Fixed Income Securities
Open University of Mauritius
Bond features
• Type of issuer (government & corporate)
• Term to maturity
• Principal
 Principal = face value, redemption value,
maturity value, par value
• Coupon rate
Coupon rate = regular payment
• Yield rate
Open University of Mauritius
Risks of investing in bonds
•
•
•
•
•
•
•
Interest rate risk
Reinvestment risk
Credit risk
Inflation risk
Exchange rate risk
Liquidity risk
Volatility risk
Open University of Mauritius
Example
• Example of a simple interest based
security: Bank-Bill
FV
P
i
n
1

100 365
– n = days to bill maturity
– i = quoted yield (nominal % pa) for simple interest
calculation
– Apply 365 day year convention
Open University of Mauritius
Example
• What is the price of a $100,000 90 day
bank-bill with yield of 5.5%. Use simple
interest for this security.
100000
P
 $98,661.98
5.5
90
1

100 365
Open University of Mauritius
Longer term securities
pricing of bonds
• Generally pay regular coupon payments (c)
with payment of the face value (FV) at maturity
(T compounding periods hence)
• Generally two 6-month compounding periods
per year with coupons (c) paid at the end of
each compounding period.
• Coupon rate is a nominal rate pa. (5% pa.
bond pays a 6 month periodic rate of 2.5%
– or c = 2.5% x face value
Open University of Mauritius
Longer term securities
pricing of bonds
• If zero coupon bond then no coupons are
paid and face value is received at maturity
• The yield used to discount cash flows (yield
or i) is quoted nominal rate pa. (i=6% pa
gives a rate of 3% per compounding period)
Open University of Mauritius
Longer term securities and
bond pricing
• Securities are broadly classed as “long
term” securities if term to maturity is longer
than 12 months.
• How do we price a bond at the beginning of
the first coupon period?
Open University of Mauritius
Fixed interest bond
• Price equals the present value of the:
– face value of the bond paid at maturity (FV)
– annuity of coupon payments (c)
– Given yield (i) and time to maturity (T)

c 1  1  i 
P
i
T

FV
T
1  i 
Open University of Mauritius
Fixed interest bond
• Example
• 7%pa 3 year $100 bond with market yield
of 8%pa

3.51  1  4
100

P
4
100
 $97.379 per $100

6


100
6
1 4
100


Open University of Mauritius
Zero coupon bond
• Pricing a zero coupon bond at the
beginning of a coupon period
• Generally one payment at maturity and 6
monthly compounding
FV
P
T
1  i 
Open University of Mauritius
Zero coupon bond
• 3 year zero coupon bond with yield 8% pa
and 6 month compounding periods
100
P
 $79.031 per $100
6
1 4
100


Open University of Mauritius
Price-coupon-yield
• Par value $100, yield 4.5%pa, valued at
beginning of coupon period, three bond types 5%pa coupon, 4.5%pa coupon, 3%pa coupon
– Where c > i then P > FV
– Where c = i then P = FV
– Where c < i then P < FV
Open University of Mauritius