How much will bond prices fall if and when interest rates go up? With many government bond yields straying into negative territory or teetering on the brink, surely this asset class now only offers the prospect of painful loss in the years ahead? Or maybe not?

You can get an intuitive feel for how big bond losses – or potential gains – can be using a bond price calculator.

And some of the results may seem a bit, well, weird…1

Let’s run through a few simulated examples of how a range of hypothetical bonds could move in response to changes in market rates.

A note on confusing bond terminology
Just to clear a few things up before we start.
Interest rates
When people talk about bond prices falling due to rising interest rates, they’re not talking about central bank interest rates like the Bank Of England’s Bank Rate. They’re talking about the market interest rate for a bond. Each and every bond is subject to a market interest rate that is the sum of supply and demand for that particular bond. The market interest rate is the return investors demand for tying up their wealth in that bond, and it fluctuates in line with the market’s view of factors such as inflation, the bond’s credit rating and maturity date, other macro-economic forces and, yes, the influence of central bank interest rates.
Bond yields
There are many different types of bond yields. Commentators often bandy about the term ‘yield’ as if it’s a unified concept that everybody understands. When I talk about yield in this piece, I’m referring to the yield to maturity (YTM), also known as the redemption yield. This is the annualised return you’d expect to receive if you invest in a bond and hold it to maturity (accounting for its market price and the remaining interest payments, which are assumed to be reinvested at the same rate). It’s the go-to yield to use when comparing similar bonds (for example gilts) that vary by price, maturity date, and coupon rate.

Scenario #1: Interest rates rise by 1%

Say we own a newly minted 30-year government bond and interest rates shoot up by 1%, with our bond’s yield rising in turn to 2%. We can use a bond price calculator to survey the damage using the following specs:

30-year bond

• Face value: £100
• Coupon rate2: 1%
• Market rate: 2%
• Years to maturity: 30

Dial that scenario into the calculator and it tells us the bond price falls from £100 to £77.52.

Capital loss: -22.5%

From our perspective here in June 2020, 30-year gilt yields have come down 1% in a year, so it doesn’t seem beyond the realms of possibility that they could rebound back, given time.

(Note: the size of your loss also varies depending on the speed of the interest rate change – we’ll come back to that.)

Now let’s replay the interest rate rise but this time with a 5-year bond:

5-year bond

• Face value: £100
• Coupon rate: 1%
• Market rate: 2%
• Years to maturity: 5
• Price falls to: £95.26

Capital loss: -4.7%

Okay, that’s a much less harrowing number. It also explains why many investors have moved to shorter-dated bonds as interest rates tumbled over the years.

The trade-off is that shorter-dated bonds offer ever less downside protection as interest rates continue their journey to the centre of the Earth. (We’ll come back to that, too.)

Let’s look at the middle ground with a 10-year bond:

10-year bond

• Face value: £100
• Coupon rate: 1%
• Market rate: 2%
• Years to maturity: 10
• Price falls to: £90.98

Capital loss: -9.0%

Tough but not awful. Stick in an instant 2% interest rate rise though (not likely, but bear with me) and the capital loss is -17.2%.

Cheaper prices = higher yields = recovery mode

Lower bond prices aren’t all bad news. Sure a chunk of your portfolio will get taken to the woodshed for a whalloping. But at least in you’ll be able to buy new bonds at higher yields.

In time, reinvesting your income into those now-cheaper bonds will offset some of the pain of that initial bond market beating.

You can use a duration calculator to see how long it would take you to make good the capital loss by reinvesting your interest payments into higher-yielding bonds after a rate rise.

Turns out the 10-year bond in my example scenario gets back to breakeven after about 9.5 years. After that point, your higher-yielding holdings would put you in profit, relative to the old bond and assuming interest rates remained stable.

The five-year bond takes just 4.9 years to breakeven.

It’s a long 25 years for the 30-year bond.

Scenario #2: Interest rates fall by 1%

So far, so traumatic. But what if interest rates are forced down even further as central banks suck up bonds with their QE 2020 giga-Dyson?

30-year bond

• Face value: £100
• Coupon rate: 1%
• Market rate: 0%
• Years to maturity: 30
• Price rises to: £130

Wait for it…

Capital gain: 30%

That’s an equity-like gain in the puff of a recession – and enough to offset a lot of stock market pain if you’re packing a large slug of long bonds.

This is why many investors hold long bonds and they aren’t mad to do so. They don’t see historic lows as an unbreakable floor. They think interest rates can fall further. Long bonds will make big gains if they do.

