 0.45% platform fee, broken down as:

• 0.35% SIPP administration charge
• 0.10% Custody service charge

Minimums

Savings amount: £1
Investment amount: £1

Plum features

From the moment you download Plum you’ll see a focus on making organising your personal finances as easy as possible.

But don’t confuse this simplicity-of-use with limited functionality. The Plum app packs a lot into its neat package.

All of your accounts in one place

Open banking was a game changer when it first came into play in 2018. Regulations forced financial institutions to open their data to third-party providers. The third-parties could then use that data to build new applications and services.

The idea was that open banking would encourage competition and prevent the largest providers from monopolising data.

And challenger fintechs – such as Plum – have been big winners from this greater financial transparency.

You’ll see how Plum makes use of open banking as soon as you load the app. That’s because, when you download Plum, you’re immediately invited to link to a bank account.

While not all bank accounts can be linked this way, most can, including all of the usual big-name players.

Once you’ve added your bank account, Plum will then assess your spending habits and determine how much you can set aside each month. And if you’ve got more than one bank account, you can connect multiple accounts.

Active budgeting

If you’re someone who struggles to understand where your money goes every month, Plum could help untangle your finances. That’s because Plum does an excellent job breaking down your monthly spending into categories.

If you’ve overspent on takeaways one month, you’ll soon know about it. (Even if you’ll then blame your high metabolism!)

Plum learns more about your spending habits the more you use the app.

True, these days even some traditional banks’ apps may include budgeting features. Challenger banks like Monzo and Revolut certainly do.

However I’ve yet to see a standard banking app that presents your income and outgoings quite as well as Plum.

Aside from analysing your spending habits, the app also assesses whether you’re being overcharged for your utility bills. Plum will even recommend alternative suppliers.

Note: On its website, Plum uses energy as a prime example of it can help find you a superior supplier. However given the current situation with energy prices, we’d say there’s little or no benefit from switching your supplier right now.

Is it the best idea to turn to Plum for utility recommendations?

Probably not. A traditional price comparison website might give you a wider choice of alternatives.

That said, I applaud Plum’s efforts to expose companies who take their customers for a ride.

Not everyone makes much effort to compare providers. If Plum encourages more people to shop around and switch then that can only be a good thing.

Automatic savings

This is potentially the biggest draw of Plum – a chance to set money aside without really noticing.

When you first download Plum’s app you’re given a polite nudge to set up a weekly deposit. Plum then deploys a nifty algorithm that calculates how much you can afford to put aside on a regular basis, based on your income and expenses.

You can also choose to round up your spending to the nearest £1. Buy a coffee for £2.60, and 40p will automatically be deposited for you.

Alongside its algorithm, the app also enables you to select your mood. You can choose from an ultra-aggressive ‘Beast mode’, but also more modest targets via ‘Ambitious’, ‘Eager’, or ‘Normal’.

The more optimistic your mood, the more the app will try to set aside for you.

If you’re keen, but not that keen, there are also ‘Chilled’ and ‘Shy’ options. These will aim to put aside smaller amounts for you. The app’s auto-deposit feature can be paused at any time too. Handy if you’re worried a short-term issue could prevent you setting aside what you normally afford.

Plum’s app also has a savings account feature called ‘Pockets.’ These little savings pots are handy for bucketing the money you’re putting away for something big, like a holiday or wedding.

You can withdraw from your Plum pockets as often as you like. There’s no need to lock the cash away.

You earn interest too

Plum’s Pockets pay interest on your cash balances. You earn 1.01% AER variable if you’ve a basic fee-free account.

Which brings me to my first minor disappointment with the app.

The interest rate isn’t exactly terrible. But with rates rising like there’s no tomorrow, it’s possible to open an easy-access savings account that will earn you more than double what basic Plum will pay you.

If you sign up to Plum’s Pro (£2.99/month), Ultra (£4.99/month), or Premium (£9.99/month) options, then you’ll earn a boosted interest rate of 1.41% AER through Plum’s ‘Easy Access Premium’ account (provided by Investec Bank Plc).

Better, but still not cigar-worthy.

Aside from a boosted interest rate, Plum’s upgraded plans also offer additional money management features, including ‘gamified’ deposit rules.

My favourite is the ‘1p Challenge’. This asks you to a squirrel away only tiny amounts to start with, but the amount you set aside increases gradually as the year progresses. Your sacrifices and savings snowball over the months to leave you with a tidy sum by the end. It’s a nice way to inoculate a savings habit.

