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# How do bonds work?

Bonds act around multiple key components:

• Face and par value
• The coupon rate
• The yield to maturity
• The interest rate of the market
• The date of maturity

## 12.1  Par and face value

The par value is the amount of money the issuer (company or government) agrees to repay (you, the buyer of the bond) when the bond reaches its maturity date. In other words, it represents the value of the bond when it reaches maturity. This is also called the face value. The face value and par value represent the same thing.

The par value of a bond is determined by the entity that issues the bond. For bonds, the par value is \$100 or \$1000 or \$5000 most of the time depending on the type of bond. If you buy a bond with a \$1000 par value and a maturity date of ten years that means the issuer has to pay you par value (\$1000) at the end of the maturity date. This is very important because as an investor, you almost never pay the exact par value when you buy a bond. The price of the bond can be above or below par value depending on the market and type of bond.

When searching on the internet for information about bonds you might also encounter the word “principal”. Principal is mostly used when talking about paying the par value when the bonds hit maturity. Paying principal is the same as paying the par value or face value. In this guide I will use principal when I’m talking about payments of the bond because this is the official term used by the U.S. Government.

The par value is the intrinsic value of the bond. In case of a bond issued at \$1000 par value, the intrinsic value is \$1000.  When a bond is trading above par, this means you have to pay more than the bonds intrinsic value. This is also called “at a premium”.  When a bond is trading below par it’s called “at discount”. Some types of bonds are always trading above or below par value. This is not a bad thing. But just like buying stocks, you should know why a bond is trading above or below par value.

• A bond with a par value of \$1000 while currently selling for \$900 is called “at discount”
• A bond with a par value of \$1000 while currently selling for \$1050 is called “at a premium”.

## 12.3 Interest rate risk

The par value of a bond is directly tied to the interest rates in the economy. Not to be confused with the interest rate or coupon rate of the bond. The FED determines the market interest rate in the economy. When interest rates are low, banks can lend more money and the customers of the bank (you) can borrow more money. At this time of writing (2021) interest rates are very low. The Fed's funds rate is only 0 - 0.25%.

• When interest rates are low, most bonds will trade above par.
• When market interest rates are high, most bonds will trade below par.

In other words, a change in market interest rates might affect the profitability of your investments. The “official” term for this is called “interest rate risk”. In general, when market interest rises, the fixed bond rate prices fall.

The market interest rate has the biggest impact on bond pricing. When market interest rates are rising, the return of the older bonds decline because new bonds will be issued with better returns. Nobody want to buy the old bonds so the price will drop.

## 12.4 The coupon rate and coupon payments

The coupon rate might be confusing because coupons are something from the old days. Many years ago when there were no computers, investors got physical certificates showing that they owned bonds or stocks. Each certificate had a certain amount of coupons. When interest payout dates are due (a few times a year) you would clip a coupon code from the certificate and send it by post. Once the coupon is received and is valid you receive the interest on your bank account. Coupons are long gone and everything is done automatically today. Coupon rate and coupon payment still exists today:

• Bonds interest payments are called coupon payments
• The interest rate is called the coupon rate

The coupon payment determines when you get your interest paid (for example, quarterly). And the coupon rate determines the amount of interest shown in percentage.

There are also zero-coupon bonds. These bonds have no coupon so you don’t receive interest. These bonds make one single payment at the end of the maturity date that is higher than the initial price you paid. These bonds are sold below par. For example, you buy a five year zero-coupon code for \$750 with a par value of \$1000. At the end of the five years you get paid the par value of \$1000 and make \$250 in profits (minus fees and inflation).

## 12.5 The yield to maturity

The yield to maturity shows how much an investor will earn if the bond is held till the maturity date. This is based on the initial price you paid for it. Yield to maturity can be used to compare bonds. As mentioned before, when market interest rates rise or fall, this will impact the price of the bond. You can calculate the yield to maturity for a bond as follows:

• Yield to Maturity = [ Annual Interest + {(PV-Price)/Maturity}] / [(PV+Price)/2 ]

Where:

• Annual interest = coupon rate * par value
• PV = par value (or face value)
• Price = current market price of the bond
• Maturity = time till maturity

Let’s compare three bonds with different prices but the same coupon rate:

 Terms Bond A Bond B Bond C Face value (par value) \$1000 \$1000 \$1000 Market price \$900 \$1000 \$1100 Coupon rate 3% 3% 3% Maturity 10 years 10 years 10 years Yield to maturity 4.1% 3% 1.9%

Bond A:

• Yield to Maturity = [30 + {(1000-900)/10}] / [(1000+950)/2] = 4.1%

Bond B:

• Yield to Maturity = [30 + {(1000-1000)/10}] / [(1000+1000)/2] = 3%

Bond C:

• Yield to Maturity = [30 + {(1000-1100)/10}] / [(1000+1100)/2] = 1.9%

When market interest goes down, the price per bond will go up and the yield to maturity will go down. Keep in mind that once you buy a bond, the coupon rate and par value will stay the same until the maturity date. However, since market interest changes all the time, the price of the same bonds also changes every time. So you can buy the same bonds for different prices and different yields of maturity. Just like stock prices can fluctuate all the time.

