This document discusses managing bond portfolios. It defines what bonds are and describes their key features like par value, coupon rate, maturity date, and yield to maturity. It also covers bond pricing concepts such as yield to maturity, duration, convexity, and how bond prices relate to interest rates. Finally, it provides examples of bonds issued in Nepal.

1. Managing Bond Portfolio
Presented By:
Group 2
Abhisek Pokhrel, 13124
Srijana Shrestha, 13130
Annapurna Sthapit, 13134
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2. What is bond?
• A long- term debt instrument under which
the issuer owes the holders a debt and
depending on the terms of the bond, is
obliged to pay them interest and/or to
repay the principal at a later date, termed
the maturity date
• Bond are sometimes called fixed income
securities
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3. Features of bonds
• Par value – face amount of the bond, which
is paid at maturity (normally $1,000)
• Coupon interest rate – stated interest rate
(generally fixed) paid by the issuer
• Maturity date – years until the bond must be
repaid
• Issue date – when the bond was issued
• Yield to maturity - rate of return earned on
a bond held until maturity (also called the
“promised yield”)
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4. Yield to maturity
• The rate of return that an investor would earn if
he bought the bond at its current market price
and held it until maturity
• Alternatively, it represents the discount rate
which equates the discounted value of a bond's
future cash flows to its current market price
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5. Yield to call
• The rate of return that an investor would earn if
he bought a callable bond at its current market
price and held it until the call date given that the
bond was called on the call date
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6. Types of bonds
Treasury bonds and notes
• A marketable government security with a
fixed interest rate. Treasury notes
maturities range up to 10 years, while
treasury bonds maturities range from 10 to
30 years.
Corporate bonds
• Like the government corporations borrow
money by issuing bonds.
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7. Contd……
Call Provisions on corporate bonds
• Call provisions allows the issuer to
repurchase the bond at a specified call price
before the maturity date
• For example: a company issues a bond with
a high coupon rate when market interest are
high , and when interest rate fall, the firm
might like to retire the high coupon debt and
issue new bonds at a lower coupon rate to
reduce interest payments. This is called
refunding.
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8. Contd……
• Callable bonds typically come with a period of call protection.
Such bonds are referred to as deferred callable bonds.
Convertible bonds
• Gives bondholders an option to exchange each bond for a
specified number of shares of common stock of the firm
Puttable bonds
• Gives option to the bondholders to extend or retire the bond.
• If the bonds coupon rate exceeds current market yields the
bondholder will choose to extend
• If the bonds coupon rate is too low it not extend instead reclaim
principals and invest in current yields
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9. Contd……
Floating rate bonds
• Floating rate bonds make interest
payments that are tiied to some measures
of current market rates
• For example the rate might be adjusted to
the current T- bills rate plus 2%
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10. Bond Pricing
Bond value= Present value of coupons+ Present value
of par value
Bond value=
P= C x PIVFA(r , n) + M x PVIF (r , n)
Where,
P= value of bond
n = number of years to maturity
C = annual coupon payment
r = periodic required return (yield return)
M= maturity value
t = time period when the payment is received
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11. Contd……
Alternative formula,
Bond value=
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12. Relationship Between Bond
Prices and Yields
Relationship Between Bond Prices and
Yields
• Bond prices are inversely related to interest rates
(or yields)
• A bond sells at par only if its coupon rate equals
the required yield
• A bond sells at a premium if its coupon rate is
above the required yield
• A bond sells at a discount if its coupon rate is
below the required yield
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13. Determinants of Bond safety
• Coverage ratio
Ratios of company earning to fixed costs,
Example: times interest earned ratio
Low or failing coverage ratio signals possible
cash flow difficulties
• Leverage ratio
Example: Debt-to equity ratio
Too high leverage ratio indicates excessive
indebtedness, signals possible cash flow
difficulties
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14. Contd…..
• Liquidity ratio
Current ratio, quick ratio
Indicates firms ability to pay bills coming due
with most liquid assets
• Profitability ratio
Indicators of a firm’s financial health
Examples: return on assets, return of equity
• Cash flow to debt ratio
Ratio of total cash flow to outstanding debt
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15. Bond portfolio risk
• Major risk: interest rate risk
• Reinvestment Risk
• Default Risk
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16. Interest rate risk
• a risk that arises for the bond owner from the
fluctuation of interest rate
• The sensitivity of risk depends on:
The time to maturity
Coupon rate
• Others things remaining same, the longer the
maturity of a bond, the higher will be its
sensitivity to the interest rate changes
• Similarly, the price of a bond with low coupon
rate will be more sensitive to the interest rate
changes
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17. Bond prices at different interest rates (8% coupon bond, coupons paid
semiannually)
Bond price at given market interest rate
Time to maturity 4% 6% 8% 10% 12%
1 year 1,038.83 1,029.13 1,000.00 981.41 963.33
10 years 1,327.03 1,148.77 1,000.00 875.35 770.60
20 years 1,547.11 1,231.15 1,000.00 828.41 699.07
30 years 1,695.22 1,276.76 1,000.00 810.71 676.77
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18. Reinvestment risk
• Risk that is concern that if r (interest rate)
will fall, and future cash flows will have to
be reinvested at lower rates, hence
reducing income
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19. Default risk
• The possibility that a bond issuer will be
unable to make interest or principal
payments when they are due
• If these payments are not made according
to the agreements in the bond
documentation, the issuer can default
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20. Interest Rate Risk
• As interest rates rise and fall, bondholders
experience capital losses and gains which
makes the fixed investment risky
• Interest rate risk arises, as bond prices
respond to interest rate fluctuations
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21. Bond Pricing Relationships
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22. Bond Pricing Relationships
1. Bond prices and yields are inversely
related
2. An increase in a bond’s yield to maturity
results in a smaller price change than a
decrease of equal magnitude
3. Long-term bonds tend to be more price
sensitive than short-term bonds
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23. Bond Pricing Relationships
4. As maturity increases, price sensitivity increases
at a decreasing rate
5. Interest rate risk is inversely related to the bond’s
coupon rate
6. Price sensitivity is inversely related to the yield to
maturity
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24. Prices of 8% Coupon Bond
(Coupons Paid Semiannually)
Yield To
Maturity
T=1 years T= 10 years T=20 years
8% 1000 1000 1000
9% 990.64 934.96 907.99
Fall in price
(%)
0.94% 6.50% 9.20%
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25. Prices of Zero-Coupon Bond
(Semiannual Compounding)
Yield To
Maturity
T=1 years T= 10 years T=20 years
8% 924.56 456.39 208.29
9% 915.73 414.64 171.93
Fall in price
(%)
0.96% 9.15% 17.46%
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26. Need for a summary measure
Bond Maturity Coupon Rate
A 30 14%
B 20 7%
Which bond is more risky?
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27. Duration
• It is the weighted average of time in which
cash flow is expected to be received
• Important measure for investors : as
bonds with higher durations are more risky
and have higher price volatility than bonds
with lower durations
• For all bonds, duration is shorter than
maturity except zero coupon bonds, whose
duration is equal to maturity
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28. Duration – Coupon rate and Yield
Coupon
Rate
Low Low
High Duration
Low Duration
Yield
High High
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29. Duration: Calculation
 
