global bond markets
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Global Bond Markets. Chapter 19. A Brief Tour of the Global Bond Market. By the end of 1998 the aggregate value of all outstanding bonds in the world was $25.4 trillion About 50% were denominated in U.S. dollars 15% were denominated in yen 10% denominated in Deutschemark - PowerPoint PPT PresentationTRANSCRIPT
Francis & Ibbotson Chapter 19: Global Bond Markets 11
Slides by:
Pamela L. Hall, Western Washington University
Global Bond MarketsGlobal Bond Markets
Chapter 19
Francis & Ibbotson Chapter 19: Global Bond Markets 22
A Brief Tour of the Global Bond MarketA Brief Tour of the Global Bond Market
By the end of 1998 the aggregate value of all outstanding bonds in the world was $25.4 trillion– About 50% were denominated in U.S.
dollars– 15% were denominated in yen– 10% denominated in Deutschemark– 26% of world’s debt originated from
Euroland in 1998
Francis & Ibbotson Chapter 19: Global Bond Markets 33
The U.S. Bond MarketThe U.S. Bond Market
U.S. Treasury is the world’s single largest
borrower—also has the most liquid market—an informal OTC market.
Francis & Ibbotson Chapter 19: Global Bond Markets 44
U.S. Government Agency BondsU.S. Government Agency Bonds
Federal government allows governmental agencies to borrow in the name of the agency– The agencies’ debts do not appear as part of the federal
government’s debt• However, federal government implicitly guarantees the
agencies’ debts
Federal National Mortgage Association (FNMA—Fannie Mae) is the second largest borrower in U.S.– GNMA (Ginnie Mae) and FHLMC (Freddie Mac) are also
large borrowers• Subsidize home ownership by issuing low interest rate bonds
guaranteed by U.S. government
Francis & Ibbotson Chapter 19: Global Bond Markets 55
Corporate Bonds in the U.S.Corporate Bonds in the U.S.
Market for corporate bonds is less liquid than market for U.S. Treasuries– IPOs for bonds are underwritten by investment
banking firms
Largest organized secondary bond market is NYSE– Uses matrix prices for most of the bonds listed on
its Automated Bond System (ABS)• Based on price quotes for similar bonds (in terms of
coupon rate, maturity, quality rating, call provisions)
Francis & Ibbotson Chapter 19: Global Bond Markets 66
Corporate Bonds in the U.S.Corporate Bonds in the U.S.
Problems with ABS– Does not provide a liquid market free
from arbitrage opportunities– Large bond orders are difficult to execute
Most U.S. corporate bonds trade OTC– OTC bond quotes are not meaningful
• Again, large orders are difficult to execute at the quoted price
Francis & Ibbotson Chapter 19: Global Bond Markets 77
Bond Markets in the U.S.Bond Markets in the U.S.
Debt Issuers Underwriter Investors
U.S. government U.S. Treasury Governments, pensions, commercial banks, insurance companies, mutual funds, foreigners, households
Federal government agencies Investment banks Governments, pensions, commercial banks, insurance companies, mutual funds, foreigners, households
Municipalities Commercial and investment banks
Governments, commercial banks, insurance companies, mutual funds, foreigners, households
Corporations Investment banks Pensions, commercial banks, insurance companies, mutual funds, foreigners, households
Home buyers, commercial real estate developers
Mortgage banks & pool operators
Pensions, commercial banks, insurance companies, REITs
Foreign governments Investment banks Pensions, mutual funds, foreigners, households
Foreign corporations Investment banks Pensions, commercial banks, insurance companies, mutual funds, foreigners, households
U.S. government
conducts regularly scheduled
auctions for Treasury securities.
Francis & Ibbotson Chapter 19: Global Bond Markets 88
Bond Markets in the U.S.Bond Markets in the U.S. Transparency in a securities market exists when accurate price
and volume information is freely available– U.S. bond market is not transparent
Internet operations help increase the market’s transparency– TradeWeb—allows institutional investors the ability to trade U.S.
