Bond Basics

The name is Bond. Treasury Bond.

First, a word on the subtitle. The reason why the 2023 bond story centers on Treasuries is because treasury yields are not only transforming Tina into Tara but also obviating riskier investments: Pension funds and insurance companies are firing pricey CIOs because they no longer need esoteric asset allocations to hedge funds, private equity funds et al; they can simply sit on Treasury Bills yielding >5%.

A bond is a tradeable loan and it is that tradeable attribute that creates all the bond math that needs to be understood by a bond investor.

The current yield of is a bond’s annual coupon payment divided by the bond’s current market value. It should be compared to the current yield of other bonds on the market in evaluating the potential profitability of a tradeable bond. Yield to Maturity, on the other hand, should be compared to the Yield to Maturity of other bonds on the market in evaluating the potential profitability of a bond held until maturity. In discussions of price relationships, the term “yield” is synonymous with “yield to maturity”, not “current yield”.

Duration (sum of discounted future cashflow / current market price) of a bond measures interest rate risk by predicting how much bond prices will change with interest rates. The Macaulay Duration is measured in years before full payback of the bond (typically 20% or so shorter than maturity). So a 10-year bond may have a calculated duration of 7 years. Once the Macaulay duration is calculated, it can be converted to Modified Duration which measures the change in bond price with a 1% change in interest rates. The 7 year Macaulay duration may translate to something like a 6.8% gain or loss on a 1% move in interest rate. Clearly, the higher the duration, the greater the interest rate sensitivity (which is either risk or reward). That is, a higher duration bond’s price will drop more (sell at a steeper discount) OR rise more (sell at a heftier premium) given the same interest rate move in the opposite direction.

Two factors affect the calculation of duration: coupon and time-to-maturity. The duration of any bond that pays a coupon will be shorter than its maturity, because some amount of coupon payments will be received before the maturity date. The lower the coupon, the longer a bond’s duration, because proportionately less payment is received before final maturity. A zero coupon bond’s duration (e.g. T Bills) is the same as its maturity (another way of saying the bond is fully exposed to interest risk because nothing is paid back until maturity).

The longer the time-to-maturity, the longer the duration (because it takes longer to receive all of the coupon payments). Longer term bonds are more exposed to interest rates moving against the investor. A 30-year tradable bond likely lose <~30% of its value if rates were to rise 1%, and a 5-year tradable bond would only lose <~5% of its value:

So now, when it comes to investment choices:

• If rates are expected to rise, consider bonds with shorter durations. These bonds will be less sensitive to a rise in yields and will fall in price less than bonds with higher durations.
• If rates are expected to fall, consider bonds with longer durations because the bond’s value would increase more than comparable bonds with shorter durations. Tech stocks — whose earnings are far into the future — are “long duration assets” because when discounted back at lower interest rates, yield much higher present values. Thus, “long duration” can apply to both long bonds and Tech stocks.

It stands to reason that duration (a measurement of risk) is related to volatility (a disagreement among market participants about an uncertain future). You don't trade duration with T-bills because there is no volatility to T-bills (the eventual outcome of a T-bill is predetermined and certain).

QE, by reducing the quantity of tradable bonds in the marketplace, boosts bond prices and reduces bond yields. In doing so, it actually reduces duration — interest rate risks — in the marketplace and eases financial conditions. In the same breath, it lowers the discount rate for DCF. Thus, risk assets rise in value. QT does the reverse. Put another way, the Fed aims to steer the economy — and redistributes wealth in the process — through the “duration channel”.

Duration — the derivative of how price moves with interest rate — is actually a linear estimation of price-yield relationship (which turns out to be curved rather than linear). As such, it loses accuracy at extremes (see chart below). Convexity — the derivative of how duration moves with interest rate — is a more accurate measurement of price-yield relationship.

If a bond’s duration rises as interest rate falls, the bond is said to have positive convexity. That is, the bond price rises at a greater rate than the rate of drop in yield AND falls at at a less rate the the rate of rise in yield. This obviously favors “long duration” positions, since gains are hefty when yields move with the position and losses are (relatively) slight when yields move against the position. So If the objective is capital gains rather than income from coupons, then obviously bonds with positive convexity are the investment of choice, and the higher convexity (expressed in “multiplier” terms) offers higher return and risk (if yield moves in the opposite direction). Bond A below is a longer duration (e.g. 30 year) AND more convex bond than Bond B (e.g. 10 year).

