This document provides an overview of bond valuation and the structure of interest rates. It defines key bond concepts like yield to maturity, effective annual yield, and bond price calculation. It also discusses how bond prices are affected by interest rate changes and risk characteristics like default risk, call provisions, and term to maturity. The shape of the yield curve is determined by the real interest rate, expected inflation, and interest rate risk premium.
by G-10
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
Rasik Rownak Hossain
Shakib Fardous
Md. Rakibul Islam
Effat Ara Saima
Rafia Sultana
Tanvir Ahmed
Md.Shahidul Islam
SK Shourov Ahemmed
Tamjedul Alam Evan
Romana Haque Saima
Sarkar Muhammad Shohag
Khademul Islam
Jannatul Ferdous
Sheikh Hamim Hasan
Toufique Ul Haque Tuhin
Kerobin Hasda
by G-10
For downloading this contact- bikashkumar.bk100@gmail.com
Prepared by Students of University of Rajshahi
Rasik Rownak Hossain
Shakib Fardous
Md. Rakibul Islam
Effat Ara Saima
Rafia Sultana
Tanvir Ahmed
Md.Shahidul Islam
SK Shourov Ahemmed
Tamjedul Alam Evan
Romana Haque Saima
Sarkar Muhammad Shohag
Khademul Islam
Jannatul Ferdous
Sheikh Hamim Hasan
Toufique Ul Haque Tuhin
Kerobin Hasda
BONDS, FEATURES OF BONDS, BOND VALUATION, MEASURING YIELD, ASSESSING RISK, TYPES OF LONG- TERM DEBT INSTRUMENTS, SERIAL BONDS, TYPES OF RISK, SEMI- ANNUAL BONDS, YIELD TO CALL, YIELD TO MATURITY, DEFAULT RISK & FACTORS AFFECTING DEFAULT RISK & BOND RATINGS, etc.
In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.
BONDS, FEATURES OF BONDS, BOND VALUATION, MEASURING YIELD, ASSESSING RISK, TYPES OF LONG- TERM DEBT INSTRUMENTS, SERIAL BONDS, TYPES OF RISK, SEMI- ANNUAL BONDS, YIELD TO CALL, YIELD TO MATURITY, DEFAULT RISK & FACTORS AFFECTING DEFAULT RISK & BOND RATINGS, etc.
In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit from price movement – stocks that are judged undervalued (with respect to their theoretical value) are bought, while stocks that are judged overvalued are sold, in the expectation that undervalued stocks will, on the whole, rise in value, while overvalued stocks will, on the whole, fall.
Fixed coupon payments and final payment at maturity, except when the borrower defaults.
Possibility of gain (loss) from fall (rise) in interest rates
Depending on the debt issue, illiquidity can be a problem. (Illiquidity means it is possible that you cannot sell these securities quickly.)
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
Most simply, bonds represent debt obligations – and therefore are a form of borrowing. If a company issues a bond, the money they receive in return is a loan, and must be repaid over time. Just like the mortgage on a home or a credit card payment, the repayment of the loan also entails periodic interest to be paid to the lenders. The buyers of bonds, then, are essentially lenders. For example, if you have ever bought a government savings bond, you became a lender to the federal government. Put differently, bonds are IOUs.
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what is the future of Pi Network currency.DOT TECH
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
Resume
• Real GDP growth slowed down due to problems with access to electricity caused by the destruction of manoeuvrable electricity generation by Russian drones and missiles.
• Exports and imports continued growing due to better logistics through the Ukrainian sea corridor and road. Polish farmers and drivers stopped blocking borders at the end of April.
• In April, both the Tax and Customs Services over-executed the revenue plan. Moreover, the NBU transferred twice the planned profit to the budget.
• The European side approved the Ukraine Plan, which the government adopted to determine indicators for the Ukraine Facility. That approval will allow Ukraine to receive a EUR 1.9 bn loan from the EU in May. At the same time, the EU provided Ukraine with a EUR 1.5 bn loan in April, as the government fulfilled five indicators under the Ukraine Plan.
• The USA has finally approved an aid package for Ukraine, which includes USD 7.8 bn of budget support; however, the conditions and timing of the assistance are still unknown.
• As in March, annual consumer inflation amounted to 3.2% yoy in April.
• At the April monetary policy meeting, the NBU again reduced the key policy rate from 14.5% to 13.5% per annum.
• Over the past four weeks, the hryvnia exchange rate has stabilized in the UAH 39-40 per USD range.