Notice how the 30% gain is larger than the equivalent -22.5% capital loss from the 1% rate rise scenario. Long bonds become more potent at ultra-low and negative rates. That’s what makes them so tempting even in the face of interest rate risk in the other direction.

A rapid 2% yield drop would mean a 70% gain for our 30-year bond. You could buy a lot of cheap equities for that, if you could stomach rebalancing into a tanking market.

Before you drool your way to your broker’s screen, note though that interest rates don’t tend to move that hard and fast for long bonds. During the coronavirus crash, for instance, the SPDR 15+ Year Gilt ETF (average maturity 29 years) spiked just 12% as equities dive-bombed.

Is a -1% yield possible for long bonds over time? Well, long-dated inflation-linked UK bonds have drilled down to near -3% yields.

Finally, the 30-year bond is again less lethal if rates rebound in the opposite direction. You’d take a -39.4% loss if interest rates rocketed by 2%.

What happens if we go for a short bond?

5-year bond

• Face value: £100
• Coupon rate: 1%
• Market rate: 0%
• Years to maturity: 5
• Price rises to: £105

Capital gain: 5%

That shallow 5% gain demonstrates that short bonds won’t do much to stabilise your portfolio if equities plummet and central banks keep firing their bazookas. The upside for short bonds is limited, especially at this end of the interest rate spectrum.

10-year bond

• Face value: £100
• Coupon rate: 1%
• Market rate: 0%
• Years to maturity: 10
• Price rises to: £110

Capital gain: 10%

Our compromise 10-year bond puts in a decent but not pyrotechnic show. If rates fell 2% it would gain 21.1%.

Again, the downside drop is amplified for intermediate bonds relative to its losses when interest rates rise, but the effect is muted in comparison with 30-year bonds.

Scenario #3: Ultra-low interest rates

The long bond effect is magnified in a low interest world (where this post certainly belongs).

Let’s cut the coupon rate down to 0% and model a 1% fall into negative yield country.

30-year bond

• Face value: £100
• Coupon rate: 0%
• Market rate: -1%
• Years to maturity: 30
• Price rises to: £135.09

Capital gain: 35%

That 35% capital gain compares with a 30% gain for the higher-yielding 30-year bond in our earlier interest rate drop scenario.

The lower-yielding long bond gains 82.8% on a -2% drop in rates, versus 70% previously.

So don’t believe bonds are necessarily firing blanks.

But what happens if we point this thing in the other direction?

You guessed it. A lower-yielding bond is more dangerous than its higher-yielding cousin when rates rise.

Imagine a 30-year bond with a 0% coupon rate, issued at the nadir of a zero-rate world that was on the turn…

30-year bond

• Face value: £100
• Coupon rate: 0%
• Market rate: 1%
• Years to maturity: 30
• Price falls to: £74.14

Capital gain: -25.9% (vs 22.5% previously)

Worse, a 2% rise would expose you to a -45% loss (vs -39% previously).

It now takes 30 years to breakeven according to the duration calculator, because with no coupons the impact upon return is driven solely by capital gains – with a 0% coupon you don’t have any interest payments to invest into higher-yielding bonds to accelerate you to breakeven.

That’s also why our 0% coupon long bond makes a big 35% capital gain when rates drop – it doesn’t receive any coupon payments that cause it to start reinvesting into lower yielding bonds after the interest rate fall.

The upshot is that lower yielding bonds are more sensitive to interest rate changes. They’ll show bigger losses and gains as we enter the negative yield underworld and the effect is particularly pronounced with long bonds.

For more on the counterintuitive impacts of interest rate changes on bonds, read this excellent piece on bond convexity from Portfolio Charts.

Scenario #4: Rate rise impacts are affected by time

What if the 1% interest rate rise happens after you’ve held our example bond for one year?

30-year bond

• Face value: £100
• Coupon rate: 1%
• Market rate: 2%
• Years to maturity: 29 (previously we calculated the rise to maturity 30 years away)
• Price falls to: £78.08

Capital loss: -22% (vs 22.5% previously)

Hahaha… -22%? Why, tis but a scratch! While we’re hopping about on one financial leg, just note that interest rate rises are less scary the longer it takes for them to gently waft upwards.

How quickly do market interest rates move?

All my examples have shown an instantaneous drop in interest rates. That isn’t very likely. Rates fluctuate daily. They will drift up or down over months and years.

What we fear most though is big interest rate rises, so let’s conclude with some of the nastiest examples I can unearth using the UK government bond data I can access.

• The worst year for gilt losses in the low interest rate world (i.e. post-Great Recession) was 2013. 15-year gilts took a -9.6% real return loss that calendar year, according to the Barclays Gilt Equity study (BEG).

