Bonds - a technical deep dive (Part 1)

Bonds are one of the most common financial instruments - as we go through the various aspects in this deep dive, one should be able to understand bond risk, know how to evaluate it for our investment portfolios and be familiar with common trading strategies.

In the simplest sense, a bond (a fixed income debt instrument) is a loan given to the bond issuer by the bond buyer who then earns an income/ interest on the given principal (series of cashflows). As an investment asset, bonds offer benefits like - income (in the form of coupon payments), capital preservation (due to principal repayment), portfolio diversification (as inflation hedge/ lower volatility) etc.?

The classification of the bonds can be done in a few different planes -?

1. Based on the kind of issuer (government, corporate, quasi-govt., municipal etc.)?
2. Based on the sovereign / credit rating (EM/ DM bonds, high quality vs high yield / junk etc.)?
3. Based on the structure of the bonds (mortgage backed, convertible, option embedded etc.)?
4. Based on the characteristics of bonds (fixed/ floating rate, zero coupon, inflation linked etc.)

You might wonder why zero-coupon or floating rate bonds would qualify for fixed income - do note, that ‘fixed income’ is not so much a fixed payment amount but an obligation to make the payment vs say the discretionary nature of the stock dividends

Above classifications should give you a sense of the vast investible universe of bonds. Add to that, from an investment and trading perspective, these bonds can differ a great deal in liquidity, in risk breakdown, in modes of trading etc. that’s why often you’ll find specialised product focus/ specialised traders for different kinds of bonds. But irrespective of the sub-classifications, some of the fundamental concepts hold true for all and form the backbone of bond mathematics.?

Irrespective of the product, the starting point of trading is to define its key characteristics or parameters that give a clear idea of the risk. Then, in primary as well as secondary market trading, the communication between two parties must take into account these parameters for correct risk transfer and understanding.

For bonds these key features or specifications are:?

• Face value/ Principal/ Notional/ Par value - amount that will be paid back at maturity
• Maturity/ Tenor - the date when bond matures and investor receives the final payment
• Coupon - interest rate that the issuer will pay to the investor?
• Credit rating - depending on the issuer each bond will have a different rating that’d make it investment grade or high-yield etc.?
• Embedded option - whether the bond has any call/ put option embedded e.g. can it be called or paid off/ redeemed before the maturity date

What’s the risk we acquire by owning bonds as an asset?

There will be few different kinds of risks that we have to be mindful of:?

• Interest rate risk - impact on bond prices with the change in interest rate environment?
• Inflation risk - how the return on bond investment get impacted with inflation changes
• Liquidity / market risk - liquidity on a given bond could change due to multiple factors impacting our ability to trade in/ out of the security
• Credit risk - primarily this refers to the inherent risk of issuer defaulting on the payment obligations, there can be sub-parts of credit risk in the form of counterparty related settlement risks etc.?
• Redemption/ call risk - bond might be callable/ puttable ahead of the maturity date?

In addition to above, one is subject to external risk factors - event risks, currency volatility risk, taxation changes risks etc. Also note these risks are not independent, they can often work in conjunction and have a cascading effect on the markets. For e.g. if the issuer missed a coupon payment, this would accentuate the default risk fears, which in turn would impact the liquidity negatively in a potential rush to sell the bond (for reference you could look at the price action in some of the Chinese property developer names like Evergrande/ Country Garden etc in 2023 etc. under similar conditions)

How should we think about bond's valuation?

The answer to that question lies in the interest rate risk element. One of the most basic concepts in bond trading is time value of money i.e. money in the present or in hand today is worth more than the money in the future, IF you can earn a positive return on the investment done today (of course that’d change if we’re in a negative interest rate environment, where the savings value will decrease over time). If we know the rate at which we can invest, we can calculate the future value of our money.?

Future Value (FV) = Present Value (PV) * (1+ r/n)^nt?

where?r = annual interest rate earned

n = frequency of payment?

t = time period in years

Alternatively, PV = FV / (1+r/n)^nt?

Put other way, the price we’d be willing to pay for a bond today would be the net present value of all the expected future cash flows. We can extend the above formula to the series of cashflows that we receive in the bond to derive the bond price. Bond price is expressed as percentage of bond face value.?

Price of bond = C1/ (1+r/n)^t1 + C2/ (1+r/n)^t2 + C3/ (1+r/n)^t3… (P+Cn)/ (1+r/n)^tn

where?C1, C2..Cn = coupon for each period?

t1, t2 ..tn = number of periods for the cashflow ?

P = principal amount to be paid back at maturity?

n = frequency of payments?

r = yield to maturity or market discount rate?

Price conventions: When trading in the market one will come across different types of conventions for bond prices - Clean Price & Dirty Price (includes accrued interest). Accrued interest is the interest or coupon that has accrued since the last coupon payment date, but it hasn’t been paid yet.? ?

