financial services

WEN.XU

lecture_4_notes.pptx

Home >Business & Finance homework help >financial services

Lecture 4

GILTS AND BONDS

Dr Jacinta Nwachukwu

Principal Lecturer in Finance

School of Economics, Finance and Accounting

[email protected]

The basics of bonds

https://www.youtube.com/watch?v=pxeg5JIfIsM

https://www.youtube.com/watch?v=LTGzJESstbo

https://www.youtube.com/watch?v=vYMPez0-Uso

Learning Outcomes

The key characteristics of bonds

The risk-return profile of bonds

Calculating bond yield to maturity

The risk factors which influence bond yield

The bond rating

The impact of credit rating on bond rate of return

Lecture Outline

1. Types of bonds and their pricing

2. Bond yields

3. Bond risks

4. Bond ratings

5. The impact of bond ratings on yields

1. Types of bonds and their pricing

Zero-coupon bonds

Coupon bonds

Consols or perpetuities

Discounts bonds

Premium bonds

Zero Coupon bonds

A zero coupon bond is issued with no coupon or interest to be paid during the life of the bond.

The buyer pays less than the par value and receives par value at maturity

The difference between the purchase and par value is the rate of return on the bond

Zero-coupon Bond

Consider a UK government bond, (also known as gilts) which promises to pay £100 at the following fixed future dates.

(i) 3 months

(ii) 6 months

(iii) 1 year

(iv) 5 years

(v) 10 years

Suppose the annual interest rate is 5 percent.

What is the price of these Treasury bonds?

Coupon bonds

Coupon Bonds

A coupon bond makes a series of fixed interest payments at regular intervals and repays the principal at the stated maturity date

The coupon payments are expressed as a percentage of face value (i.e., amount borrowed ) and are known as the coupon rate

The amount and date of each payment are known at the time the bond is issued

Failure to pay either interest or principal on a bond constitutes default and could lead to bankruptcy unless the company takes action to quickly remedy this including reaching a voluntary agreement with the creditors

The price of the bond at any time before the specified maturity date will depend on the level of market interest rates at the time

So, if the annual coupon rate is 5 percent, then the issuer pays the bondholder £5 per year per £100 borrowed

The repayment of the initial £100 loan is made at the maturity date

Pricing a coupon bond

Assuming that the current interest is 10 percent, compute the price of a 5-year, 8-percent coupon bond with a face value £1000

What happens when the interest rate goes up to 12 percent?

What happens when the interest rate goes down to 4 percent?

What happens when the bond pays coupons every six monthly, assuming a current interest rate of 10 percent

The price of the coupon bond is calculated using the equation:

Consols and Perpetuities

Consols or perpetuities

Consols offer only fixed periodic payments. This means that the issuer of the bond pays only interest or coupon, never repaying the principal since the bond never matures

Typically consols are largely issued by governments since they are the only borrowers that can credibly promise to make fixed regular payments forever.

The price of a consol is the present value of all the stated future interest payments.

The formula for the price of a consol that makes a coupon payment every year forever is summarised as follows:

Pricing consols

You just purchased a bond which promises to pay £10 per year forever.

How much should you pay for the bond if the current market interest rate is:

5 percent?

4 percent?

8 percent?

Discount bonds

Discount Bonds

A discount bond has a price below its par value or issuance price.

For example, a bond issued with a £100 face value that currently sells at £90 is trading at a discount of £10.

This arises because the fixed coupon rates are below the prevailing market interest rates on comparable new issues

The fall in quoted price for the bond ensures that the yield to maturity equals the yields to maturity on the newly issued bonds

The discount on a bond gradually declines to zero as the bond’s maturity date approaches the time the bond returns to its full face value at issuance.

Absent of any unusual economic and political conditions, the shorter the time until a bond’s maturity, the lower the potential discount.

Premium bonds

Premium bonds have prices above the par value at the date of its issuance.

This arises when the coupon rate is higher than the prevailing interest rate on a comparable new issue when market rate falls after the bond was sold.

For example, a bond issued with a £100 par value that currently trades at $110 is trading at a premium of £10

The premium of £10 on the bond gradually falls to zero as the bond’s maturity date approaches

Time path of the value of a coupon bond

2. Bond yields

Yield to maturity

Current yield

Capital gains yield

Holding period returns

Yield to Maturity

Yield to maturity (YTM) is the expected rate of return on holding a bond to its maturity if all the promised coupon and financial principal payments are made

For example, take a £1000 face value 5 percent per annum coupon bond with one year to maturity selling for £900.