• 10-year gilt yields rose around 1% that calendar year according to this aggregation of Bank of England data by Data Hub.

• 30-year gilt yields rose about 0.5% that year according to the Debt Management Office’s records.

• 1994’s -13.8% was the worst calendar year return for 15-year gilts since the BEG study started tracking them in 1990.

• The 10-year gilt yield rose just over 2% from 1 January to 30 September that year (Data Hub again).

The worst post-war year for gilts came with the -29% loss suffered by 20-year gilts when stagflation was all the rage in 1974 (BEG). Using a bond price calculator and an 11% guesstimate for the coupon rate on 20-year bonds in 1974, that implies a rough(ly) 4.75% increase in market interest rates that year.

If somebody out there has access to more accurate data, I’d love to hear more.

Unbroken bonds

Interest rate rises as violent as those I’ve simulated are possible. Shorter-dated government bonds will shrug off those hikes better than long government bonds.

But the capacity of bonds to protect diversified portfolios against a crash is far from exhausted at low interest rates, except in as much as short bonds run increasingly out of puff the lower we go.

The extreme volatility of long bonds in this environment suggests we may need to think about them in a new way.

Would you be interested in an asset that’s negatively correlated to equities that could help offset a market crash – but which entails big-kahuna level risks of its own?

If long bonds are too risky to properly belong in the defensive part of the portfolio, then what if a 5%-10% allocation was carved out of the equity side?

That is how the Permanent Portfolio works. With cash acting similarly to short bonds, long bonds provide the best protection against a deflationary recession, while equities are for growth and gold for when nothing else does it.

A risk-portfolio allocation to long bonds could also make sense for somebody whose holdings are dominated by extremely risky equities (think risk factors, emerging markets, and sector bets) or even a young adventurer who would-be all-in on 100% equities but would also be happy to have the best dry powder to hand when the market crashes again.

Personally, I’m happy to keep holding intermediate gilts as a muddy compromise between knowing that interest rates could go either way and needing some decent crash protection for my portfolio.

I recommend playing with a bond price calculator for yourself though, as an easy way of visualising more ‘What If?’ scenarios.

Take it steady,

The Accumulator

Bonus appendix: Bond funds, duration and bond price calculators

It’s simplest to use duration as an approximate guide to your bond fund’s prospects when its market interest rate changes.

As a rule of thumb, a bond fund (or bond) with a duration of 7 will:

• Lose 7% for every 1% rise in its yield.
• Gain 7% for every 1% fall in yield.

Whatever your bond fund’s duration number, that’s roughly how big a gain or loss you can expect for every 1% change in its yield. The duration number should be published on the fund’s home page.

However, duration is a moving target. Duration increases as yields fall (and vice versa) which means losses and gains are amplified the lower we go. Again, as we saw earlier that super-charges the volatility of long bonds in particular, and the same goes for long bond funds.

Still, this stuff only really sunk in for me once I started running my bond fund numbers through the calculator.

First go to your bond fund’s home page. Look up its average coupon and average maturity metrics.

Vanguard UK Gilt ETF – interest rate falls by 1%

• Face value: £100
• Coupon rate: 3.1% (fund’s average coupon)
• Market rate: 2.1%
• Years to maturity: 19.7 (fund’s average maturity)
• Price rises to: £116

Capital gain: 16%

This happy 16% gain is a little more than implied by the fund’s average duration of 15 (we’d expect a 15% lift) but this brings me to a good point about all the calculations I’ve used in this piece.

They cough up results to however many decimal places but the equations whirring away in the background use a ‘best fit’ process. They ‘guess’ at the final value and then modify it until further iterations don’t make much difference.

The bottom line is that these calculations aren’t precise answers but they are close enough.

Inputs matter, too. If I change the ETF’s coupon rate to 3.05% then the calculator hands me a 15% gain. So perhaps Vanguard rounded the average coupon number up and that threw the calculator off.

Similarly, a newly minted bond with a 1% coupon won’t behave quite the same as its secondary market equivalent with a 2% coupon.

Nevertheless the calculators help illustrate what we’re in for – even though they have to use a little guesswork.

1. If you want to understand the maths behind the calculator a tiny bit better, see these musings by The Investor on a potential bond market crash from… gulp… 2012! (You see why we keep warning that people have feared a bond market correction for donkey’s years? [↩]
2. Assume a semi-annual interest payout in every example. [↩]

What caught my eye this week.

I have a soft spot for income investing. I haven’t actually (naughtily, actively) invested with a focus on income since the financial crisis, though.