Plum’s Ultra and Premium tiers also come with a debit card – only recently introduced – plus a ‘Money Maximiser’ tool, which aims to further prevent you from overspending.

Plum’s debit card isn’t anything remarkable. But it will be useful if you want to spend directly from your savings pots. Beyond Visa’s daily exchange rate, there’s also no charge for using it abroad – a decent perk.

Plum’s subscription features and benefits illustrated

Plum flavours: Click to enlarge each, click back in your browser to return.

In all honestly, I think Plum’s fee-free basic option will do for most readers. But the subscription options do offer additional features.

Scan what’s on offer to see if it’s worth ponying up. The sums being charged per month are quite modest if something especially useful to you is available.

Helpfully, Plum offers a 30-day free trial for its subscription options. This means you can give them a go without being charged.

If you do sign-up for a free trial but decide you don’t want to continue with the subscription features, make sure you cancel before the trial ends.

Investing with Plum

Aside from saving and budgeting, Plum also enables you to invest your money in a General Investing Account, ISA, or pension (see below).

Plum says its investing options are suitable for first-timers or ‘seasoned pros’.

I think though that it’s beginner investors who will be more impressed by Plum’s uncomplicated interface. I’ve never seen an investing platform that’s so straightforward to use.

And the fact that you can invest from as little as £1 is a boon for those who want to test the choppy waters of the stock market.

If you want to invest with Plum, there is a fairly limited range of options – 12 funds on most plans, or 21 on the £9.99 a month Premium plan.

These funds are rebranded offerings from the likes of Vanguard and Legal and General.

That’s reassuring in that you’re not putting your money into sub-scale funds run by a fintech start-up, but rather into funds run by industry giants. On the other hand it is an extra layer to dig through to the fund detail, if you’re so-minded.

For instance, there’s a ‘Tech giants’ fund, consisting of Apple, Facebook shares and the like. This is actually a fund called the ‘Legal and General Global Technology Trust’.

Incidentally, remember that sector bets like that one often disappoint. To put it simply, what seems like no-brainer theme often fails to live up to the hype – at least when it comes to investing returns.

The Monevator house view would be that nearly everyone is best off looking to Plum’s so-called Basic funds. These simply split your investment money between equities and bonds. There are three variations to suit your risk tolerance.

The underlying funds here are Vanguard’s LifeStrategy 20%, 60%, and 80% equity funds (with the balance being in bonds).

We’re unabashed fans of these products, which offer all most people need to get an instant and diversified portfolio.

Still, if you’re more of a naughty active investor you can choose to buy stocks through Plum instead. But note that many of the most well-known stocks are only accessible on Plum if you have a Premium account.

Once again you can set your account to invest automatically on your behalf. It works the same way as Plum’s auto-deposit offering. You’ll rely on Plum’s algorithm to invest for you, based on how much it thinks you can afford to put aside. You can also round up your spending and invest the change.

Plum seems very keen to get its customers to open an investing account. I received a notification to learn more about Plum’s investing options within just 24 hours of opening my account.

Plum pension

You can invest in Self Invested Personal Pension (SIPP) too through Plum. You can open this from scratch or else transfer in an existing pension.

If you transfer, you’ll probably have to choose to move your money into one or more of Plum’s fund range.

Plum also offers what it claims is a risk-managed AI pension service. Just tell the app your age and target retirement date and it says it will do the rest.

Various funds are on offer for SIPP investors. I perused a long-term ‘Retirement 2050’ fund, a ‘Future Planet’ fund consisting of ethical investments, and a ‘Global Equity’ fund that includes large and medium-sized companies.

Again we’d suggest keeping it simple. A big broadly diversified global equity and bond fund from Vanguard will do the trick for most.

Anything else?

The main USP of Plum is its algorithm feature. It’s impressive how much it learns about your spending habits over time.

Plum also does an effective job of communicating with you via regular, personable messages.

These notifications mainly give an overview of your spending behaviour. You can switch them off if you find it too intrusive.

User experience

While not everyone will be a fan of its purple colour scheme, the Plum app should prove a pleasure to use.

Whether you want to save, invest, view your accounts, or open a pension, Plum makes it easy.

There’s also a notification tab within the app which keeps you updated on your progress.

