Investment portfolio

1. CHAPTER THREE
FIXED INCOME SECURITIES
1

2. BOND BASICS
• Bond is a debt instrument issued for a period of more than one
year with the purpose of raising capital by borrowing.
• So bonds are long-term debt or funded debt, issued by
corporations, and governments and their agencies to finance
operations or special projects.
• Corporations pay back interest and principal from earnings,
whereas governments pay from taxes, or revenues from
special projects.
2

3. Most individual bonds have five features when they are issued:
issue size, issue date, maturity date, maturity value, and
coupon.
1. Issue size – is the number of bonds issued multiplied by the
face value. For example, if an entity issues two million bonds
with a 1,000 Birr price, the issue size is 2 billion Birr.
2. Issue date – The issue date is simply the date on which a
bond is issued and begins to accrue interest. For example, if
bond is issued on January 1st then the bond issuer will have to
pay coupon/interest from that day to the bond holders.
3

4. 3. Maturity date – the date on which an investor can expect to
have his or her principal repaid.
4. Maturity value – the amount of money the issuer will pay the
holder of a bond at the maturity date.
5. Coupon – The coupon rate is the periodic interest payment
that the issuer makes during the life of the bond.
–For instance, if a bond with a 100,000 Birr maturity value
offers a coupon of 14%, the investor can expect to receive
14,000 Birr each year until the bond matures.
4

5. How are bonds different from stocks?
• Bonds are considered debt investments.
• On the other hand, a stock purchase is considered an equity
investment because the investor (also known as the
stockholder) becomes a part owner of the corporation.
• While bonds generally don’t provide an opportunity to share in
the profits of the corporation, the stockholder is entitled to
receive a portion of the profits and may also be given voting
rights.
5

6. • Bondholders earn interest while stockholders typically receive
dividends.
• Because bondholders are creditors rather than part owners, if a
corporation goes bankrupt, bondholders have a higher claim on
assets than stockholders.
– This provides added security to the bond investor – but does not
completely eliminate risk.
6

7. Benefits of Investing in Bonds
1. Income predictability
2. Safety
3. Diversification and
4. Choice
7

8. Risks of Bond Investing
1. The risk of default (also known as credit risk)
– An issuer of debt is said to be in default when the issuer is unable to
repay the principle or interest as scheduled.
– Most of the time government bonds have virtually no risk of default.
– Corporate bonds are more exposed to default risk because
companies cannot raise taxes when there is a cash shortfall or take
advantage of other options available to governments.
8

9. Price risk
– If you sell your bonds prior to their maturity, their price or market
value may be lower than the price at which you bought them.
Demand and supply
– The availability of bonds and the demand for them also affects the
price of bonds.
– As demand increases, prices raise, all other factors remaining the
same.
– Also, as the supply of bonds decline, prices generally also rise.
– Similarly, when demand falls or supply increases, prices fall and yield
to maturity declines.
9

10. Pricing of Bonds
• The price or value of a bond is determined by discounting the
bond's expected cash flows to the present using the
appropriate discount rate.
• The price of the bond should equal the present value of its
expected cash flows.
• The coupons and principal repayment of 1,000 Birr are known
and the present value, or price, can be determined by
discounting these future payments from the issuer at an
appropriate required yield, r, for the issue.
10

11. This relationship is expressed for coupon bond by the following
formula:
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 𝐶 ×
1 − (1 + 𝑖)−𝑛
𝑖
+
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
(1 + 𝑖)𝑛
Where,
C = the annual coupon payment,
i = the required return on the bond, and
n = Number of compounding in a year.
11

12. Example-1- If a 1,000 Birr face value bond paying 15% coupon is maturing in
10 years and the interest rate is 12%. How much should you pay for this bond?
Given:
– The annual coupon payment (C)= 1,000 x 0.15 = 150
– The required return on the bond (i)= 0.12
– Number of compounding in a year (n)= 10
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 𝐶 ×
1 − (1 + 𝑖)−𝑛
𝑖
+
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
(1 + 𝑖)𝑛
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 150 ×
1 − (1 + 0.12)−10
0.12
+
1,000
(1 + 0.12)10
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 847.5334 + 321.973 = 1,169.50
So, an investor should pay maximum 1,169.50 Birr for this bond. 12
Face Value Coupon rate Maturing time Interest rate
1,000 15% 10 years 12%

13. Example 3.2: If a 12% semi-annual bond maturing in 10 years is
selling in the market for 750 Birr when the market interest rate is
16%. Should you buy this bond at 750 Birr?
Given:
– The annual coupon payment (C)= 1,000 x 0.06 = 60
– The required return on the bond (i)= 0.08
– Number of compounding in a year (n)= 20
13
Face Value Coupon rate Maturing Interest rate
1,000 Annual 12% or 6%
semi-annual
10 years or 20 semi-
annual
Annual 16% or semi-
annual 8%