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
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USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
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Eligibility Criteria:
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USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
how to sell pi coins in all Africa Countries.DOT TECH
Yes. You can sell your pi network for other cryptocurrencies like Bitcoin, usdt , Ethereum and other currencies And this is done easily with the help from a pi merchant.
What is a pi merchant ?
Since pi is not launched yet in any exchange. The only way you can sell right now is through merchants.
A verified Pi merchant is someone who buys pi network coins from miners and resell them to investors looking forward to hold massive quantities of pi coins before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
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Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
2. Learning Objectives
1. Describe the market for corporate bonds and
three types of corporate bonds.
2. Explain how to calculate the value of a bond
and why bond prices vary negatively with
interest rate movements.
3. Distinguish between a bond’s coupon rate,
yield to maturity, and effective annual yield.
3. Learning Objectives
4. Explain why investors in bonds are subject to
interest rate risk and why it is important to
understand the bond theorems.
5. Discuss the concept of default risk and know
how to compute a default risk premium.
6. Describe the factors that determine the level
and shape of the yield curve.
4. Corporate Bonds
o Market for Corporate Bonds
• Life insurance companies and pension funds buy
most corporate bonds
• Transactions tend to be in very large dollar
amounts.
• Less than 1% of all corporate bonds are traded
on organized exchanges
• Most transactions take place through dealers in
the over-the-counter (OTC) market.
5. Corporate Bonds
o Market for Corporate Bonds
• At the end of 2007, the amount of corporate and
foreign debt outstanding was $10.1 trillion,
ranking the debt market second behind the
market for corporate equity ($20.8 trillion).
6. Corporate Bonds
o Market for Corporate Bonds
• Only a small fraction of the bonds outstanding are
traded each day.
• The market is thin compared to markets for money-
market securities and stocks.
• Corporate bonds are less marketable than securities
with large daily trading volumes.
• Prices in the market tend to be more volatile than
those of securities with greater trading volumes.
7. Corporate Bonds
o Bond Price Information
• Corporate bond pricing is not considered
transparent.
• It is difficult for investors to obtain important
information on prices and volume.
• Many transactions are negotiated directly
between buyer and seller with little centralized
reporting of transaction details.
8. Corporate Bonds
o Features of Corporate Bonds
• long-term claims against company assets
• face (par) value is $1,000
• coupon rate is the annual coupon payment (C)
divided by a bond’s face value (F)
• fixed amounts paid to lenders for the life of the
contract
9. Vanilla Bonds
o Types of Corporate Bonds
• Vanilla bond
• coupon payments fixed for the life of the bond
• repay principal and retire the bonds at maturity
• contracts have the features and provisions found
in most bond covenants.
• annual or semiannual coupon payments
10. Zero Coupon Bonds
o Types of Corporate Bonds
• Zero coupon bond
• no coupon payments
• pays face value at maturity.
• sell at deep discount
11. Convertible Bonds
o Types of Corporate Bonds
• Convertible bonds
• may be exchanged for shares of the firm’s stock
• sells for a higher price than a comparable non-
convertible bond
• bondholders benefit if the market value of the
company’s stock gets high enough
12. Bond Valuation
o bond price
• In an efficient market, the price of an asset
equals the present value of its future cash flows.
• To calculate a bond’s price, follow the same
process used to value any financial asset.
13. Bond Valuation
calculate bond price
• Determine the required rate-of-return
• Determine expected future cash flows – the
coupon payments and par value
• Compute the current market value, or price (PB)
by calculating the present value of the expected
cash flows
PB = PVCoupon Payments+ PVPar Value
14. Bond Valuation
o general equation for the price of a bond
)1.8(
)1(
...
)1()1( 2
2
1
1
n
nn
B
i
FC
i
C
i
C
P
+
+
++
+
+
+
=
16. Bond Valuation
o Bond Valuation Example
• Calculator solution
• Determine the price of the bond in Exhibit 8.1
with a financial calculator
Enter
Answer
N i PMTPV FV
3 10 80 1,000
-950.26
18. Bond Valuation
o Par, Premium, and Discount Bonds
• If a bond’s coupon rate is equal to the its yield, its
price equals its face value; it is a par bond
• If a bond’s coupon rate is less than its yield, its
price is less than its face value; it is a discount
bond
• If a bond’s coupon rate is greater than its yield, its
price is greater than its face value; it is a premium
bond
19. Bond Valuation
o Semiannual Compounding
• Most bonds issued in Europe pay annual
coupons, most issued in the U.S. pay
semiannual coupons
• Eq. 8.2 shows how to value bonds that pay semi-
annual coupons
)2.8(
)1(
...