I’ve used Plum for a while now and I haven’t encountered any bugs.

Plum review summary

The most impressive thing about Plum is just how many features it crams into one nifty app. Whether you want to improve your budgeting, boost your savings, or see an overview of all your bank accounts, Plum delivers.

Plum makes investing easy too. Even if it isn’t the absolute cheapest platform around.

I like the fact that Plum’s basic, fee-free option has pretty much all you need. This is not a deliberately-hobbled experience.

However, this does bring into question whether it’s worth shelling out a monthly fee for the subscription features.

All in all, I really like the Plum app. True, I’m not someone who really needs help to save. (Is my wallet glued into my pocket, friends ask?) But I can certainly see myself using Plum’s personal spending insights in the future. I also liked looking at all my bank accounts in one place.

I’ll probably give Plum’s investing services a miss myself, but that’s only because I already passively invest via an established investing platform with low fees.

For investing newbies, Plum’s offering could be an attractive way to get started.

Trustpilot review score: 4.5

Plum regulation

Interest Pockets are provided by Investec Bank Plc. (Opt-in).

Plum investment funds are held by Gaudi Regulated Services Ltd. (An FCA regulated custodian).

Plum savings are covered under the Financial Services Compensation Scheme.

Alternatives to Plum

Chip and Moneybox are two apps that do much the same thing as Plum. They have their own quirks.

Have you used Plum for a while? Share your thoughts in the comments to the article below.

Like many other sites, we may be paid a small commission if you sign-up to Plum via affiliate links. This does not affect the price you pay. Our reviews are editorially independent.

UK government bonds have given investors a painful kick in the portfolio recently. Many of us found out bond funds are riskier than we realised. But with one simple(-ish) metric you can assess the riskiness of your bond assets ahead of any market crash. That metric is bond duration.

Quick note – Duration applies to bond funds, individual bonds, and portfolios of individual bonds. I’ll mostly just refer to ‘bonds’ throughout the article because it’s snappier. I’ll specifically call out bond funds when duration applies differently to them. Please check out our bond jargon buster for a brief refresher on confusing bond terminology.

What is bond duration?

Bond duration expresses a bond’s vulnerability to interest rate risk. The larger the bond duration number, the more reactive a bond’s price is to interest rate changes, as the bond’s yield adjusts to reflect those changes.

For example, if a bond’s duration number is 11, then it:

• Loses approximately 11% of its market value for every 1% rise in its yield1
  
• Gains approximately 11% for every 1% fall in its yield

Whatever your bond’s duration number2, that’s how big a gain or loss you can expect for every 1% move in its yield.

A duration three bond will rise or fall in value by approximately 3% if its yield moves by 1%.  

In a rising interest rate environment? Shorter duration bonds will be less risky than longer duration equivalents. But they won’t do much for you when rates fall. 

Conversely, long duration bonds are more comforting than your favourite teddy bear when interest rates fall. They go up in price!

But that would-be teddy bear is about as welcome as a grizzly at a picnic when interest rates rise. 

What affects bond duration? 

A bond’s time to maturity, yield, and coupon rate determine its duration:

Remaining time to maturity  

The more coupon payments a bond has yet to make until it matures, the more price-sensitive it is to interest rate changes.

That’s because a long-dated bond is stuck with its fixed interest advantage or disadvantage for many years in the future. A short-dated bond has only a few more payments due. 

• A distant maturity date implies a higher duration.
  
• A near-term maturity date implies a lower duration. 

Yield and / or coupon payment

Bonds with lower yields / coupon payments are more price-sensitive than similar types with higher yields / coupons. 

• A higher yield implies a shorter duration – because the bond returns your money at a faster rate.
  
• A lower yield implies a longer duration. 
  

The diagram below shows the tug-of-war that resolves a bond’s duration:

• Higher durations are primarily a function of longer bond maturities. Low bond yields / coupons also contribute. 
  

• Lower durations are primarily a function of shorter bond maturities. High bond yields / coupons also contribute. 

Higher durations equate to a more volatile bond price (up or down) when interest rates change.

Lower durations mean smaller price swings.   

All this helps explain why long duration bonds took horrible losses in 2022. As interest rates escalated, bonds trading in the market became less valuable.

Though it’s little comfort right now, duration also sheds light on why long bonds stepped up in value when interest rates plunged during the Global Financial Crisis. 

