Fixed Income Valuation and

Derivatives for Risk Hedging

Russ Jason Lo

Economic Research and Regional Cooperation

Department, Asian Development Bank

Fixed Income Valuation

• Appropriate Rate of Return

• Identifying the appropriate risk-free rate benchmark

• Identifying risks inherent in the bond

• Price Paid for a Bond

• Difference between yield-to-maturity and coupon rate

• Discounted cash flows formula

Valuation and Pricing of Bonds

• How do investors assess investment opportunities?

• Based on investment requirements

• Comparison between different options

• Adjustment for some risk factors

• Importance and use of a risk-free benchmark

• Minimum rate of return that investors will demand for

investing

• Basis for assessing rates of return of other (more risky)

investments

Assessing Appropriate Rate of Return

Risk-Free Yield Curve

Thailand Viet Nam Singapore

Indonesia Malaysia

Observations on Risk-Free Yield Curves

• The yield curve is mostly upward sloping

• Yields of different maturity segments are correlated

Yield Curve Theories

• Pure Expectations Theory

• Liquidity Preference Theory

• Preferred Habitat Theory

Pure Expectations Theory

0 t t+1 t+2 t+3 t+4 t+5 t+6

Expected Real Interest Rate

Expected Inflation

Liquidity Preference Theory

0 t t+1 t+2 t+3 t+4 t+5 t+6

Expected Real Interest Rate

Expected Inflation

Liquidity Premium

Preferred Habitat Theory

0 t t+1 t+2 t+3 t+4 t+5 t+6

Expected Real Interest Rate

Expected Inflation

Other Risk Premium

Liquidity Premium

• Required Rate of Return on Bond = Real Risk Free

Rate + Inflation + Term Premium + Liquidity

Premium + Credit Risk Premium

Appropriate Rate of Return

• Inflation Risk

• Liquidity Risk

• Credit Risk

• Foreign Exchange Risk

• Interest Rate Risk

• Reinvestment Risk

Risks of Bonds

Credit Risk

• Default Risk

• risk that the issuer may fail to fulfill its promised

payments of coupon and/or principal

• Credit Spread Risk

• risk that the spread between the rate of a risky

bond and that of a risk-free bond may change

• Downgrade Risk

• risk that the rating of a bond may be lowered by

major credit rating agencies

Inflation Risk

• High inflation erodes the real value of conventional

bonds (i.e., bonds with fixed coupon).

• Expectations of higher inflation induce higher bond

yields and lower bond prices

• Longer-tenor bonds tend to have higher inflation

risk.

• Inflation-linked bonds provide a fixed return

regardless of inflation by adjusting coupon

payments in line with inflation

Liquidity Risk

• Liquidity refers to the ease with which a reasonable

size of a bond can be traded within a short notice,

without adverse price reaction

• Illiquid bond markets tend to have:

• Fewer dealers

• Low depth

• Wide bid-ask spreads

• Government bonds tend to be more liquid than

corporate bonds

Interest Rate Risk

• Risk to bonds with fixed coupon rates.

• Interest rates and bond prices move in opposite directions: when interest rates decrease (increase), bond prices increase (decrease).

• With an increase (decrease) in the price of a fixed-rate bond following a decrease (increase) in interest rates, the yield-to-maturity of the bond decreases (increases).

Bond prices

Interest rates

Fixed Income Valuation

Source: Asia Bond Monitor

• Unlike loans, bonds are traded on the secondary

market

• Bonds can be traded via OTC markets or on an exchange

• Pricing Convention

• Generally quoted in price per hundred

• Some markets quote in terms of yield to maturity

• Dirty Price Versus Clean Price

• The trading convention is to quote clean price

• Dirty price will include accrued interest

• Dirty price reflects the full cost of the bond

Fixed Income Terms

• Coupon Rate

• The stated rate of interest that the bond will pay periodically

• Coupon payment = (Coupon Rate x Face Value)/Frequency

• Face Value

• The amount of principal that the investor will receive when the bond

matures

• Yield to Maturity

• The rate of return on the bond, assuming that the bond is held to

maturity and coupon payments are reinvested at the same rate.