14. Solution:
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 𝐶 ×
1 − (1 + 𝑖)−𝑛
𝑖
+
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
(1 + 𝑖)𝑛
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 60 ×
1 − (1 + 0.08)−20
0.08
+
1,000
(1 + 0.08)20
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 589.088 + 214.548
PV of Bond = 803.63
Yes, we should buy the bond because its intrinsic value 803.63 Birr is
higher than the market price of 750 Birr.
14

15. Exercise:
Assume that you wish to purchase a bond with a 30-year maturity, an
annual coupon rate of 10 percent, a face value of Birr 1,000, and
semiannual interest payments. If you require a 9 percent nominal yield to
maturity on this investment, what is the maximum price you should be
willing to pay for the bond?
Given:
– The annual coupon payment (C)= 1,000 x 0.05 = 50
– The required return on the bond (i)= 0.045
– Number of compounding in a year (n)= 60
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 𝐶 ×
1 − (1 + 𝑖)−𝑛
𝑖
+
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
(1 + 𝑖)𝑛
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 𝐶 ×
1 − (1 + 0.045)−60
0.045
+
1,000
(1 + 0.045)60
= Birr 1,103.19 15

16. Exercise 2: You intend to purchase a 10-year, Br 1,000 face
value bond that pays interest of Birr 60 every 6 months. If your
nominal annual required rate of return is 10 percent with
semiannual compounding, how much should you be willing to
pay for this bond?
Given:
– The annual coupon payment (C)= 1,000 x 0.06 = 60
– The required return on the bond (i)= 0.05
– Number of compounding in a year (n)= 20
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 𝐶 ×
1 − (1 + 𝑖)−𝑛
𝑖
+
𝐹𝑎𝑐𝑒 𝑉𝑎𝑙𝑢𝑒
(1 + 𝑖)𝑛
𝑃𝑉 𝑜𝑓 𝑎 𝐵𝑜𝑛𝑑 = 60 ×
1 − (1 + 0.05)−20
0.05
+
1,000
(1 + 0.05)20
Birr 1,124.62 16

17. Discount and premium bonds
• A bond whose market price is less than its par value is selling
at a discount. It is called discount bond.
• If the market price is more than the par value, the bond is
selling at a premium. It is called premium bond.
17

18. • Yield on the bond
• The return of a bond is largely determined by its interest rate,
which, in turn, is determined by the prevailing interest rate and
the creditworthiness of the issuer, assessed by credit rating
companies.
• A higher credit rating allows the issuer to sell its bonds for a
higher price, i.e. at a lower interest rate.
• Nominal yield, or the coupon rate, is the stated interest rate
of the bond, which is a percentage of par values.
• The coupon is usually paid semiannually. Thus, a bond that
pays 14% interest pays 140 Birr per year in 2 semi-annual
payments of 70 Birr.
18

19. • Bonds trading in the secondary market will usually have prices
that are less or more than par value, thus yielding an interest
rate that differs from the nominal yield, called the current yield,
or current return.
• So the price of bonds moves in the opposite direction of
interest rates.
19

20. • Current Yield:
• Because current bond prices fluctuate, an investor can pay
more or less than the par value for a bond.
• Current yield measure looks at the current price of a bond
instead of its face value and
• It represents the return an investor would expect if he or she
purchased the bond and held it for a year.
• This measure is not an accurate reflection of the actual return
that an investor will receive in all cases because bond prices
are constantly changing due to market factors.
20

21. Current Yield Formula
Current Yield =
Annual Interest Payment
Current Market price of Bond
• Example: If a bond is paying 14% annual coupon having value
of 1,000 Birr which is now selling in the market for 880 Birr,
what is the current yield of this bond?
Current Yield =
140
880
= 15.91 %
• Recall that if the market price of a bond goes down, the current
yield will go up. Using the above example, if the current bond
price goes down to 700 Birr instead 880 Birr, the current yield
would be: 140/700 = 20%.
21

22. • Yield to Maturity:
• The yield-to-maturity, or true yield, of a bond that is held to
maturity will have to account for the gain or loss that occurs
when the par value is repaid.
• The yield to maturity generally will yield an interest rate
comparable to newly issued bonds with the same credit rating.
The following formula provides an approximation of YTM.
Approximate YTM =
Coupon payment +
(Face value − Market value)
No of Years in maturity
(Face Value + Market Value)
2
22

23. • Example: If a 1,000 Birr face value with 12% annual coupon
with maturity of 6 years is now trading for 900 Birr and
assuming that the investors buys it for 900 Birr and hold it until
maturity. YTM is calculated as follows:
Approximate YTM =
Coupon payment +
(Face value − Market value)
No of Years in maturity
(Face Value + Market Value)
2
Approximate YTM =
120 +
(1,000 − 900)
6
(1,000 + 900)
2
Approximate YTM =
120 + 16.67
950
= 𝟏𝟒. 𝟑𝟖𝟓 %
23