The ups and downs of being a bond

Bear in mind that duration is an approximate measure. It makes various simplifying assumptions about the relationship between interest rates, bond prices, and yields. 

But it helps to remember these opposing bond dynamics:

• When interest rates rise, bond prices fall. 
  
• When interest rates fall, bond prices rise.
  
• When bond prices fall, yields rise.
  
• When bond prices rise, yields fall.

Long bonds react more violently to these forces, for good or for ill. 

When interest rates rise, investors demand more compensation for tying up their money in bonds.

New bonds entering the market must have higher coupon payments to match the rate increase. 

But longer bonds are saddled with their old, lower, coupon payments for years – even decades. So their price falls to reflect their less competitive fixed rates. 

That price cut pushes the old bond’s yield up. It rises to the point where it’s just as attractive to a buyer as a new bond (of the same type) that waltzes in flashing its higher coupon payment. 

An analogy with cash savings accounts might help.

Let’s say you’re in the market for a fixed-rate savings account. Now suppose that interest rates had just risen from 3% to 4%. There’s no way you’d pick the same 3% account you might have gone for yesterday. At least not without a hefty bribe cashback offer. 

Bonds on sale

The discounted price of a less competitive bond is a bit like cashback given to new buyers to make it just as profitable as the new bonds they’d otherwise choose. 

In the savings business, banks withdraw old, fixed-interest accounts from the market. Existing savers, however, are stuck with their outmoded choice. Curses. 

With government bonds, debt obligations are seldom taken off the market. Instead they’re priced at a discount or premium to reflect their altered competitiveness, as interest rates yo-yo. 

Naturally, the process works in reverse, too. You earn a premium on bonds boasting a yield higher than prevailing interest rates.

Bond duration captures the short-term capital gain (price premium) or loss (price discount) part of these moves in one simple number. 

(Although even this this isn’t the end of the story. Counterintuitively, bond funds have higher expected returns after a price drop. That’s due to the impact of rising bond yields.)

How far do bond yields move? 

It’s all very well saying duration measures the price change sparked by a 1% yield move. But how far – and how fast – can bond yields bounce in the real world?

It’s the size and speed of your bond’s yield change that determines the scale of your capital loss or gain. 

Below is a snapshot of UK gilt yields, with changes in yield over the course of a day, month, and year: 

Source: Trading Economics.12 October 2022.

The daily, monthly, and annual shifts in yield shows you the impact of recent changes in market interest rates for each UK government bond in the table. 

You can see, for instance, that the yield (note: not the price) on the UK’s benchmark ten-year gilt rose 1.4% in the last month. In the last year the yield is up 3.5%. 

Indeed, every gilt with a maturity of three years or more saw its yield increase at least 1.35% in the last month, up to 3.8% over the past year. 

If you multiply shifts of that size by duration then that’s going to hurt. As every bond fund owner knows all too well in 2022!

Moving too fast

The duration calculation assumes instantaneous moves. But the longer the change actually takes to unfold, the less violent the price swing. Reinvested cashflows mitigate the impact. 

So it’s not quite right to multiply duration by real world movements that evolve over a year.

All the same, the size of the yield rises in the table above show us that just multiplying your bond’s duration by 1% doesn’t nearly capture the scale of the drama that can engulf us. 

Which bond is my bond fund like? – Compare your bond fund to individual bonds of the same type. Look up your fund’s weighted average maturity. It’ll behave similarly to an equivalent individual bond with approximately the same maturity. The yield-to-maturity of the fund and the bond should be pretty close. Do check the dates though. Published bond fund yields can be quite stale.

Bond duration: making your money back

There’s another aspect of bond duration which is much more debatable. 

This assertion is that your bond’s duration number tells you how many years it takes to recover from a capital loss after a yield rise – your breakeven point. 

Or, to put it another way: how long it will take to make the annualised returns you expected before rising yields put a dent in your portfolio. 

Let’s say you own a duration 11 bond fund, with a yield-to-maturity of 4%.

Interest rates go up, prices go down, and your bond’s value takes a hit.  

However, your bond fund fully makes up that lost ground by the 11 year mark. At that point, you’ve now earned a 4% annualised return over the entire period going back 11 years. The scar of the price drop has healed. It’s as if the interest rate rise never happened. 

Beyond 11 years, you’re up on the deal. That’s because your higher-yielding bonds pay you a better return than you would have received without the rate rise, when the yield would have remained lower.