)1()1()1( 321 mn
mn
B
mi
FmC
mi
mC
mi
mC
mi
mC
P
+
+
++
+
+
+
+
+
=
20. Bond Valuation
o Semiannual Compounding Example
• What is the price of a three-year, 5% coupon
bond with a market yield of 8% and semi-
annual coupon payments?
• Semi-annual market yield = 8%/2 = 4%
• Semi-annual coupon payment = $50/2 = $25
36.921$
07.810$55.20$37.21$22.22$11.23$04.24$
)04.1(
1000$25$
)04.1(
25$
)04.1(
25$
)04.1(
25$
)04.1(
25$
)04.1(
25$
654321
=
+++++=
+
+++++=B
P
21. Bond Valuation
o Calculator Solution
• Semiannual Compounding Example
Enter
Answer
N i PMTPV FV
6 4 25 1,000
-921.37
22. Bond Valuation
o Zero Coupon Bonds
• Zero coupon bonds do not make coupon
payments but pay their face value at maturity
• The price (or yield) of a zero coupon bond is a
special case of Equation 8.2, where all coupon
payments equal zero
23. Bond Valuation
o Zero Coupon Bonds
• Pricing equation for a zero coupon bond
• Zero coupon bonds pay cash only at maturity and
must sell for less than similar bonds which make
periodic interest payments
)3.8(
)1( mn
mn
B
mi
F
P
+
=
24. Bond Valuation
o Zero Coupon Bond Price Example
• What is the price of a zero coupon bond with a
$1,000 face value, 10-year maturity, and
semiannual compounding? The market rate on
similar bonds is 12%.
80.311$
)06.01(
1000$
)212.01(
1000$
2020
=
+
=
+
=B
P
25. Bond Yields
o Yield to Maturity (YTM)
• YTM
• the rate that makes the present value of the
bond’s cash flows equal the price of bond
• the rate a bondholder earns if the bond is held to
maturity and all coupon and principal payments
are made as promised
changes daily as interest rates change
26. Bond Yields
o Effective Annual Yield
• In bond trading, the EAR is called the effective annual
yield (EAY). The way to annualize a bond yield
• Simple annual yield is yield per period multiplied by the
number of compounding periods; for bonds with annual
compounding, simple annual yield = semiannual yield × 2
1-rate/m)Quoted(1EAY m
+=
27. Bond Yields
o Yield to Maturity and Effective Annual Yield
Example
• An investor buys a 30-year bond with a $1,000
face value for $800. The bond’s coupon rate is
8% and interest payments are made semi-
annually. What are the bond’s yield to maturity
and effective annual yield?
28. Bond Yields
o Yield to Maturity and Effective Annual Yield
Example
• Step 1:
Enter
Answer
N i PMTPV FV
60
5.07
40 1,000-800
29. Bond Yields
o Yield to Maturity and Effective Annual Yield
Example
• Step 2:
• Calculate YTM
Enter
Answer
x =
.0507 2
.1014
30. Bond Yields
o Yield to Maturity and Effective Annual Yield
Example
• Step 3:
• Calculate EAY
Enter
Answer
X2
- =1.0507
1
.1040
31. Bond Yields
o Realized Yield
• The return earned on a bond given the cash flows
actually received by investor
• The interest rate at which the present value of
actual cash flows generated by the investment
equals bond’s price
• The realized yield is important because it allows
investors to see what they actually earned on their
investments.
32. Interest Rate Risk
o Bond Theorems
• Bond theorems are statements about the math used in bond
pricing.
• Bond prices are inversely related to interest rate movements.
• As interest rates decline, prices of bonds rise; as interest rates
rise, prices of bonds decline.
• For a given change in interest rates, prices of longer-term bonds
change more than prices of shorter-term bonds.
• Interest rate risk increases as maturity increases, but at a
decreasing rate.
33. Relation Between Bond Price Volatility and
Maturity
Exhibit 8.2 Relation Between Bond Price Volatility and Maturity
34. Interest Rate Risk
o Bond Theorems
• For a given change in interest rates, prices of
lower-coupon bonds change more than prices of
higher-coupon bonds.
36. Interest Rate Risk
o Bond Theorem Applications
• If interest rates are expected to increase, avoid
long-term bonds – they will experience the
largest price declines.
• If interest rates are expected to decline, buy
zero-coupon bonds. Their prices will increase
more than those of coupon-paying bonds.