Treasury securities– Broker Tec—online interdealer bond brokerage– Trading Edge—operates a trade matching system for bonds– Bond Book—allows institutional investors and dealers to
anonymously trade corporate, junk and municipal bonds Bond markets are never expected to enjoy the same
transparency and liquidity as U.S. stock markets– There are 11,000 individual U.S. stocks vs. 4.5 million bond
issues
Francis & Ibbotson Chapter 19: Global Bond Markets 99
Sectors of the Industrialized Sectors of the Industrialized World’s Bond MarketsWorld’s Bond Markets
In almost every country, the federal government is that country’s largest debt issuer
Corporate sector for Japan, Italy and Germany is relatively small compared to their overall bond markets– Due to custom of borrowing from a bank
vs. issuing bonds
Francis & Ibbotson Chapter 19: Global Bond Markets 1010
International BondsInternational Bonds
Represent a rapidly growing category– Reflects willingness of borrowers to borrow
across borders
International bond investors face two types of political risk– Repatriation-of-funds risk
• A government may block payments of principal or interest
– Sovereign risk• A government may refuse to honor its debts
Francis & Ibbotson Chapter 19: Global Bond Markets 1111
International BondsInternational Bonds
Can be organized into the following categories– Domestic bonds
• Issued by a local borrower and denominated in local currency
– Foreign bonds• Issued in one country and denominated in that
country’s currency by a bond issuer from another country
– Eurobonds• Any bond not issued in a domestic market regardless of
its currency denomination and the issuer’s nationality
Francis & Ibbotson Chapter 19: Global Bond Markets 1212
Foreign BondsForeign Bonds
Categories of foreign bonds– Yankee bonds
• Issued by non-U.S. borrowers within the U.S.
– Samurai bonds• Yen-denominated bonds issued in Japan by non-
Japanese borrowers
– Shogun bonds• Non-yen-denominated bonds issued in Japan by non-
Japanese borrowers
– Bulldog bonds• Issued by non-British borrowers in the U.K.—
denominated in pounds
Francis & Ibbotson Chapter 19: Global Bond Markets 1313
Foreign BondsForeign Bonds
Yankee bonds are popular because liquid markets in high quality corporate bonds are nonexistent in many countries– Because governments encourage firms to
borrow from banks rather than issuing bonds
Francis & Ibbotson Chapter 19: Global Bond Markets 1414
The Eurobond MarketThe Eurobond Market
Fastest growing, most diverse bond market Include the following bond types
– Fixed coupon bonds, floating rate bonds, zero coupon bonds
– Renewable ordinary bonds– Ordinary bonds containing embedded options– Exchangeable floating rate notes– Convertible bonds– Bonds with warrants attached– Index-linked bonds– Dual currency bonds
Francis & Ibbotson Chapter 19: Global Bond Markets 1515
Primary and Secondary Markets for EurobondsPrimary and Secondary Markets for Eurobonds
Underwriting syndicates can be complex– Management group—can have from 4 to 30
member firms– Assemble an underwriting group—ranging from
20 to 300 banks– A selling group is also created
• Three groups split underwriting fees—ranging from 1.25% to 2.5% of the value of issue
Market’s untaxed and unregulated– Time schedule for issuing new bonds can be as
short as six weeks
Francis & Ibbotson Chapter 19: Global Bond Markets 1616
Primary and Secondary Markets for EurobondsPrimary and Secondary Markets for Eurobonds
Eurobonds begin trading in the gray market weeks before final offering price is set– A forward market for bonds that do not yet exist
Most Eurobonds are listed on the Luxembourg Stock Exchange, but they don’t actually trade there– Most trades occur in the OTC market
• Similar to NASD but free from SEC-like regulation
Francis & Ibbotson Chapter 19: Global Bond Markets 1717
Bearer Bonds Vs. Registered BondsBearer Bonds Vs. Registered Bonds
Registered bonds—send coupon checks to registered bond owners
Bearer bonds—have no list of registered owners– Investor must submit a dated coupon to a
bank to receive coupon payments• Many Eurodollar bonds are of this type
• Owner’s identity is unknown
Francis & Ibbotson Chapter 19: Global Bond Markets 1818
Eurodollar BondsEurodollar Bonds
U.S. dollar denominated bonds– Issued as bearer bonds
– Underwritten by an international syndicate
– Issued and traded outside the jurisdiction of any single country
– Largest component of Eurobond market
Who issues Eurodollar bonds?– National governments and their agencies
– Corporations• Some countries with stringent regulations do not allow corporations
to issue bonds similar to Eurodollar bonds in their country– Thus, these corporations issue Eurodollar bonds outside their country
Investors & multinational issuers like the lack of regulation and taxes
Francis & Ibbotson Chapter 19: Global Bond Markets 1919
Accrued InterestAccrued Interest
Market price of bond (or its clean price) is:
1 2 T T
1 2 T Tbond
Present Value of Coupon Payments Present Value of Par
Coupon Coupon Coupon ParPrice1 k 1 k 1 k 1 k
Bonds pay coupon payments periodically Annually, semi-annually, quarterly, etc.