(Why not? That’s a whole other story.)

I still expect to live off investment income when I’ve had enough of spinning the wheel on my net worth (and of work, of course). But it’s been more than a decade since replacing my salary with the readies from a growing collection of income-producing assets guided my portfolio.

Thinking back, when I began investing I feel it was the aim of most serious private investors I came across to someday live off dividends, bond coupons, interest on cash, and perhaps a buy-to-let or two.

But that’s not the case any longer.

Obviously, the utter squashing of fixed income yield hasn’t done income investing any favours, although those who owned such inflating assets enjoyed a lucrative ride on the way to today’s miserly yields. And interest on cash is a bygone luxury.

More recently dividends have gotten the chop. It all adds up!

But I believe wider cultural influences are at work beyond the numbers.

Imported Americana

When my co-blogger The Accumulator began talking about his planned drawdown strategy – to sell a certain amount of capital every year, with the aim of running it down to near-zero by death – it sounded foreign to me.

And I mean that very specifically.

I was familiar with such strategies – although newer investors would be shocked how rarely you heard terms like ‘safe withdrawal rate’ 20 years ago.

But to me the plan sounded American. I associated it with the American market, which taught different lessons from those I picked up from the curmudgeonly band of 30- and 40-something dotcom bust survivors who frequented the UK investing landscape at the turn of this century.

In contrast The Accumulator was schooled by Bogleheads at the Temple of Vanguard. I sensed he found my income-fantasies atavistic.

I believe he’s made his peace with the concept – writing numerous articles on the intricacies of the safe withdrawal rate will show anyone that all strategies come with their own mental and practical fudges – but he still definitely wouldn’t advise it.

To him, income-investing as a drawdown strategy is at best a retirement hobby for rich people. Like raising alpacas.

You say milllionaire, I say million-a-year

The US market hasn’t yielded much by the way of income for many years. I always assumed that was the main reason for the disinterest in income.

There are big tax disadvantages to dividends in the US, too, although this is also true in the UK nowadays outside of ISAs and SIPPS.

But I was interested to read a post on The Rational Walk blog suggesting there were deeper cultural habits at work, too. Only this author is American, looking in the UK’s direction:

I find the British manner of thinking about wealth much more satisfactory for several reasons that are worth exploring in greater depth.

He believes we still focus on income. The following section from a famous investing book, Where Are The Customer’s Yachts, is fingered for this trans-Atlantic supposition…

Have you ever noticed that when you ask a Britisher about a man’s wealth you get an answer quite different from that an American gives you?

The American says, “I wouldn’t be surprised if he’s worth close to a million dollars.”

The Englishman says, “I fancy he has five thousand pounds a year.”

The Englishman’s habitual way of speaking and thinking about wealth is of course much closer to the nub of the matter.

A man’s true wealth is his income, not his bank balance.

…which does indeed sound familiar, but only to those who’ve read the likes of P.G. Wodehouse, Somerset Maugham and their contemporaries, not to today’s British investing forums.

Because as dedicated investing nerds all know, author Fred Schwed published Where Are The Customer’s Yachts in 1940!

It’s still a timeless read, mind you. Even if I think that this British/American distinction is more dated than many of its other observations. (It’s funny, too, so check it out if you’ve never had the pleasure.)

Also be sure to read that Rational Walk post: What’s Your Magic Number?

Who knows? You might just find some of your native income-seeking spirit rekindled, after all!

Have a great weekend.

[continue reading…]

Anyone cited by Warren Buffett as a super-investor is worth knowing more about. Walter Schloss is one such man.

Walter Schloss was born in 1916. He began working on Wall Street at aged 18, while the stock market was still recovering from the Great Crash.

Schloss took investing classes from Benjamin Graham, who also taught Warren Buffett. He went on to work for Graham’s fund (where he met Buffett) before setting up his own partnership in 1955.

Schloss was an excellent investor:

• His fund achieved an average compound return of 15.5% a year until he closed it in 2000.

• The S&P 500 returned 10% a year over the same period.

If you had been able to invest $10,000 in the S&P 500 in 1955, then by 2000 you’d have had:

• $729,000

Not bad – but $10,000 given to Walter Schloss in 1955 would have grown to:

• $5,388,000

Nice returns if you can get them!

How Walter Schloss managed money

Most super-successful investors must change their tactics as their funds get larger. Schloss invested for fewer than 100 clients. He was therefore able to invest in small companies and special situations throughout his career.