All this assumes that your coupon payments and maturing bonds are reinvested.

The maths work the other way round, too.

If yields fall, then your bond return immediately jacks up (capital gain). But ultimately your returns soften like a tyre with a slow puncture. Beyond your duration number (expressed in years), you’re worse off over the whole period, because your cashflows are reinvested into lower-yielding bonds. 

The downgrade in return happens to a duration 3 bond after three years. A duration 11 bond has more staying power. It wouldn’t show a worse annualised return until 11 years passed. 

Here for the duration

All this is rule-of-thumb stuff. It works just fine for an individual bond that’s held until maturity, declining in duration as its coupons pay out. 

However ‘holding for the duration’ is less applicable to bond funds operating in the real world. 

In reality, bond funds turn over their holdings to keep the fund’s average maturity and duration relatively stable. The same goes for rolling portfolios of individual bonds. 

Moreover, interest rates don’t change course only once, and then remain static. They weave around like a drunk at a wedding reception. 

The traditional advice is to match your bond duration to your time horizon to ensure you get your money back. 

But that is based on assumptions that are about as realistic as diesel emissions tests. 

Indeed, there’s evidence to suggest you may have to wait for up to twice your bond fund’s initial duration in years to earn your initially expected yield-to-maturity. 

The twice duration rule-of-thumb

This rule of thumb says that twice your bond fund’s initial duration is a better guide to your breakeven point. 

Of course, you could earn your initially expected return faster if interest rates trend down and you enjoy a series of capital gain boosts. 

But when your holding period is dominated by rising rates then twice duration is a more pragmatic time horizon. 

This bracing finding comes from a research paper: Constant-Duration Bond Portfolios’ Initial (Rolling) Yield Forecasts Return Best at Twice Duration. The author is Gabriel A. Lozada, associate professor of economics at the University of Utah. 

A hat tip to Occam Investing. Occam pointed to Lozada’s research as part of a very good piece on bond returns.

The ‘twice duration’ paper specifically investigates the returns of bond portfolios held at constant durations. It employs a more realistic model for fluctuating interest rates than allowed for above. 

The author also empirically tested his model versus 60-years worth of historical returns. 

Lozada’s conclusion is you’re more likely to earn your initial yield-to-maturity over a twice duration timespan in a world where interest rates can go for a random walk, or trend upward for decades.

A better, not perfect, guide

Here’s the key finding for ordinary investors:

In summary, almost all the time, initial yield was within a percent or two of average annual realized return with a horizon of twice initial duration.

Are you a fellow glass-half-empty type? Then know this rule-of-thumb looks more rigorous than the happy-clappy ‘just hold for the duration’ advice of old.  

But the message isn’t that it will definitely take 22 years to earn say a 4% annualised return from a duration 11 bond fund. We’re not trapped by some boa constrictor of fate. 

If interest rates stayed relatively flat for the next eleven years, your bond’s yield would be about what you could expect. 

And if rates go down then you may earn more for a while. Though longer-term you’ll likely earn less. 

But given that interest rates are inherently unpredictable – and could relentlessly trend up – estimating that it could take somewhere between your bond fund’s duration and twice its duration to earn its yield is the hardheaded approach. 

Even then, this doesn’t tell you much about real returns.3

Other complicating factors

If inflation is higher than expected, nominal bonds do poorly. If inflation is lower than expected, nominal bonds do relatively well. 

It’s true too that if you pound-cost average into your bond fund then you’ll: 

• Shorten your path to higher overall returns in a rising rate environment 
  
• Shorten your path to worse overall returns in a falling rate environment 

Lozada says his findings apply to default-free bonds that aren’t callable (i.e. high-grade government bonds), but notes they aren’t a good fit for long bond portfolios.

Sometimes the best fit was 1.25 times duration or 1.75 times. Much depended on the type of bonds and the time period Lozada put under examination. 

Lozada also didn’t look at what happens if you periodically rebalance, withdraw cash, or spend interest. Or any other of the common investor behaviours that influence your particular outcome. 

Twice duration then is no more than a rule-of-thumb for short and intermediate government bond fund risk. Albeit a more steely-eyed (steely-thumbed?) one. 

If that doesn’t sound especially reassuring then check out the Banker On Wheels bond ETF calculator.

This suggests the twice duration rule should be reserved for gloomy scenarios when rates rise constantly during your time horizon. 