When a bond is purchased on a day between its scheduled interest payment, buyer must pay seller for accrued interest Interest that has been earned but not yet paid by
issuer
Francis & Ibbotson Chapter 19: Global Bond Markets 2020
Accrued InterestAccrued Interest
Accrued interest calculation:
Accrued
# of days since last coupon payment Coupon Payment Interest
# of days between scheduled coupon payment datesCalculation
Thus, the actual price for a bond is the bond’s clean price plus the accrued interest Known as the bond’s invoice price, full price or dirty price
U.S. newspapers quote clean prices But buyers must pay the dirty price, which is always higher
if bond is between coupon payment dates• However, difference is not substantial
Francis & Ibbotson Chapter 19: Global Bond Markets 2121
Dirty Bond Prices Experience an Dirty Bond Prices Experience an Ex-Coupon Price Drop-offEx-Coupon Price Drop-off
Some countries use different bond invoicing methods– Quote prices with accrued interest
included (dirty prices)• Called a cum coupon price
• The quoted price will experience a drop-off in price immediately after a coupon payment is made
– Because accrued interest drops to zero
Francis & Ibbotson Chapter 19: Global Bond Markets 2222
Day Counting ConventionsDay Counting Conventions
The convention used in counting days is important when calculating accrued interest– Many countries use 360-day conventions
• Corresponds to twelve 30-day months
– U.K., Canada & Japan use 365-day convention
Francis & Ibbotson Chapter 19: Global Bond Markets 2323
Compounding ConventionsCompounding Conventions
The length of time between coupon payments impacts bonds’ yields and prices
Francis & Ibbotson Chapter 19: Global Bond Markets 2424
Yield-to-Maturity (YTM): A First LookYield-to-Maturity (YTM): A First Look
A simple approximation of yield-to-maturity is:
Rate of Cash FlowRate of price appreciation or depreciation
Par - Current PriceYears until maturity
Non compounded YTM Coupon RateCurrent Price
Above formula does not involved compounding Used in Japan, but not in U.S.
Ignoring compounding will result in a YTM only a few basis points different than the correct YTM But a few basis points can be thousands of dollars for a
multi-million dollar bond transaction
Francis & Ibbotson Chapter 19: Global Bond Markets 2525
Compounded YTMCompounded YTM
YTM defined as the discount rate equating the present value of a bond’s future cash flows to its current market price– For bonds paying coupon payments semi-
annually, the correct formula is:
1 2 2T
1 2 T 2T
Present 2 2 2Coupon Coupon Coupon ParValue 1 YTM 2 1 YTM 2 1 YTM 2 1 YTM 2
•The YTM is identical to IRR
Francis & Ibbotson Chapter 19: Global Bond Markets 2626
Compounded YTMCompounded YTM
Another method for calculating YTM– Effective YTM
• For a semi-annual coupon bond this method is:
1 2 T
0.5 1 2T 2T
Present 2 2 2Coupon Coupon Coupon ParValue 1 YTM 1 YTM 1 YTM 1 YTME E E E
Cuts the years in half rather
than the YTM.