## 12.6 Coupon rate, maturity, yield till matirity and interest rate risk

If we compare two bonds with different coupon rates, the bond with the lower coupon rate will decrease more in value when interest rates (determined by the FED or other central banks) are high.

[keypoint text=

• Low fixed-rate coupon rates = higher interest rate risk
• High fixed-rate coupon rates = lower interest rate risk]

When you buy a bond with a low coupon rate and market interest goes up, new bonds will hit the market with higher coupon rates. Nobody would buy bond A with a coupon rate of 3% if there are new bonds that offer 4%. To keep bond A competitive, the market price goes down. So bond A becomes less valuable on the second hand market if you want to sell.

Example:

• Market interest rates go up
• Bond A hits the market with a coupon rate of 3%
• After one year, market interest went further up and the company issues another bond B with a coupon rate of 3.5%
• Nobody would buy bond A with a 3% coupon rate if they could buy bond B with 3.5%
• In response, the market price of bond A goes down so it eventually has the same yield till maturity as bond B
• If you bought bond A before market interest went up, you paid more and won't be able to sell that bond on the second hand market for the same price

And the opposite is also true, when a company issues a bond with a higher coupon rate and market interest rates fall, new bonds will hit the market with lower coupon rates. That means the par value of the first bond needs to rise to mitigate the change in coupon rate.

Example:

• Market interest rates go down
• Bond A hits the market with a coupon rate of 3%
• After one year, market interest went further down and the company issues another bond B with a coupon rate of 2.5%
• Nobody would buy bond B with a 2.5% coupon rate if they could buy bond B with 3%
• In response, the market price of bond A goes up so it eventually has the same yield till maturity as bond B

The yield till maturity is an offset between the coupon rate, price, par value and maturity. Meaning, bonds with different fixed coupon rates can have the same yield till maturity because bond A is cheaper to buy vs bond B. For example:

• Bond A with par value of \$1000, market price of \$1000 and coupon rate of 4%
• Bond B with a par value of \$1000, market price \$1000 and coupon rate of 4.5%
• To make bond A competitive with the same yield till maturity, the market price of bond A rises to \$1125
• Bond B nets \$45 a year (\$1000 * 4.5%) and bond A also nets \$45 (\$1125 * 4%)

Because the yield of maturity for the same bond always stays the same, either the coupon rate goes up/down or the market price of newly issued bonds change.

A high yield is actually a bad thing. Because that means the issuer had to up the yield to attract new investors. Meaning there is no interest in the bond market. When the bond yield goes down that means there are many buyers and indicates a positive bond market condition.

It’s important to look at the interest rate risk when purchasing bonds. As interest rates are pretty much the lowest they can be at this time of writing (2021), you should be aware that low coupon rates will decrease in value if you purchase them right now while chances are interest rates will rise anytime soon. Update: just a few months later (jan 2022) inflation is at the highest point in over four decades. Interest rates will probably rise very soon because inflation and interest rates are also connected. More on that in a later chapter.

You should be aware and cautious of bonds selling below par with low coupon rates when the market interest is low. Because they will only decrease in value over time while the market interest rates can’t go any lower at this moment (2021).

Another factor that has a big impact on interest rate risk is maturity. If you buy a bond with a maturity of only one year, then chances are market interest rates won’t fluctuate that much and you have less risk.

• Bonds with long maturity = higher interest rate risk
• Bonds with short maturity = lower interest rate risk

To balance things off, bonds with longer maturity have higher coupon rates:

• Higher interest rate risk = higher coupon rates
• Lower interest rate risk = lower coupon rates

The calculations and examples are just a simplification to the process.

[keypoint text=Key Concepts:

• Par value is the value the bond is issued for. These are fixed prices most of the time like \$100, \$1000 or \$5000.
• Par value and face value refer to the same thing and are interchangeable.
• Principal is used to describe payments of bonds when they mature. For example, at the end of maturity a bond will pay the principal. Par value and principal represent the same.
• Coupon rate is interest paid annually or quarterly based on par value.
• Coupon payment is the annual interval payment.
• The market price is the price you pay for a bond regardless of par value.
• The yield till maturity shows how much you’ll earn if you held the bond till maturity.
• When market interest is high, most bonds will trade below par value. This is called interest rate risk.
• Bonds with long maturity and low coupon rates have the highest amount of interest rate risk.
• Keep in mind that market interest rates and interest paid by the coupon rate are two different things.