24. Example 2: The price of a bond is 920 Birr with a face value of
1,000 Birr which is the face value of many bonds. Assume that
the annual coupons are 100 Birr, which is a 10% coupon rate,
and that there are 10 years remaining until maturity.
What is the YTM of this bond?
Approximate YTM =
Coupon payment +
(Face value − Market value)
No of Years in maturity
(Face Value + Market Value)
2
Approximate YTM =
100 +
(1,000 − 920)
10
1,000 + 920
2
Approximate YTM =
100 + 8
960
= 𝟏𝟏. 𝟐𝟓 %
24

25. Example 3: If a 1,000 Birr face value bond paying 15% coupon
whereas it is maturing in 10 years and the interest rate is 12%. If
it is trading for 1,150 Birr, what is the current yield and YTM?
Current Yield =
Annual Interest Payment
Current Market price of Bond
Current Yield =
150
1,150
= 𝟏𝟑. 𝟎𝟒 %
Approximate YTM =
150 +
(1,000 − 1,150)
10
(1,000 + 1,150)
2
Approximate YTM =
150 + (−15)
1,075
=
135
1,075
= 𝟏𝟐. 𝟓𝟓 %
25

26. Example 4: If a 12% annual bond having 1,000 Birr face value
maturing in 10 years is selling in the market for 750 Birr when the
market interest rate is 16%. What is the current yield and YTM of
this bond?
Current Yield =
Annual Interest Payment
Current Market price of Bond
Current Yield =
120
750
= 𝟏𝟔 %
Approximate YTM =
Coupon payment +
(Face value − Market value)
No of Years in maturity
(Face Value + Market Value)
2
Approximate YTM =
120 +
(1,000 − 750)
10
(1,000 + 750)
2
= 𝟏𝟔. 𝟓𝟕 %
26

27. Example 5: A corporate bond has a face value of $1,000, and
pays a $50 coupon every six months (i.e., the bond has a 10
percent semiannual coupon). The bond matures in 12 years and
sells at a price of $1,080. What is the bond’s nominal yield to
maturity?
Approximate YTM =
Coupon payment +
(Face value − Market value)
No of Years in maturity
(Face Value + Market Value)
2
Approximate YTM =
100 +
(1,000 − 1,080)
12
(1,000 + 1,080)
2
= 𝟖. 𝟗𝟎 %
27

28. Bond rating:
Agencies ratings are an integral part of the bond market because
most corporate and municipal bonds are rated by one or more of
the rating agencies.
There are three major rating agencies:
(1) Fitch Investors Service,
(2) Moody’s, and
(3) Standard and Poor’s (S and P)
28

29. • Bond ratings provide the fundamental analysis for thousands of
issues.
• The rating agencies analyze the issuing organization and the
specific issue to determine the probability of default and inform
the market of their analyses through their ratings.
• The agencies assign letter ratings depicting what they view as
the risk of default of an obligation.
• The letter ratings range from AAA (Aaa) to D.
• Table below describes the various ratings assigned by the
major services.
29

30. FITC
H
MOO
DY’S
S & P DEFINITION
High
grade
AAA Aaa AAA The highest rating assigned to a debt instrument,
indicating an extremely strong capacity to pay principal
and interest. Bonds in this category are often referred to
as gilt edge securities.
AA Aa AA High-quality bonds by all standards with strong
capacity to pay principal and interest. These bonds are
rated lower primarily because the margins of protection
are less strong than those for Aaa and AAA bonds.
Medi
um
grade
A A A These bonds possess many favorable investment
attributes, but elements may suggest a susceptibility to
impairment given adverse economic changes.
BBB Baa BBB Bonds are regarded as having adequate capacity to pay
principal and interest, but certain protective elements
may be lacking in the event of adverse economic
conditions that could lead to a weakened capacity for
payment. 30

31. FITCH MOODY’
S
S AND P DEFINITION
Speculative
BB Ba BB Bonds regarded as having only moderate protection
of principal and interest payments during both good
and bad times
B B B Bonds that generally lack characteristics of other
desirable investments. Assurance of interest and
principal payments over any long period of time may
be small.
Default
CCC Caa CCC Poor-quality issues that may be in default or in
danger of default.
CC Ca CC Highly speculative issues that are often in default or
possess other marked shortcomings.
C The lowest-rated class of bonds. These issues can be
regarded as extremely poor in investment quality.
C C Rating given to income bonds on which no interest is
being paid
DDD, D Issues in default with principal or interest payments in
arrears. Such, bonds are extremely speculative and
should be valued only on the basis of their value in
liquidation or reorganization. 31

32. End of
Chapter 3
32