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Fixed Income SecuritiesConcepts and Valuation

Rustam Jamilov

State Committee of SecuritiesCapital Markets Training Center

[email protected]

April 9, 2015

Jamilov (CMTC) Fixed Income Baku, 2015 1 / 31

Table of Contents

1 Concepts

2 Valuation

3 Making Money


Basic Features of FI Securities

Fixed income as an asset class

Bond as a fixed income instrument

Bond as an asset/debt

Issuer of the bond

Maturity date

Principal value

Coupon rate

Currency of denomination






Issuer of the bond

Maturity date

Principal value

Coupon rate







Issuer of the bond

Maturity date

Principal value

Coupon rate







Issuer of the bond

Maturity date

Principal value

Coupon rate







Issuer of the bond

Maturity date

Principal value

Coupon rate







Issuer of the bond

Maturity date

Principal value

Coupon rate







Issuer of the bond

Maturity date

Principal value

Coupon rate







Issuer of the bond

Maturity date

Principal value

Coupon rate



Fixed Income Market Size

Global fixed income market size in 2010 surpassed $150 trillion. The figure is closer to $200 trillion today.

This includes both pure loans and bond-style public/financial securities.


Bonds as Debt/Asset

Liability

When a government or corporationissues bonds in order to financeoperations, they become legaldebtors. They are mandated to repaythe par and all coupons (if any) tothose who buy the bonds. Bond is aliability.

Asset

When an investor (pension fund,wealth fund) buys a bond issued by acorporation/government, the investorbecomes entitled to the par and allcoupons (if any). The investor ownsa stream of future payments. Bond isan asset


Issuers of Bonds

1 Corporations: financial and non-financial

2 Sovereign national governments

3 Local governments

4 Supranational entities

5 Companies


Bond Maturity

The maturity date of a bond is the date on which the principal value is tobe repaid. For example, if a government issues a 10-year bond worth $1billion USD, then exactly 10 years from now the principal value of $1billion USD must be repaid in full amount.

Bonds that have no maturity are called perpetual bonds.

Bonds with maturities of one year or less are referred to as money marketsecurities.

Bonds with maturities of more than one year are capital market securities.


Par Value

Principal value, or par value, of a bond is the amount that the issueragrees to repay the bondholders on the maturity date. For example,assume the principal of a bond is $1000. If the bond is currently priced at$1000 then we say it is at par. Above par - bond is trading at a premium.Below par - at a discount. Par value could be any amount.


Coupon Rates

Plain Vanilla (Fixed)

A plain vanilla bond pays a predetermined fixed rate of interest. This ratecan be paid annually/quarterly/monthly. For example, annual coupon rateof 6% for a $1000 par value bond is $60.

Floating-rate Notes (FRN)

Floating rate notes pay non-fixed coupons that depend on a reference rate.A widely used reference is the London interbank offered rate (LIBOR).Usually, bonds are issued at LIBOR + Spread rate, where spread reflectsthe credit risk of the issuer. For example, Apple issues a 10 year FRNbond at LIBOR + 50 bps. Bps = basis points. 1 basis point = 0.01.There are 100 bps in 1%. If LIBOR is 1.2% (120 bps) then Apple mustpay 1.7% (120 bps) in its next coupon installment.


Coupon Rates 2

Zero-coupon Bonds (ZCB)

ZCBs pay no periodic payments via coupons. They just repay the parvalue at maturity. ZCBs may be purchased at a price different from par.For example, a bond purchased at price $95 pays back $100 at maturity(in 1 year). This implies a 5% rate of interest. The interest is implied, i.e.not actually paid via installments but embedded into the discounted price.


Coupon Rates 3

Index-Linked Bonds

An index-linked bond pays its principal and coupon payments linked to aspecified index. The most popular type of indexed bonds isinflation-linked. They provide protection against rising prices. Forexample, the United Kingdom issues an 1.5% 10-year inflation-protectedbond. Inflation rate in the UK is 2%. If this bond was plain vanilla, thenthe investor holding the bond would only earn negative 0.5% of realinterest. In general, the real rate of return is what we care about becausereal purchasing power is our main goal.


Currency Denomination

Bonds can be issued in any currency, although most bonds are issued ineither USD or EUR - these 2 are called hard currency. Any government,corporation, agency can in principle issue bonds in USD or EUR. It makesissuance easier, even if your local currency is not USD or EUR. Manyagents issue bonds in local currencies (GBP, JPY, KRW, TRY, RUB) tofinance expenditures in the local market. Demand for local currenciesvaries across markets and on a cyclical basis.


Global Bond Market - Bloomberg Terminal

Here we see bonds of different issuers, prices (bid and ask), yields (to be discussed further), and

historical performance.

Values swing dramatically over time; markets have high volatility and tens of millions worth of

sovereign debt move around every hour.


Global Currency Market - Bloomberg Terminal

Bonds denominated in local currencies have billions in size. When deciding to purchase a bond

in a foreign (non-USD or non-EUR) currency, one must carefully study the FOREX market.