• Maturity/Tenor

• The life of the bond

Valuation of a Bond

• Value of the Bond

• Present value of the expected cash flows of the bond (coupon

payments + face value)

• Discount rate to be used is the yield to maturity

• Face Value

• The amount of principal that the investor will receive when the bond

matures

Bond Valuation Formula

CF = Cash flow

PV=Present value

FV=Face Value

y = interest rate

N = years

m = interest compounding

𝑃𝑉 = (𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒∗𝐹𝑉)/𝑚

1+𝑦

𝑚

𝑁𝑚𝑁𝑚𝑡=1 +

𝐹𝑉

1+𝑦

𝑚

𝑁𝑚

Example

Note: Emerging East Asia comprises the People’s Republic of China; Hong Kong, China; Indonesia; the Republic of Korea; Malaysia; the Philippines; Singapore;

Thailand; and Viet Nam.

Source: AsianBondsOnline.

Coupon Bond (Semi-annual Coupon Payments)

𝑃𝑉 =

(𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ∗ 𝐹𝑉)2

(1 +𝑦2)1

+

(𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ∗ 𝐹𝑉)2

(1 +𝑦2)2

+

(𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ∗ 𝐹𝑉)2

(1 +𝑦2)3

+

(𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ∗ 𝐹𝑉)2

(1 +𝑦2)4

+

(𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ∗ 𝐹𝑉)2

(1 +𝑦2)5

+

(𝐶𝑜𝑢𝑝𝑜𝑛 𝑅𝑎𝑡𝑒 ∗ 𝐹𝑉)2

(1 +𝑦2)6

+𝐹𝑉

1 +𝑦2

6

Year 1 Year 2 Year 3

Building a Benchmark Risk Free

Yield Curve

Methods

• Creating or designating benchmark bonds or tenors

• Establishment of market makers to provide liquidity

• Creating/releasing “fixing” rates

• Using an exchange or bond pricing agency

Interpolation

?

Linear Interpolation

𝑌𝑖𝑒𝑙𝑑𝑏 − 𝑌𝑖𝑒𝑙𝑑𝑎𝑇𝑒𝑛𝑜𝑟𝑏 − 𝑇𝑒𝑛𝑜𝑟𝑎

= 𝑌𝑖𝑒𝑙𝑑𝑐 − 𝑌𝑖𝑒𝑙𝑑𝑎𝑇𝑒𝑛𝑜𝑟𝑐 − 𝑇𝑒𝑛𝑜𝑟𝑎

𝑌𝑖𝑒𝑙𝑑𝑏 = 𝑌𝑖𝑒𝑙𝑑𝑎 +

𝑌𝑖𝑒𝑙𝑑𝑐 − 𝑌𝑖𝑒𝑙𝑑𝑎 ∗ (𝑇𝑒𝑛𝑜𝑟𝑏 − 𝑇𝑒𝑛𝑜𝑟𝑎)

𝑇𝑒𝑛𝑜𝑟𝑐 − 𝑇𝑒𝑛𝑜𝑟𝑎

𝑌𝑖𝑒𝑙𝑑𝑏 = target rate to be interpolated

𝑌𝑖𝑒𝑙𝑑𝑎 = available rate with shorter maturity

𝑌𝑖𝑒𝑙𝑑𝑐 = available rate with longer maturity

𝑇𝑒𝑛𝑜𝑟𝑏 = maturity of 𝑌𝑖𝑒𝑙𝑑𝑏

𝑇𝑒𝑛𝑜𝑟𝑎 = maturity of 𝑌𝑖𝑒𝑙𝑑𝑎

𝑇𝑒𝑛𝑜𝑟𝑐 = maturity of 𝑌𝑖𝑒𝑙𝑑𝑐

Derivatives for Risk Hedging

What is a Derivative?

• A financial agreement or contract between two

parties in which its value is “derived” from an

underlying asset or index.

• Uses:

Risk hedging

Speculative or investment motive

Forwards

• Forwards are derivative contracts that will allow

parties to exchange assets at a future data at a

specified price.

• Allows for hedging of price risk.

• Typically, cash is exchanged for another asset.

Terms Used for Derivatives

• Spot Price

• the current price of the asset

• Forward Price

• the agreed upon transaction price of the asset

• Underlying

• the asset that is being referred to in the forward

contract

• Notional

• the size or amount of the underlying

Sample Transaction

T=0 T+1 month

Party A

Party B

Forward

Contract

Party A

Party B

Cash Security or

Commodity

Risks in a Forward Transaction

Party A

Party B

Cash Security or Commodity

Financial/Commodities Market

Cash Security or Commodity

Examples of Forwards

• Commodity Forwards

• Equity Forwards

• Bond Forwards

• Interest Rate Forwards or Forward Rate Agreements

Forward Rate Agreement

• Used to hedge a change in interest rate.