Francis & Ibbotson Chapter 19: Global Bond Markets 2727
Example: Comparing a Bond’s Example: Comparing a Bond’s Conventional and Effective YTMConventional and Effective YTM
Given information– Par value: $100
– Coupon rate: 10% (semi-annual)
– Time to maturity: 10 years
– Purchase price: $106.59
Using the conventional YTM formula, we calculate a YTM of 8.8973%
1 2 20
$10 2 $10 2 $10 2 $100$106.59
1 0.089873 2 1 0.089873 2 1 0.089873 2
Francis & Ibbotson Chapter 19: Global Bond Markets 2828
Example: Comparing a Bond’s Example: Comparing a Bond’s Conventional and Effective YTMConventional and Effective YTM
Using the effective YTM (EYTM) formula, we calculate an EYTM of 9.1892%
0.5 1 20
$10 2 $10 2 $10 2 $100$106.59
1.091892 1.091892 1.091892
Difference is about 20 BPs 9.1892% - 8.9873% = 0.2019
The difference between conventional YTM and EYTM is (1 + EYTM) = (1+YTM/2)2 or YTM + YTM2/4 Or: 0.089873 + (0.089873)2/4 = 0.091892 or 9.1892%
Francis & Ibbotson Chapter 19: Global Bond Markets 2929
Comparing Various YTMs for a BondComparing Various YTMs for a Bond
Many people think YTM is a very precise measure– YTM depends upon assumptions and techniques
used
– For example, a bond with a $100 par, a 10% coupon, a 10-year maturity and a current price of $106.59 can have several YTMs
• Conventional semi-annual: 8.9873%
• Effective semi-annual: 9.1892%
• Japanese semi-annual: 9.3187%
Francis & Ibbotson Chapter 19: Global Bond Markets 3030
Conditions Required to Earn a Conditions Required to Earn a Bond’s Expected YTMBond’s Expected YTM
A bond’s computed YTM will only actually be earned if:– The bond is held to maturity– The bond issuer does not default in the
timing or amount of scheduled payments– All the cash flows are immediately
reinvested to earn the bond’s YTM
Francis & Ibbotson Chapter 19: Global Bond Markets 3131
Reinvestment Rate Affects A Bond’s YTMReinvestment Rate Affects A Bond’s YTM
Different reinvestment rates impact the investor's actual rate of return– Example: An investor buying an 8% coupon bond at par
will expect a YTM of 8%• However, his actual return hinges on the reinvestment rate
earned on the coupon income receivedReinvestment
RateTotal Realized
Yield
0% 4.84%
5 6.64
6 7.07
7 7.53
8 8.00
9 8.50
10 9.01
Only if the reinvestment rate = YTM will the investor actually realize the YTM.
Francis & Ibbotson Chapter 19: Global Bond Markets 3232
A Bond’s Holding Period ReturnA Bond’s Holding Period Return
An investor’s holding period return (r) is:
1 0
0beginning of holding period
CFPrice change Cash Flow P Pr
Price P
Can be positive, negative or zero Depends on how the price moved over the
holding period• A bond’s price movements are determined by
fluctuations in the bond’s YTM
Francis & Ibbotson Chapter 19: Global Bond Markets 3333
Inverse Relationship Between a Inverse Relationship Between a Bond’s Price and YTMBond’s Price and YTM
The price and YTM of a bond move inversely
NOTE: Price-yield curves are convex to the origin.
Francis & Ibbotson Chapter 19: Global Bond Markets 3434
Other Measures of Bonds’ YieldsOther Measures of Bonds’ Yields
Yield-to-call (YTC)– A bond issuer may call a bond before its
original maturity date• Need to calculate the bond’s YTC
– Similar to YTM, except replace T as the time-to-call rather than time-to-maturity
Francis & Ibbotson Chapter 19: Global Bond Markets 3535
Example: Comparing a Callable Example: Comparing a Callable Bond’s YTC & YTMBond’s YTC & YTM
Compute the YTC:
20
201
$175 $10,000$8,140.32 or YTM = 6% a year
1.03 1.03tt
Given information– Par value: $10,000
– Time to maturity: 10 years
– Coupon rate: 7% (3.5% semi-annually)
– Current price: $8,140.32
– Call premium: 7% in 5 years (meaning the bond is callable at 107% of par in 5 years)
Compute the YTM:
10
101
$175 $10,000 1.07$8,140.32 or YTM = 9.373% a year
1.04686 1.04686tt
Francis & Ibbotson Chapter 19: Global Bond Markets 3636
Other Measures of Bond’s YieldsOther Measures of Bond’s Yields
Floaters– A bond with a fixed par but a fluctuating (or
floating) interest rate• Rate varies according to a specified reference rate