The YTM is typically calculated as the interest rate which equates the expected cashflows to the current price of the bond as shown in the following equation:

When an investor purchases a bond and holds it until maturity, he/she receives the YTM that existed on the purchase date

But the bond’s calculated YTM will change frequently between purchase date and the maturity date whenever interest rates in the economy change.

Current Yield

Current yield (or interest yield) is the yearly coupon payment divided by the current price of the bond.

For example, assume that a £1000 face value 5 percent per annum coupon bond is currently selling for £985.

The bond’s current yield is:

Capital Gains Yield

Capital gains (or losses) yield is the price appreciation or (depreciation) component of a security's (such as a bond or common stock) total expected return.

For example, assume that an investor purchased a bond at a price of £1500 and then sold it one year latter for £1525.

The capital gains yield for that investment would be:

Holding Period Return

Holding period return (HPR) is the expected return on buying a bond and selling it before it matures.

For example, assume that Mr Smith pays £900 for a 10-year, 6 percent coupon bond with a face value of £1000.

He intends to hold the bond for one year and expects to get £1100

The return from holding this bond comprises the £60 coupon payment and the £200 difference between the predicted sale and purchase price. That is:

To generalise:

Bond risks

Maturity risk

Inflation risk

Liquidity risk

Default risk

Overall,

;

Maturity Risk

This arises from changes in interest rate. When market interest rates change, bond prices move.

An increase in market interest rates leads to a decline in the price of outstanding bonds (i.e., discount bonds)

A decrease in market interest rates leads to a rise in the price of outstanding bonds (i.e., premium bonds)

The longer the maturity term for the bond, the larger the price change for a given movement in interest rate.

So, an investor who buys a long-term bond and needs to sell it before it matures, should be worried about what will happen if interest rate changes.

Whenever, there is a mismatch between a holding period and a bond’s maturity, there is a maturity risk arising from interest-rate risk

Other things being equal, the more likely interest rates are to change during the bondholder’s investment horizon, the larger the risk of loss or of gain holding a bond.

The greater the maturity risk, the higher the bond’s yield to maturity

Value of Long and Short-Term 10% Annual Coupon Bonds at Different Market Interest Rates

1-year bond 5 10 15 20 25 30 35 40 1047.6190476190477 1000 956.52173913043475 916.66666666666674 880 846.15384615384608 814.81481481481478 785.71428571428578 10-year bond 5 10 15 20 25 30 35 40 1386.0867464592407 1000 749.06156870728864 580.75279144492288 464.42450944000001 381.69210019093714 321.23930148292652 275.92870977520579 20-year bond 5 10 15 20 25 30 35 40 1623.11051712 69992 1000 687.03342631351768 513.04202665229445 406.91752902764108 336.84118883131549 287.48112315779281 250.89639732080911

Market interest rates (%)

Bond value (£)

Inflation Risk

Inflation risk relates to the fact that investors don’t know what the inflation rate will be during the holding period

Such uncertainties in inflation rate affects the real interest rate on bonds with associated purchasing power.

Higher inflation risk is related to a decline in the purchasing power of the fixed coupon payments and invested principal amount.

The greater the chances for changes in the inflation rate, the larger the additional inflation premiums demanded by investors to compensate for the loss of purchasing power risk

Thus, we would expect that bonds issued by developed countries such as the United States and the UK, with stable inflation rates, have lower bond yields compared with the bonds issued by emerging country governments.

The greater the inflation risk, the higher the bond’s yield to maturity

Liquidity Risk

Liquidity risk is associated with the speed with which the bond can be bought and sold without significant price loss.

The more quickly a bond can be sold at close to face value as possible the lower the liquidity risk

U.S treasury bills are commonly assumed to have little or no liquidity risk

Bonds issued by small and medium sized enterprises have substantial liquidity risk

The greater the liquidity risk, the higher the bond’s yield to maturity

Default Risk

This is the risk that the issuer may not make all the promised coupon payments and face value.

So, the quoted interest rate on bonds includes a default risk premium to compensate bondholders for this additional risk.