His investing style was pure Benjamin Graham. In Warren Buffett’s 1984 essay, The Superinvestors of Graham and Doddsville, Buffett wrote:

Walter has diversified enormously, owning well over 100 stocks currently. He knows how to identify securities that sell at considerably less than their value to a private owner. And that’s all he does. He doesn’t worry about whether it it’s January, he doesn’t worry about whether it’s Monday, he doesn’t worry about whether it’s an election year. He simply says, if a business is worth a dollar and I can buy it for 40 cents, something good may happen to me. And he does it over and over and over again.

He owns many more stocks than I do — and is far less interested in the underlying nature of the business.

I don’t seem to have very much influence on Walter. That’s one of his strengths; no one has much influence on him.

By age 80, Schloss hadn’t changed much, according to Buffett’s biography, The Snowball:

Walter Schloss still lived in a tiny apartment and picked stocks the same way he’d always done.

A few chapters on we find Schloss playing tennis at 90. That definitely qualifies him for the Great Old Investor club!

The rules of Walter Schloss

If you’d like to follow in the footsteps of Walter Schloss – to try to beat the market rather than ‘merely’ tracking it – then you’ll want to know how he invested.

As a pupil of Benjamin Graham and a fellow traveller of Warren Buffett, Schloss was obviously a value investor. Your first port of call should therefore be Ben Graham’s The Intelligent Investor.

Like all investors who do achieve the very difficult – but not impossible – and beat the market, Walter Schloss had his own quirks though.

In 1994 Schloss typed them up onto a single sheet of paper. No book, no speaking tour – just 16 bullet point guidelines.

And here they are, near-verbatim.

Factors needed to make money in the stock market: Walter Schloss

1. Price is the most important factor to use in relation to value.
2. Try to establish the value of the company. Remember that a share of stock represents a part of a business and is not just a piece of paper.
3. Use the book value as a starting point to try and establish the value of the enterprise. Be sure that debt does not equal 100% of the equity. (Capital and surplus for the common stock).
4. Have patience. Stocks don’t go up immediately.
5. Don’t buy on tips or for a quick move. Let the professionals do that, if they can. Don’t sell on bad news.
6. Don’t be afraid to be a loner but be sure you are correct in your judgement. You can’t be 100% certain but try to look for weaknesses in your thinking. Buy on a scale and sell on a scale up.
7. Have the courage of your convictions once you have made a decision.
8. Have a philosophy of investment and try to follow it. The above is a way that I’ve found successful.
9. Don’t be in too much of a hurry to sell. If the stock reaches a price that you think is a fair one, then you can sell but often because a stock a goes up say 50%, people say sell it and button up your profit. Before selling try to reevaluate the company again and see where the stock sells in relation to its book value. Be aware of the level of the stock market. Are yields low and P-E ratios high? Is the stock market historically high? Are people very optimistic etc?
10. When buying a stock, I find it helpful to buy near the low of the past few years. A stock may go as high as 125 and then decline to 60 and you think it attractive. Three years before the stock sold at 20 which shows there is some vulnerability to it.
11. Try to buy assets at a discount [rather] than to buy earnings. Earnings can change dramatically in a short time. Usually assets change slowly. One has to know much more about a company if one buys earnings.
12. Listen to suggestions from people you respect. This doesn’t mean you have to accept them. Remember it’s your money and generally it is harder to keep money than to make it. Once you lose a lot of money it is hard to make it back.
13. Try not to let your emotions affect your judgement. Fear and greed are probably the worst emotions to have in connection with the purchase and sale of stocks.
14. Remember the work of compounding. For example, if you can make 12% a year and reinvest the money back you will double your money in six years, taxes excluded. Remember the rule of 72. Your rate of return [divided] into 72 will tell you the number of years to double your money.
15. Prefer stocks over bonds. Bonds will limit your gains and inflation will limit your purchasing power.
16. Be careful of leverage. It can go against you.

Sounds straightforward, doesn’t it?

It’s not! The alchemy of super-rare successful active investing is simple but not easy.

That’s why Schloss’ rules have aged so well. I’d say rule three – to favour book value as a foundation of value – is the only one that’s (arguably) out of date.

Modern companies’ greatest strengths are often intangible assets that aren’t accurately reflected by book value. Think of today’s technology giants, for instance.

Perhaps Schloss would just ignore those. There are still plenty of companies where old-school value investing metrics are relevant. If you’re turning over thousands of stones looking for a few gems – and trading your portfolio rather than aiming to buy and hold the next Microsoft – then valuing hyper-growth tech firms is someone else’s problem.

According to Smart Money, Walter Schloss was still running his own portfolio as of April 2009, aged 95. Schloss passed away on 19 February 2012.