– LIBOR or U.S. T-bill rates are commonly used
Current yield—every non-zero bond has a positive current yield
Annual coupon $ interestCurrent Yield
Current price of bond
Investors desiring high investment cash flows are interested in a bond’s current yield
Francis & Ibbotson Chapter 19: Global Bond Markets 3737
Brady Bonds Aid Emerging CountriesBrady Bonds Aid Emerging Countries
An international debt crisis occurred in late 1980s due to falling commodity prices and recessions– Many loans were defaulting ($200 billion)
• Mostly from Latin America
– Many emerging countries vanished from international financial markets
Debt banks created Paris Club organization– Also organized a secondary market for the non-
performing bank loans• Typically priced at less than half original face value
Francis & Ibbotson Chapter 19: Global Bond Markets 3838
Brady Bonds Aid Emerging CountriesBrady Bonds Aid Emerging Countries
In 1989 the U.S. Secretary of Treasury, Nicholas Brady proposed the Brady Plan– Provided a way to finance the defaulted loans
until they could be paid off• Emerging country must get an economic reform plan
approved and obtain loans through International Monetary Fund and World Bank or elsewhere
– Development banks established repayment plans
» Made the defaulted debt marketable by guaranteeing repayments
» Allowed troubled banks to exchange illiquid defaulted bank loans for liquid Brady bonds
Francis & Ibbotson Chapter 19: Global Bond Markets 3939
Brady Bonds Aid Emerging CountriesBrady Bonds Aid Emerging Countries
No Brady bonds are 100% guaranteed Types of Brady bonds
– Most popular• Discount bonds (AKA: principal-reduction
bonds)– Issued at a deep discount from par
• Par bond (AKA: interest-reduction bond)– Face value equals par value of defaulted debts
» Debt reduction occurs by setting coupon rate below current market rate
Francis & Ibbotson Chapter 19: Global Bond Markets 4040
Brady Bonds Aid Emerging CountriesBrady Bonds Aid Emerging Countries
Less popular Brady bonds– Debt-conversion bonds (DCBs) and new-money
bonds (NMBs)• Each dollar invested in NMBs can be converted into a
larger amount of more desirable DCBs
– Front-loaded interest-reduction bonds (FLIRBs)• Pay low coupon rates during early years but coupon
rate increases over time
– Past-due interest bonds (PDIs)• Issued to pay for past omitted interest payments
Francis & Ibbotson Chapter 19: Global Bond Markets 4141
Brady Bonds Aid Emerging CountriesBrady Bonds Aid Emerging Countries
Outcome of the Brady Plan– Emerging nations able to settle defaulted debt at
a reduced cost– Reduced debt allowed countries to renew
economic growth– Troubled countries able to regain access to
capital markets
Critics of Brady Plan argue– Too costly
• Developed nations finance the development banks
– Subsidizes financial mismanagement
Francis & Ibbotson Chapter 19: Global Bond Markets 4242
International Bond Index StatisticsInternational Bond Index Statistics
U.S. $ U.K. Pound Hong Kong $ German Mark
Return SD Return SD Return SD Return SD
Australia 8.5% 15.5% 9.9% 18.3% 9.5% 16.4% 5.0% 20.2%
Belgium 11.6 17.2 13.0 14.7 12.7 16.2 8.1 8.6
Canada 9.3 10.4 10.7 19.3 10.3 13.2 5.8 17.0
France 10.8 15.6 12.2 15.3 11.8 15.6 7.2 12.2
Germany 12.0 14.9 13.4 16.7 13.0 13.4 8.4 8.4
Japan 12.2 17.5 13.7 18.4 13.3 18.3 8.7 17.3
Netherlands 11.7 14.2 13.1 15.8 12.7 14.0 8.1 8.2
Switzerland 10.2 17.1 11.6 16.8 11.2 16.0 6.7 9.8
U.K. 10.2 22.3 11.6 17.2 11.6 17.2 11.3 23.4
U.S. 9.3 12.2 10.6 21.3 10.3 14.7 5.8 16.8
No single bond
investment appears to be the most or least risky.
Francis & Ibbotson Chapter 19: Global Bond Markets 4343
Components of International Bond ReturnsComponents of International Bond Returns
Capital Appreciation
Income Return
Currency Return
Total Return (US$)
Australia -1.2% 10.4% -1.3% 8.5%
Belgium 0.3 9.1 1.6 11.6
Canada 0.1 9.6 -0.9 9.3
France 0.3 9.7 0.3 10.8
Germany 0.5 7.6 3.2 12.0
Italy 0.1 12.2 -3.3 9.5
Japan 1.0 6.4 4.1 12.2
Netherlands 0.3 8.0 2.7 11.7
Switzerland 0.4 5.0 4.2 10.2
UK 0.2 11.0 -1.3 10.2
US 0.4 8.4 N/A 9.3
Returns are from the
standpoint of a U.S. investor.