T
 
D wt t
where wt
, 1

1
T
t
t

1
w  t CF (1 
y) t
 Price
t CFt=cash flow at time t
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30. Calculation of duration of 8%
Coupon bond with YTM 10%
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31. Calculation of duration of zero
coupon bond with YTM 10%
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32. Modified duration
• It is the measure of bond’s exposure to
changes in interest rates
• To calculate the percentage change in
price
• % change in price= Modified Duration * %
change in YTM
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33. Formula
• Modified duration (Md) =
Duration/ (1+r)
• % change in price =
ΔP/P= -Md* Δr
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34. Modified Duration (calculation)
• Previous example of 8% coupon bond with
YTM=10%
• Duration= 1.8852 years
• Duration of bonds is 1.8852 x 2 = 3.7704
semiannual periods
• Modified D = 3.7704/1+0.05 = 3.591 periods
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35. Example 16.1 Duration
• Suppose the semiannual interest rate
increases by 1%. Bond prices fall by:
P    d
M r
P
=-3.591 x 0.01% = -0.03591%
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36. Rules for Duration
Rule 1 The duration of a zero-coupon bond equals
its time to maturity
Rule 2 Holding maturity constant, a bond’s duration
is higher when the coupon rate is lower
Rule 3 Holding the coupon rate constant, a bond’s
duration generally increases with its time to
maturity
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37. Rules for Duration
Rule 4 Holding other factors constant,
the duration of a bond is higher when
the bond’s yield to maturity is lower
Rules 5 The duration of a level perpetuity
is equal to: (1+y) / y
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38. Table 16.3 Bond Durations (Yield to
Maturity = 8% YTM; Semiannual Coupons)
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39. Figure 16.2 Bond Duration versus
Bond Maturity
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40. Implications of duration
• It allows bonds of different maturities and
coupon rates to be directly compared
• Construction of bond portfolio based on
weighted average duration
• Reduce interest rate risk by changing the
overall value of duration i.e. by adding
shorter maturities or higher coupon bonds
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41. Limitation of duration
• Duration assumes that relationship
between change in interest rate and price
is linear
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42. Convexity
In reality, the relationship between the changes in price and yield
is convex
Price
Yield
As indicated, the larger the change in interest rates, the larger the error in estimating the
price change of the bond.
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43. Convexity contd..
• Convexity is degree to which the duration
changes when the yield to maturity changes
• Higher the coupon, the lower the convexity
• Bond A and Bond B:
– Assume Same Duration and yield
– greater convexity bond less affected by interest
rate change.
1
M r Convexity y
P
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 2
( )
2
P
  d    


44. Convexity: Graphical Illustration
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45. Conclusion
• Duration and convexity allow investors to
quantify the uncertainty of change in
interest rate and are useful tools in the
management of fixed-income portfolios
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46. Bonds in Nepalese Context
• Nepse has not seen transaction of any single bond unit since it
began listing bonds
• From fiscal year 2008-09 till 2011-12, NRB has issued Citizens
Saving Bonds and Foreign Employment Bonds worth Rs 19.6
billion -only Rs 2.75 million were subscribed (Source: Nepalsharemarket.com)
• Mostly issued at par irrespective of the difference between
market interest rate and bond coupon
• Coupon rate fixed as per the trend or whatever institutions like
• Corporates and the government bonds primarily absorbed by
banks and financial institutions to maintain their Statutory
Liquidity Ratio
• Vast unawareness in the market
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47. Examples:
• Siddhartha Bank Limited Debenture
– Coupon 8.5% issued in 2067
– 7 years maturity
• Nepal SBI Bank Ltd. Debenture
– Coupon 7.9% issued in 2070
– 10 years of maturity
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