37. The Structure of Interest Rates
o Risk Characteristics of Bonds
• Four features of debt instruments are responsible for
most of the differences in corporate borrowing costs
and determine the level and structure of interest
rates:
• Marketability
• Call feature
• Default risk
• Term-to-maturity
38. The Structure of Interest Rates
o Marketability
• How quickly and easily a security can be sold at
at low transaction cost and at fair market value
• The selling price varies directly with the degree of
marketability.
• The transaction cost varies inversely with the
degree of marketability.
• The yield-to-maturity varies inversely with the
degree of marketability.
39. The Structure of Interest Rates
o Marketability
• The difference in yields between a highly marketable
security (ihigh mkt) and a less marketable security
(ilow mkt) is the marketability risk premium (MRP)
• U.S. Treasury bills are considered the most
marketable of all securities
0- iiMRP low mkthigh mkt
>=
40. The Structure of Interest Rates
o Call Provision
• Bond issuer’s option to purchase a bond from
the bondholder at a predetermined price before
maturity.
• When bonds are called, bondholders suffer
financial loss because they must surrender
higher-yield bonds and replace them with lower-
yield bonds.
41. The Structure of Interest Rates
o Call Provision
• The difference in interest rates between a callable bond and a
non-callable bond is the call premium (CIP)
• Callable bonds sell for lower prices and higher yields than non-
callable bonds
• Bonds paying high yields are more likely to be called when
interest rates decline; these bonds have a high CIP
0- iiCIP callnocall
>=
42. The Structure of Interest Rates
o Default Risk
• Risk that a borrower may not make payments as
promised
• Lenders are paid a default risk premium for
purchasing securities with default risk
• The default risk premium (DRP) is the difference
between the yield on a security with default risk, idr,
and the risk-free rate, irf
• Yield on T-bills is a proxy for the risk-free rate.
43. The Structure of Interest Rates
o Bond Ratings
• Individuals and small businesses rely on outside
agencies for information on the default potential
of bonds.
• The two most prominent credit rating agencies
are Moody’s Investors Service (Moody’s) and
Standard & Poor’s (S&P).
Both services rank bonds in order of probability of default and
publish ratings as letter grades.
44. The Structure of Interest Rates
o Bond Ratings
• The highest grade bonds have the lowest default
risk and are rated Aaa or AAA.
• Investment grade bonds are rated Aaa to Baa.
• State and federal laws typically require
commercial banks, insurance companies, pension
funds, certain other financial institutions, and
government agencies to purchase only
investment-grade securities.
46. Default Risk Premiums for Selected Bond
Ratings
Exhibit 8.5 Default Risk Premiums for Selected Bond Ratings
47. The Structure of Interest Rates
o Term Structure of Interest Rates
• The term structure of interest rates
• the relationship between yield to maturity and
term-to-maturity on a bond
• the graph of the term structure of interest rates
is a yield curve
The shape and position of the yield curve are not constant.
As the overall level of interest rates changes, the yield curve
shifts up and down and changes its shape and slope.
48. The Structure of Interest Rates
o basic shapes (slopes) of yield curves
1. Ascending or normal yield curves slope upward
from left to right and imply higher interest rates
are likely
2. Descending or inverted yield curves slope
downward from left to right and imply lower
interest rates are likely
3. Flat yield curves imply interest rates unlikely to
change
49. The Structure of Interest Rates
o Shape of the Yield Curve
• Three factors that influence the shape of the
yield curve
• 1) Real rate of interest
• 2) Expected rate of inflation
• 3) Interest rate risk
50. The Structure of Interest Rates
o The Real Rate of Interest
• The real rate of interest changes with the
business cycle.
• Highest rates occur at the end of an economic
expansion.
• Lowest rates occur at the end of an economic
contraction.
• Changes in the expected future real rate of
interest can affect the slope of the yield curve.
51. The Structure of Interest Rates
o The Expected Rate of Inflation
• If higher inflation is forecast, the yield curve
will slope upward because longer-term yields
will contain a larger inflation premium than
shorter-term yields
• If investors believe inflation will subside, the
yield curve will slope downward
52. The Structure of Interest Rates
o Interest Rate Risk
• The longer the maturity of a security, the
greater its interest rate risk – the risk of selling
the security at a lower price - and the higher its
yield-to-maturity
• The interest rate risk premium adds upward
bias to the slope of the yield curve
53. Yield Curves for Treasury Securities at Three
Different Points in Time
Exhibit 8.6
54. The Structure of Interest Rates
o Cumulative Effect of Factors
• In an economic expansion, the real rate of
interest and the inflation premium increase
monotonically . Interest rate risk increases.
• In an economic contraction, the real rate of
interest and inflation premium decrease
monotonically. Interest rate risk decreases.