How are price and return of a bond determined?

How is the price of a bond determined? Why does the price of a bond fluctuate? The price of a bond, and therefore its yield to maturity, is determined by a number of factors. The most important are:

The market rate and the coupon If a given bond offers a coupon that is considerably higher than the market rate, that bond will be quoted at a high price. After all, who wouldn't be interested in investing in a bond that pays 10%, when the market rate is only 3%? The bond will therefore become more expensive (the price will rise, and the yield to maturity will fall) as the market rate falls. The price of the bond will also fall (the actuarial yield will rise) if the market rate rises.

The remaining life of the bond Unlike share prices, bond prices will not rise without limit. This is because each bond has a maturity date, at which point the bond will be redeemed at its face value (often 100%). The closer you get to the maturity date (when the bond is redeemed at 100%), the more limited the upside and downside potential. A short-term bond will therefore always fluctuate less than a long-term bond. The quality of the issuer If you have the choice of investing in two identical bonds, one issued by a highly solvent multinational company and another by a company in financial difficulty, you will choose the more solvent issuer. This bond will therefore be more expensive than the same bond issued by a weakened company. In other words, the actuarial yield of the weaker issuer will be higher than that of the stronger issuer. The extra return you can receive by investing in a less creditworthy bond you can think of as a "risk premium". If you have a bond in your portfolio whose rating (which is a good measure of the issuer's creditworthiness) suddenly improves (e.g. Standard & Poor's raises the rating from A to AA ), this will lead to a rise in the price of the bond and therefore a fall in the actuarial yield.

What is the difference between "market rate" and "actuarial yield"? The "market rate" is the current yield applicable to benchmark interest products. The interest rate is always indicated for a specific term, e.g. 1 month, 1 year, 3 years, 5 years, etc. Most often, government bonds or interbank products (such as swaps) are used as benchmarks. It is generally accepted that these products carry no (government bonds) or virtually no (interbank swaps) credit risk. The market rate therefore corresponds to the interest rate on government bonds or swaps. This market rate is constantly changing. The short-term market rate (from one day to one year) is mainly determined by the central bank's monetary policy, while the long-term market rate is more a reflection of the macroeconomic climate. In a recession, for example, long-term rates will often fall, while in good times they may rise sharply.

The actuarial yield is the yield an investor obtains if he buys a bond at a given price and holds it until maturity. An investor who buys the same bond an hour later at a higher price will obtain a lower actuarial yield on that same bond. This is why the market rate and the (actuarial) yield on bonds are closely linked. This means that when the market rate rises, so does the (actuarial) yield on the bond. And usually in more or less similar proportions. The same thing happens when market rates fall: bond yields also fall. Example: The 5-year market rate (for government bonds) is 4.25%. The 5-year yield to maturity for a Ford Motor Company bond is 6.75%. Now, suppose the 5-year market rate starts to fall from 4.25% to 4.00%, the Ford bond yield will also fall by around 0.25%: from 6.75% to 6.50%. Since the fall in yields is always coupled with a rise in the price of the bond, the Ford bond will increase in value.

It is therefore essential for a bond investor to keep a close eye on changes in market rates.

What is the relationship between the actuarial yield and the price of a bond? The actuarial yield and the price of a bond are linked to each other, but in reverse. If the price of a bond rises, its actuarial yield falls. If the price of a bond falls, its actuarial yield rises. The exact relationship is determined by (complicated) financial mathematics formulas. Excel users can calculate a bond's yield using the "yield" function and its price using the "price" function.

What is YTM? YTM is the abbreviation for Yield To Maturity. The corresponding graph shows the evolution of the bond's actuarial yield.

What is accrued interest and who has to pay it to whom? With the exception of zero-coupon bonds, all bonds pay the investor a periodic (often annual) coupon. In the case of an annual coupon, this interest payment is made only once (on a single day) in the year, on the coupon date. If you hold a bond that you wish to sell one day before it pays its coupon, you will receive a pro-rata coupon. You will then be paid 364/365 of the coupon. This is known as accrued interest. The buyer of the bond will have to pay this accrued interest. On the coupon date, the buyer will receive the entire coupon. In other words: the seller receives a pro-rata share of the coupon for the period running from the last coupon payment date to the date on which he sold his bond. It is always the buyer of the bond who must pay this amount as accrued interest to the seller of the bond. Herein lies an essential difference with the payment of share dividends: an investor who sells his share one day before the dividend payment will not receive any dividend. The buyer of a share will never have to pay the seller a pro-rata share of the dividend to which the seller thought he was entitled.

As a bond investor, you don't have to wait for the coupon date before selling your bond either. You are always paid the accrued interest to which you are entitled.