Duration and convexity

Duration simplifies the real world complexity of bond maths to broad strokes. Convexity fills in more of the detail. 

Convexity provides more accurate insights into bond price sensitivity because it accounts for the fact that yield changes also alter a bond’s duration.  

Picture the difference in price outcomes between the two measures like this:

The relationship between bond prices and yields is curved, whereas duration assumes it’s linear.

The practical outcome is:

• Duration (white line) tends to underestimate the bond price rise (green line) when yields fall. (Left-hand side of pic).
  
• Duration typically overestimates price drops when yields rise. (Right-hand side).

The difference between the green line and the white line reveals convexity at work. The convex curve of the bond price shows how it differs from the duration estimate as yields change.

When bonds exhibit positive convexity (as pictured above):

• Yield falls, price spikes, duration lengthens (duration underestimates actual price rise)
  
• Yields rise, price drops, duration shortens (duration overestimates actual price fall)

Essentially, the lower yields go, the faster bond prices accelerate versus duration’s estimate. 

Meanwhile, the higher yields float, the slower bond prices decline vs duration’s readout. 

Convexity amounts to a welcome tailwind. One that enhances your portfolio protection in a falling rate environment. And moderates expected bond damage in rising rate conditions. 

The effect is barely noticeable for short bonds. But is pronounced at extreme ends of the yield curve, as bond maturities head over 15 years until maturity. 

Portfolio Charts has produced some fantastic graphs that give you a proper feel for convexity. 

And we demonstrate convexity’s effects in our bond prices post. 

Incidentally, watch out for negative convexity. This occurs when bonds become less price sensitive as yields fall. (And vice versa). It’s the exact opposite of what you’d want to happen.  

Negative convexity is not a concern for default-free, non-callable government bonds. It is a worry if you stray into corporate / municipal bond territory where call options rear their heads. 

If convexity is more accurate then why does everyone use duration? Mainly because it’s simpler, but also because duration is good enough in most circumstances. 

Where to find bond duration numbers

A bond fund’s home page should tell you its duration number.

Though as usual, providers love to shower us with a confusion of different terms.

Average duration – A bond fund’s duration is the weighted average of the individual bond durations that it contains. So no cause for alarm if you see this label.

You can flip Vanguard’s site to the financial advisor view (wee dropdown menu, top-right, on desktop) to see its duration figures. For some unearthly reason you can’t see them on the consumer site.  

Modified duration – Strictly-speaking the correct term for the type of duration that measures price sensitivity to interest rate changes. Use this number where you see it. 

Effective duration – Modified duration diluted by the effect of any bonds with call options in the portfolio. Effective duration trumps modified duration if a fund gives you the choice. 

Use Trade Web to find out the modified duration for individual gilts. 

If you’d like to calculate bond duration then check out this calculator. 

Beware that duration doesn’t capture every dimension of bond risk. Credit quality is another major factor – and duration does not address this at all. 

Bond risk: higher or lower? 

As a Brucie Bonus, bond funds actually become less risky after the yield rises and the price falls.

I appreciate that’s in complete contrast to our instincts after big capital gains and losses. But the eagle-eyed might have noticed their own bond fund’s duration shorten following the recent falls.

For instance, here’s how the key numbers have moved for the SPDR’s intermediate gilt ETF (ticker: GLTY):

On 30 April 2020:

• Duration: 13.85 
• Yield-to-maturity: 0.35% 

On 30 September 2022:

• Duration: 10 
• Yield-to-maturity: 4.09% 

The fund’s yield is vastly improved while its lower duration number shows its price sensitivity is less volatile than a couple of years ago. 

The fund is now a better investment prospect than it was in 2020! But as ever after a big investment shock, some people will be too bruised to go back for more. 

Investing often defies our human intuitions. And bond investing perhaps most of all. 

Take it steady,

The Accumulator

PS – When we mention ‘interest rates’ in this post we’re referring to bond market interest rates, not central bank interest rates. References to ‘yield’ mean yield-to-maturity. Please see our bond jargon buster for more.

1. Yield to maturity. You can think of it like the interest rate you’ll get if you hold the bond to maturity. [↩]
2. Technically, it’s called ‘modified duration’. [↩]
3. Real returns subtract inflation from your investment results. In other words, they’re a more accurate portrayal of your capital growth in relation to purchasing power than standard nominal returns. [↩]