The greater the default risk, the higher the bond’s yield to maturity.

In general, it is commonly assumed that:

The default risk on the US Treasury Bills is zero.

The default risk for corporations and emerging country governments can be substantial.

Issuers can influence default risk by managing the components of the factors which are considered by the rating agencies.

Bond ratings criteria comprise both qualitative and quantitative factors, such as labour unrest, accounting policies, environmental policy and safety of product.

Bond Rating

Bond ratings reflect the assessment of the relative probability default by the issuer by an independent agency.

A high rating suggests that the providers of the rating currently believe that the bond issuer will have little problem in meeting payment obligations compared with a benchmark lender in the same category

Thus, the rating is merely a reflection of the current opinions on the relative quality of the bond. It is in effect credit analysis of the bond issuer

The three major rating agencies are:

Moody’s, Standard and Poor’s (S&P) and Fitch

The designations assigned by Moody’s and Standard and Poor’s are shown in Table below

A Guide to Bond Rating

	Moody’s	S&P	Description
Investment grade	Aaa	AAA	Bonds with the smallest risk of default. The issuers are stable and dependable
	Aa	AA	Bonds have slightly higher degree of long-term risk compared with tripple A
	A	A	Bonds are somewhat more vulnerable to changing economic conditions compared with AAA and AA rated bonds
	Baa	BBB	Usually unreliable over the long-term
Speculative grade	Ba	BB	Have moderate security but are not well safeguarded
	B	B	Able to pay now, but at risk of default in the future
Highly speculative	Caa	CCC	Poor quality, clear danger of default
	Ca	CC	Highly speculative quality, often in default
	C	C	Poor prospects of repayment, though may still be paying
	D	D	In default

The impact of ratings on bond yield

The Impact of Ratings

The lower a bond’s rating, the lower its price and the higher its yield

For ease of comparison, U.S Treasuries serve as the benchmark bonds.

The yields on other bonds are measured in terms of the spread over these Treasuries, known as risk spread.

To capture the impact of bond rating on yield, the following equation is used:

The two predictions from this equation are:

(i) The lower the quality rating of the issuer relative to a U.S Treasury of comparable maturity term, the higher the default-risk premium, resulting in higher bond yield vis-à-vis the benchmark U.S bond

(ii) When the yield on the benchmark U.S Treasuries move, all other bond yields move with them

Overall,

End of lecture

Take home Assignment 1

Suppose that the one year risk-free interest rate is 5 percent. Flim.com, an Internet firm hoping to market its own brand of e-cash called “FLAM” has issued one year 8 percent coupon bonds with a face value of £1000.

Q1. What is the fair price of this bond?

Suppose that there is a 10 percent chance that Flim.com may go bankrupt before paying bondholders their promised cashflow at the maturity date. The Table below shows the payoff and probability that Flim will pay its bondholders.

Q2. Re-calculate the fair price of this bond

Possibilities	Payoff (coupon plus face value)	Probability	Payoff *probability
Full payment	£1,080	0.70
Partial payment	£580	0.20
Total default	£0	0.10
Expected value (i.e., sum of payoffs * probabilities)

Take home Assignment 2

You are sitting at the dinner table and your father is extolling the benefits of investing in bonds.

He insists that as a conservative investor he will only make investments that are safe, and what could be safer than bonds, especially UK Treasury bonds?

You are required to explain to him:

(i) The characteristics of bonds/gilts emphasising why some conservative investors might see them as a safe option?

(ii) Explain to him the risks associated with investment in bonds.

(iii) Explain to him how credit rating agencies might help reduce default risks associated with investment in bonds

Take home assignment 3

(i) Critically evaluate the characteristics of bonds

(ii) Why would an investor choose to invest in these financial products rather than depositing the money in a savings account?

(iii) Search the website and financial newspapers to locate the yields on government bonds for various countries. Find a country whose 10-year government bond yield was above that on the US 10-year Treasury bond and one whose 10-year yield is below the Treasury yield in the past year. What might account for these differences in yield

Types of investment

https://www.moneyadviceservice.org.uk/en/categories/investment-types

Britain’s debt bombshell

https://www.youtube.com/watch?v=WF3Lp88CsZA

https://www.youtube.com/watch?v=X5oYba7zzVc