Let's use an example per table below. The table gives dirty and clean price of the bond at different intervals. At T= 0Y, 5 coupon payments are remaining. Now at T = 0.3Y, still 5 coupon payments are remaining, but the first coupon has ‘accrued’ for 0.3Y i.e. the bond holder is eligible for that coupon even if he sells the bond at this juncture. So the overall settlement amount will take into account this accrued interest.

Above calculations have been done using the bond price formula shared earlier, you could use excel to derive those, but more importantly would like to highlight a couple of things -

1. As can be seen the dirty price will change almost daily and exhibit a more zig-zag movement, it rises in between coupon dates and falls on the payment dates. This is due to the accrued interest component, which increases each day until the coupon payment is made. The clean price and dirty price will be the same on coupon payment dates.
2. Dirty price is usually called the invoice price while clean price is called the quoted price -> which means the actual payment exchange post a bond trade happens based on dirty price factoring the accrued, however, during trading clean price is quoted. This also makes intuitive sense, as the volatility of dirty price can make it difficult to evaluate and compare bonds.

This concept and calculation is important to understand - there could be occasions when you're trading on the actual coupon payment date of a bond, in such cases it is important to factor in the paid coupon.

What is Yield to Maturity (YTM) or Internal Rate of Return (IRR) or Reinvestment Yield??

We used YTM in calculating the bond price and as can see from the formula above, one way to think of YTM is, it is the singular implied market discount rate or the discount rate at which the present value of all future cash flows equals the price of the bond or YTM is the annual total return earned by an investor if the bond is held till maturity and all intermediate coupon payments are received and reinvested at the same rate.? ?

Note a few key points here:?

• While the coupon will be fixed for a given tenor of the bond, its YTM will keep fluctuating - so a calculated YTM is typically just a snapshot of the return at a given time based on certain bond price or market interest rate levels.?
• YTM typically doesn’t take into account the tax adjustments (capital gains or withholding tax). When comparing the investments, one should also consider these implications separately. E.g. Indonesian bonds could have 20% withholding tax which will be accounted for on a post trade basis
• Higher YTM is not always a better investment, unless it makes sense from a fundamental perspective, comparable asset yields and hedging costs. E.g. if 10Y Indian Govt. bond offers 7% and 10Y Indonesian Govt. bond offers 7.5% yield it’s not sufficient information to conclude that Indonesian bond shall be a better investment.?

Example: Let's consider the bond prices for following scenarios

A. Coupon rate 8% (annual), Tenor 5 years, YTM 6% and face value 100,000$ (Price: 108.42)

B. Coupon rate 5% (annual), Tenor 5 years, YTM 6% and face value 100,000$ (Price: 95.79)

C. Coupon rate 5% (annual), Tenor 5 years, YTM 7% and face value 100,000$ (Price: 91.80)

D. Coupon rate 5% (annual), Tenor 5 years, YTM 5% and face value 100,000$ (Price: 100)

You can also calculate these on your own, but from the answers of above exercises we can infer a few important things -

1. There is an inverse relationship between bond’s price and YTM/ interest rates As the yield rises, the discounted value of cashflows and thus the price goes down and vice-versa (e.g. B vs C)?
2. Bond could sell at a discount, at a premium or at par - if a bond sells at a price below the par value it’s at discount, if it sells above par it’s at premium. As can be seen in examples above, if the coupon rate is trading above the market return rates, then the bond trades at a premium and if it’s lower the bonds trade at a discount. (e.g. A vs B)

Should we buy the bonds at premium or discount?

It’s important to note though that bonds could sell at a discount or premium due to other leading factors too, for e.g. a shift in issuer’s credit rating. Additionally, while the intuitive trading sense says that buying something at a discount is better than buying at a premium (buy low, sell high) - it’s not always true in the context of bonds. The decision should be made based on investment objective and the factors driving the price shift. Premium bonds could offer a higher interest or income while the discounted bonds could give a better opportunity for capital appreciation. In terms of risk, a discount bond could have a higher default risk and premium bond could be more prone to call risk (if issuer wishes to issue at a lower prevailing rate).

Note, at maturity both premium and discount bonds will pull-to-par or return face value i.e. as a bond gets closer to maturity the price of the bond converges to par value (as the coupons are largely paid). This is also why investors look at Zero coupon bonds even though they do not pay any interest. One could buy them at a meaningful discount to the face value and be assured to get the par value later if held to maturity, thus giving a fixed return (price vs face value).?

Different markets, different yield conventions

Tip: Some of the other bond yield measures include Current Yield and Simple Yield, which are not as comprehensive but still used in certain scenarios. Current yield is just the coupon income relative to clean price of the bond (annual coupon / bond price). Simple yield takes the capital gain/loss into account alongside the coupon income. When trading across different markets, be mindful of the kind of yield measure used while trading. As an example, in Japan typically a simple yield measure is used, but when trading bond-swap spreads, one will have to convert and take into account the compound yield on the bond leg.?

Hope you find this useful, we shall dive into one of the most interesting and crucial concept of Duration in the next part.