• The payout is based on a difference between the

agreed upon interest rate at the time the contract is

entered into and the current market rate of the

reference interest rate.

• Normally used to hedge interest rate risk exposure

before entering into a loan.

• The asset exchanged is an interest payment.

Forward Rate Agreement

Life of the FRA

Period of the loan

𝑃𝑎𝑦𝑜𝑢𝑡 =𝑁𝑜𝑡𝑖𝑜𝑛𝑎𝑙 ∗ (𝑐 − 𝑟) ∗

𝑡360

1 + 𝑟 ∗ 𝑡/360

Futures Versus Forwards

Futures Forwards

Marked-to-market Not marked-to-market

Traded on a centralized exchange Traded on the over-the-counter

(OTC) market

Standardized Not standardized

Settled daily Settled at the end of the contract

Margin requirements No Margin Requirements

Methods of Settlement

• Physical Delivery

• Cash Settlement

• Offsetting Position

Bond Futures/Forwards

• A type of derivative contract used to hedge or gain

exposure to bond investments.

• Settlement can be cash-settled or physical delivery,

depending on market.

• A hypothetical bond is used as the underlying.

Bond Futures/Forwards China,

People’s

Republic

of

Hong

Kong,

China

Korea, Republic of Malaysia Thailand

Instrument 5-year

Treasury

Bond Futures

3-year

EFN

Futures

3-year

KTB

Futures

5-year

KTB

Futures

10-year

KTB

Futures

3-year

MGS

Futures

5-year

MGS

Futures

5-year

Government

Bond

Futures

Settlement Physical Physical Cash Cash Cash Cash Cash Cash

Contract

Size

HKD5M KRW100

M

KRW100

M

KRW100

M

MYR0.1

M

MYR0.1

M

THB1M

Exchange China

Financial

Futures

Exchange

Hong

Kong

Futures

Exchange

Korea Exchange

Bursa Malaysia Thailand

Futures

Exchange

Swaps

• A type of derivative contract wherein periodic exchanges

or payments are made over the life of the contract.

• Can be viewed as a series of forward transactions.

Interest Rate Swaps

• A type of swap wherein one party pays a periodic

payment based on a fixed interest rate, while the other

pays based on a variable interest rate.

• No exchange of principal

Interest Rate Swaps

Counterparty Swap

Dealer

T + 20 bps

8%

Uses of Interest Rate Swaps

• Allows for transformation of a liability or asset.

• Converts exposure to a fixed rate to a floating rate or

vice versa.

• Can hedge against either a fall or a rise in interest rates.

Example

LIBOR Floating

Payment

Fixed

Payment

Net

Q2 2013 4.2%

Q4 2013 4.8% 2.1 2.5 -0.40

Q2 2014 5.3% 2.4 2.5 -0.10

Q4 2014 5.5% 2.65 2.5 0.15

Q2 2015 5.6% 2.75 2.5 0.25

Q4 2015 5.9% 2.80 2.5 0.30

Q2 2016 6.4% 2.95 2.5 0.45

Use of Netting

• Not just for ease of payment.

• Mitigates credit risk.

• Netting applies if one counterparty should become

bankrupt.

• Also reduces systemic risk of derivatives, by reducing

total exposure.

Credit Default Swaps

• A type of derivative transaction used to hedge credit risk.

• Credit default swaps are similar to insurance, wherein

the triggering event for a payout is a credit event.

• Does not remove credit risk, merely transfer burden to

the seller of the credit default swap.

Credit Default Swaps

Reference Bond

CDS Buyer CDS Seller

Interest Payment

Premium

Settlement for Credit Default Swaps

Reference Bond

CDS Buyer • Buyer delivers the bond, seller delivers cash equivalent

to par value.

• Seller delivers cash value equal to par value less market

value of bond.

Trigger Events for Credit Default

Swaps

Reference Bond

CDS Buyer

• Bankruptcy

• Failure to pay

• Restructuring

• Repudiation or moratorium

• Obligation acceleration or default