Conversely, if a bond’s duration falls with interest rate, the bond is said to have negative convexity. Mortgage-backed securities — with yields higher than traditional bonds — typify these bonds whose prices will fall at a greater rate with a rise in yields than if yields had fallen. Therefore, if a bond has negative convexity, its duration would lengthen as the price falls and vice versa. These bonds are almost always callable because when the prevailing interest rate falls below the interest rate on the bond, the issuer can save money by paying off the bond and issuing another bond paying less interest, — no different than refinancing a mortgage for lower monthly payments. Bonds with negative convexity work against “long duration” positions.

When choosing between 2 different issues of the same maturity, the higher the yield to maturity, the better. Then it comes down to choosing between a zero-coupon issue and an issue that carries coupon. A “zero”:

• will almost always have the deepest discount (lowest current market price), which makes entry cost lower.
• will usually have higher returns than a regular bond with the same maturity because of the shape of the yield curve.
• are more volatile to change in prevailing interest rates which can bring traders short-term price movements.
• can help investors to avoid gift taxes, but they also create phantom income tax issues.

Breakeven Inflation Rate (nominal yield — real yield) is a predictive measurement that helps investors gauge how two bonds of different maturities are likely to perform guessing at how future interest rates move with future inflation. They tell the investor how far prevailing rates would need to rise or fall by the time the shorter-term bond matures in order to make up for its smaller interest payments.

The tradable portion of a bond portfolio, intended for capital gains rather than predictable income from coupon, should be constructed out of predicting future yield curve movement, proper choice of duration and convexity as a function of risk appetite, and comparison of Current yield between available bonds on the market. Using convexity, an investor can calculate potential profit and loss of a trade. Once the tradable portion of the bond portfolio is constructed, the DV01 calculation should be used to monitor the P&L impact from daily change in price and yield of the bond holding, in order to either take profit or loss on a timely basis. That all said, capital gains from trading bonds can only be attained in a bond bull market, with interest rates trending down.

All good things come to an end, and it is safe to assume that the 40 year bond bull market that started in the early 80s ended in 2022. Even with rapid rate hikes in 2022–2023, the current Fed Funds Rate at 5 1/4% is relatively low by historical standards. The current trend of de-globalization and reshoring will increase friction and cost in supply chains and is thus inflationary. So are sanctions and trade wars, not to mention kinetic wars, in a multipolar world. Meanwhile, monetary inflation, as explain here, will only increase, globally. Finally, the next 1st Turning will kick off with arguably the biggest technological wave in history, — the AI Revolution, detailed here. AI is not just about software development but requires vast supporting infrastructure from super fast chips to immense data centers, — all requiring quantum jump in energy consumption. This too is inflationary. So despite deflationary demographics, the next several decades are likely to be inflationary. This means stubbornly elevated, if not upwardly trending, interest rates. This is by definition a secular bond bear market.

One telltale sign of an impending bond bear market is bear steepening of the yield curve, whereby long bond rates rise faster than short term rates. (This is bearish for the equity market since rising long-term rates indicate inflation and future interest rate hikes by the Fed.)

During the last bond bear market from 1960–1981, 10-year US Treasury yield rose from 3.9% to 15.8%, clearly resulting in excruciating bond price depreciation. Yet, the average treasury bond portfolio managed an annualized return of 4% (despite wild swings from -5.4% to 18.3%) because of reinvested income and principal at ever higher rates. This is all to say that since capital gains are unattainable, total return for bond holders is muted in a secular bond bear market (kind of like only getting dividends from a stock whose price is constantly dropping). Despite that, risk-free bonds still have a place in one’s overall portfolio, purely from a risk management (capital preservation) standpoint, — even if the total return falls somewhat short of inflation. Focus on forward returns and continue to ladder in short term bills/notes and reinvest at higher yields, — especially when traders sell such instruments following an increase in rates, pushing down prices and pushing up yields. In other words, the BTFD mentality should apply to bonds just as they do stocks, except the focus is on future interest income rather than future price rise.

In favoring corporate bonds over Treasuries make sure the yield spreads are high enough (3% or so for IG and 7% or so for HY). Why? Because during recession, stock prices drop because of sell-off due to earnings drop, whereas treasury prices rise because of flight to safety. This translates to declining maturity for corporate bonds and rising yield to maturity for treasury bonds. The yield spreads at the point of purchase must provide a sufficient cushion to warrant favoring corporate bonds over treasury bonds. They are nowhere close to that right now. When they get there, make sure the yield (“to worst”) is high enough to warrant investing in callable corporates.

Footnote —

“Bond” is the root for “bondage”. Milton Berg quotes about Treasury bonds:

“A ‘Treasury’ is a place to store wealth. We only have debt and no wealth. So it should be called ‘Ministry of debt’ instead.”

“A Treasury bond is a certificate of wealth confiscation — first through inflation (by further creation of debt), or eventual default”