In connection to last week’s post about **Bonds vs Bond Funds** a good follow-on mid-week post would be a short discussion on what we understand by a bond’s **yield** or **yield to maturity** . Once we understand this concept better we can then go on to see how bond price movements can be explained better.

## The Basics of a Bond

Lets start with the basics, a bonds as we discussed is essentially a loan. So it is a debt obligation with a maturity of more than one year. When for example a company wants to make a long-term investment, of say opening up a new plant, it can borrow the money from investors by issuing a bond. In return it promises to pay a series of pre-determined interest payments and the original value of the loan at the end. In technical words the interest payments are known as the **coupon****,**** **the end date is known as the **maturity date** and the final value or original capital is know as the **principal**, **face value** or **par value** of the bond.

Once a bond has been issued to investors, it is then traded in the bond market. Therefore, although a bond may have a maturity of 10 years for example, an investor can cash in his investment earlier by selling the bond on the market. A bond’s par, or nominal, value is typically €100, however its actual value will vary according to the cash flows it pays (interest and repayments) and the prevailing rate of interest for the type of bond. The fair price is the present value of the future interest and final capital payment.

Value of a Bond = Present Value of the interest payments + Present Value of the principal value

## Present Value

In simple terms the present value of any cash flow is the current worth of such future cash flows, As you often hear people say “€100 today is not the same as €100 in 10 years time”. This is all related to the concept of the **Time Value of Money**. There is a price to lending money to a firm by buying a bond. Therefore, the return paid by a bond must reflect the time value of money, and it comprises:

(a) the risk-free rate of return rewarding investors for forgoing immediate consumption,

plus

(b) compensation for risk and loss of purchasing power.

## Yield to Maturity (YTM)

To understand the concept of yield or yield to maturity we must first recognise that the return an investor received form a bond is not just the regular coupon payments (which we will assume are always fixed), but also the capital gain or capital loss that the investor would benefit from or lose from. This capital gain or loss is directly related to the price at which the bond is purchased. So if for example I buy a regular bond that has a €100 maturity value, but I buy it at a price of €95, then at maturity I will eventually make a capital gain of €100-€95 = €5 per 100 bonds I own. On the other hand, if I buy the same bond at a price of €105 per 100 then at maturity I will eventually make a capital loss of €100-€105 = -€5 per 100 bonds I own.

When one buys a bond below its par value it is said that one has bought the bond at a **discount**. On the other hand if the bond is bought above the par value then it has been bought at a **premium**. This is why the YTM is such an important concept. The YTM tells you the true return that you will make if you buy a certain bond that has a certain interest for a certain price. An example will clarify this better.

## YTM – an Example

Imagine company LOL Ltd had issued a 5% bond last year with a maturity in 2024 and the bond is currently trading at a price of €109 per 100 on the market. As an investor I would know that if I buy this bond today I will be losing €109-€100=€9 per 100 bonds I buy. I also know that I will lose this value once the bond matures in 9 years time and pays the €100 back to me. In the mean time I am earning 5% on every bond that I bought. So if we ignore the present value complication we can estimate that roughly I will be losing around 1% per year (€9 capital loss that will be realised in 9 years time) but I will be gaining 5% per year from the coupon. Hence my true interest rate is roughly 5%-1%=4% per year. This 4% is the yield or YTM on this bond. In reality the calculation is a bit more complicated but you can easily get the figure by using a **YTM calculator**.

Therefore, when an investor wants to decide if it is worth investing into a bond that is trading on the market it is important for that investor to consider the YTM and not simply the coupon rate. The YTM gives you the full picture since it considers both the interest income and the capital gain or loss.

## YTM and Bond Price Movements

By understanding this very important concept it is now easy to understand why bond prices go up when interest rates go down and vice versa. Lets go back to our example of the 5% LOL Ltd 2024 bond. When LOL Ltd issued the bond last year the price it issued it at was €100 per 100 bonds. At that time, 5% was the market rate of interest on a bond issued by any company with the same risk as LOL Ltd, that also had the same maturity in years as this particular bond. Now lets us consider that the central bank decided to increase interest rates and so the market interest rate on a bond issued by LOL Ltd that also matures in 2024 is now 6%. What would a rational investor do in such a situation?

So you have the following options:

- Bond A – 5% LOL Ltd 2024
- Bond B – 6% LOL Ltd 2024

Any investor who held the original bond would want to sell it immediately so that they could buy the second bond. Why? Simple really, for the same risk and the same amount of years the rational investor would prefer to earn 6% rather than 5%. This brings us to the most basic concept in finance – any price of any investment is ultimately determined by **demand** for and **supply** of that investment.

Therefore, as investors start to sell the 5% bond the supply of this bond on the market will increase which will consequently bring about a fall in the price of that bond. Conversely, as many investors are now trying to buy the 6% bond the demand for this bond is increasing and ultimately its price will go up.

How much will the price of the 5% bond go down and how much will the price of the 6% bond go up? The answer to this should be simple now, the prices will change until the yield on both bonds is the same, why? Since both bonds are issued by the same company and are for the same amount of years (i.e. they have the same risk), they should technically pay the same return. In our example, we can assume that the price of the 6% bond will rise until the yield on it is 5.5%, while the price of the 5% bond will fall until the yield is also 5.5% on this bond.

A simple video to help you understand YTM better:

A final word of caution is that YTM is valid only, as the name states, **assuming that the bond will be held until maturity**. If an investor sells a bond before its maturity date that bond could be trading at a higher or a lower price to what it would had been bought at. Therefore, the YTM should only be considered when the intention is to keep the bond until maturity and of course, assuming there is no default.

A great use of the YTM is to be able to compare the expected return an investor could earn from different bonds that have different coupon rates and different prices. Since the YTM gives you an annual ‘total’ return figure, you can easily compare the YTMs of different bonds to see which one would give you the highest return. Of course return is just half the story, one also has to consider the risk involved – but that is a total other discussion in itself which will be covered in a separate post.

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KD

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