fixed income valuation and derivatives for risk hedging
TRANSCRIPT
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