Results suggest investor needs to
analyze all three
components.
Francis & Ibbotson Chapter 19: Global Bond Markets 4444
Correlations of International Bond ReturnsCorrelations of International Bond Returns
Aus’l A’str Belg Can Fra Ger Ire Ita Jap Net NZ Safr Swi UK US
Australia 1.00
Austria 0.22 1.00
Belgium 0.20 0.86 1.00
Canada 0.28 0.22 0.25 1.00
France 0.20 0.82 0.82 0.25 1.00
Germany 0.20 0.91 0.86 0.28 0.82 1.00
Ireland 0.24 0.59 0.60 0.27 0.59 0.61 1.00
Italy 0.17 0.50 0.47 0.22 0.52 0.47 0.46 1.00
Japan 0.19 0.59 0.59 0.26 0.57 0.59 0.45 0.33 1.00
Netherlands 0.21 0.88 0.83 0.30 0.83 0.93 0.57 0.47 0.59 1.00
New Zealand 0.32 0.26 0.27 0.07 0.24 0.23 0.24 0.21 0.23 0.26 1.00
South Africa 0.21 0.39 0.35 0.06 0.34 0.37 0.29 0.26 0.25 0.34 0.14 1.00
Switzerland 0.18 0.82 0.77 0.24 0.75 0.83 0.56 0.39 0.61 0.82 0.18 0.31 1.00
UK 0.23 0.43 0.46 0.30 0.45 0.47 0.74 0.34 0.40 0.46 0.23 0.23 0.42 1.00
US 0.16 0.18 0.22 0.67 0.24 0.26 0.23 0.18 0.21 0.29 -0.05 0.05 0.24 0.21 1.00
High correlations result from:•Bilateral trade agreements•Policies to align currencies•Cultural similarities
Francis & Ibbotson Chapter 19: Global Bond Markets 4545
Correlations of International Bond ReturnsCorrelations of International Bond Returns
What’s important is the fact that there are some relatively low correlations among international bond returns resulting from– Dynamics of business cycles within countries
– Different monetary policies
– Different government financing practices
– Differing inflation levels
– Social trends, foreign policies ad political forces
Correlations are unstable over time
Francis & Ibbotson Chapter 19: Global Bond Markets 4646
Markowitz Analysis of Markowitz Analysis of International Bond PortfolioInternational Bond Portfolio
U.S. investor can achieve a
dominant position by
investing 40% of portfolio in
non-U.S. bonds.
Caveats:
• Based on historical data—no guarantee future will be the same
• Ignores commissions and other expenses
Francis & Ibbotson Chapter 19: Global Bond Markets 4747
Actively Managing International Actively Managing International Bond InvestmentsBond Investments
Active international bond investors can use different approaches:– Political analysts begin with a top-down approach and
analyze sovereign risks, etc.– Macro-economists study macro factors (income,
employment, etc.) to determine which nations are economically strong
– Monetary economists forecast a nation’s level and structure of market interest rates by analyzing central bank and their policies, etc.
– Industry analysts analyze financial data from different industries
– Security analysts have a bottom-up approach—focus on bond issuer’s financial conditions, protective provisions, etc.
Francis & Ibbotson Chapter 19: Global Bond Markets 4848
The Bottom LineThe Bottom Line
Governments are the largest borrowers in the world Most rapid growth occurring in Eurobond market
– Unregulated and untaxed
Some countries publish clean bond prices while others publish dirty prices which includes accrued interest
Day counting conventions differ across countries YTM calculations methods also differ across
countries
Francis & Ibbotson Chapter 19: Global Bond Markets 4949
The Bottom LineThe Bottom Line
If a bond’s cash flows are not invested at the bond’s YTM the investor will not earn the YTM
Other yield measures exist– Holding period return– Current yield– Yield to call
Francis & Ibbotson Chapter 19: Global Bond Markets 5050
The Bottom LineThe Bottom Line
Brady Plan generated an array of packages of defaulted bank loans from emerging countries
Investors need to analyze capital appreciation, coupon interest return and foreign exchange return when considering investments in international bonds
Markowitz portfolio analysis is applicable for international bond investing