Table of Contents

1 Concepts

2 Valuation

3 Making Money


Time Value of Money

Definition

A dollar invested today is not the same as the dollar invested tomorrow.You can earn interest i on 1 dollar invested today, and tomorrow yourwealth becomes 1$+i . The value of money grows over time. The skill offinance is to develop and price instruments whose value grows over time.The art of finance is knowing which instrument to buy/sell and at whatmoment.


Bond Pricing - No Coupons

Formula

Present Value =Future Value

(1 + i)t

where i is the market discount rate, aka required yield of the bond

t is the maturity length of the bond.


Example

Let’s price a zero-coupon bond with maturity 7 years, paying $1000 atmaturity, and the required rate of return 5%.

Price =1000

(1 + 0.05)7= 710.68


Bond Pricing - With Coupons

Formula 2

Present Value =t∑

k=1

Coupon

(1 + i)k+

Future Value

(1 + i)t

where i is the market discount rate, aka required yield of the bondt is the maturity length of the bond k is the current time period

Do not forget to add the future value to the stream of coupons!


ExampleThe same bond with maturity 7 years, paying $1000 at maturity, and the required rate of return

5%, is now paying annual coupons of $20. The price is now:

Price =20

(1 + 0.05)+

20

(1 + 0.05)2+

20

(1 + 0.05)3+

20

(1 + 0.05)4+

20

(1 + 0.05)5+

+20

(1 + 0.05)6+

20

(1 + 0.05)7+

1000

(1 + 0.05)7= 826.41


Yield to Maturity

The problem can be solved in reversed order. If we have a known marketprice for a bond, we can calculate its yield to maturity. YTM is the impliedmarket discount rate which makes the future discounted cash flows equalto the today’s market price. Market players may speculate on the price ofthe bond, and the YTM will respond to price fluctuations. Suppose, a4-year bond with 5% annual coupon payment is priced by traders at 105per the par value of 100. The YTM can be solved numerically from:

105 =5

(1 + i)+

5

(1 + i)2+

5

(1 + i)3+

5

(1 + i)4+

100

(1 + i)4

Which gives i=3.634%. Notice how the yield is lower than the coupon rate,which is normal for bonds priced above par. Also, negative relationshipbetween asset prices and yields is one of the major laws in finance.


Pricing using Spot Rates

In the previous examples, we made a big assumption that drove the result.We assumed that the required return is constant until bond maturity. Amore fundamental approach is to discount every cash flow using its spotrate, i.e. the actual interest rate observed at the period. Spot rates arenot necessarily equal to assumed constant yields. This can generatepricing distortions across the two approaches. For example, consider thatthe one-year spot rate is 2%, 2-year is 3%, and 3-year is 4%. Coupon is5%. Pricing is:

Price =5

(1 + 0.02)+

5

(1 + 0.03)2+

5

(1 + 0.04)3+

5

(1 + 0.04)3= 102.960


Bond Pricing - Bloomberg Terminal

This is a 5-year corporate bond. Issuer is IBM. Coupon rate is 1.875%. Yield to maturity is

0.53%. Current market price is $107.4. Bond is priced above par. Currency of denomination is

EUR. Yes, interest rates (yields) are very low in Europe nowadays . . .


Table of Contents

1 Concepts

2 Valuation

3 Making Money


Yields Differential

There are plenty of reasons why yields on any two bonds are different. Themajor drivers causing yield differentials include:

1 Currency

2 Credit risk

3 Liquidity

4 Tax Status

5 Periodicity

Another obvious driver is the maturity structure. Bonds with longertenures (maturity terms) have, in general, higher yields ceteris paribus.


Term Structure of Interest Rates

This is the term structure for US Treasuries. Notice the 40bps drop in 10-year treasuries, just over the past 6 months . . .


Forecasting Yields

Bond prices and yields are negatively related. When interest rates godown, prices go up. If you can predict the right moment of the rate drop -you can position yourself for the event by buying lots of the asset and thenselling it after interest rates fall. The market generally has a very goodunderstanding of which way the interest rates will go. Usually, even aslight 5bps move (0.05%) can make a big difference. E.g.: multiply 0.05by a $100 million investment and get $5 million in profit.

The best way to get an idea of future interest rate movement is theforward rate matrix. Forward rate is the future yield on a bond calculatedusing the yield curve. For example, the yield on a 3-month Treasury bill sixmonths from now is a 6-month - 3-month forward rate. By pricing aforward rate for every maturity we construct a forward curve.


Forward Curve

As of today, the spot 10-year rate is 1.95%. In 1 year, the expectation is that the 10-year becomes 2.2%. Most financial

contracts will be signed using this as a benchmark of expectations. BUT, if the future 10-year rate one year from now will in

fact be 2.0% (different from the forward rate), you can capture a profit by correctly positioning yourself on the curve. This is

how millions are made (or lost).


Relative Value

This is the spread of a 5-year Deutsche-Telecom bond over the 5-year German Bund. Spread has been narrowing greatly for the

past 2 years.


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