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.
Fixed Income securities- Analysis and Valuation. Very useful for CFA and FRM level 1 preparation candidates. For a more detailed understanding, you can watch the webinar video on this topic. The link for the webinar video on this topic is https://www.youtube.com/watch?v=r9j6Bu3aUNI
This presentation provides readers with an introduction to bonds and their many characteristics. Topics discussed such as types of bonds, bond trading, valuing bonds and much more are highlighted in this presentation and can be further discussed on our site www.finpipe.com.
Fixed Income securities- Analysis and Valuation. Very useful for CFA and FRM level 1 preparation candidates. For a more detailed understanding, you can watch the webinar video on this topic. The link for the webinar video on this topic is https://www.youtube.com/watch?v=r9j6Bu3aUNI
This presentation provides readers with an introduction to bonds and their many characteristics. Topics discussed such as types of bonds, bond trading, valuing bonds and much more are highlighted in this presentation and can be further discussed on our site www.finpipe.com.
A bond is a (written and signed promise) debt investment in which an investor loans money to an entity (typically corporate or governmental) which borrows the funds for a defined period of time at a variable or fixed interest rate (Coupon Rate).
Bond Valuation, Bond Types, Bond Characteristics, Reasons for issuing Bonds, Bond Risks, Bond Measuring Yield, Bond Pricing Theorems, Factors that Influence Bond Prices, Primary Bond Market, Secondary Bond Market, Bonds in Nepal.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
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A bond is a (written and signed promise) debt investment in which an investor loans money to an entity (typically corporate or governmental) which borrows the funds for a defined period of time at a variable or fixed interest rate (Coupon Rate).
Bond Valuation, Bond Types, Bond Characteristics, Reasons for issuing Bonds, Bond Risks, Bond Measuring Yield, Bond Pricing Theorems, Factors that Influence Bond Prices, Primary Bond Market, Secondary Bond Market, Bonds in Nepal.
The presentation slide is on stock valuation. We have tried to present the various techniques to stock valuation under which different methods are discussed with illustrations. Key concepts:
Zero Growth Model
Balance sheet Technique
Constant Growth Model
Two-stage growth Model
Feel Free to comment.
Hey, Do you want to know something about Debt or Equity? Then just one click on Link is given in PPT and you will get import information on it which will help you. So, Do just One Click on Link.....
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Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
1. Managing Bond Portfolio
Presented By:
Group 2
Abhisek Pokhrel, 13124
Srijana Shrestha, 13130
Annapurna Sthapit, 13134
11/26/2014 1
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
11/26/2014 2
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”)
11/26/2014 3
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
11/26/2014 4
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
11/26/2014 5
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.
11/26/2014 6
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.
11/26/2014 7
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
11/26/2014 8
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%
11/26/2014 9
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
11/26/2014 10
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
11/26/2014 12
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
11/26/2014 13
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
11/26/2014 14
15. Bond portfolio risk
• Major risk: interest rate risk
• Reinvestment Risk
• Default Risk
11/26/2014 15
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
11/26/2014 16
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
11/26/2014 17
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
11/26/2014 18
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
11/26/2014 19
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
11/26/2014 20
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
11/26/2014 22
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
11/26/2014 23
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%
11/26/2014 24
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%
11/26/2014 25
26. Need for a summary measure
Bond Maturity Coupon Rate
A 30 14%
B 20 7%
Which bond is more risky?
11/26/2014 26
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
11/26/2014 27
28. Duration – Coupon rate and Yield
Coupon
Rate
Low Low
High Duration
Low Duration
Yield
High High
11/26/2014 28
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
11/26/2014 29
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
11/26/2014 32
33. Formula
• Modified duration (Md) =
Duration/ (1+r)
• % change in price =
ΔP/P= -Md* Δr
11/26/2014 33
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
11/26/2014 34
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%
11/26/2014 35
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
11/26/2014 36
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
11/26/2014 37
38. Table 16.3 Bond Durations (Yield to
Maturity = 8% YTM; Semiannual Coupons)
11/26/2014 38
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
11/26/2014 40
41. Limitation of duration
• Duration assumes that relationship
between change in interest rate and price
is linear
11/26/2014 41
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.
11/26/2014 42
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
11/26/2014 43
2
( )
2
P
d
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
11/26/2014 45
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
11/26/2014 46
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
11/26/2014 47