Test 2 Flashcards
(113 cards)
1
Q
What are CAT Bonds
A
CAT bonds stand for “catastrophe bonds”
> issuers = insurance companies who want to raise money in the event of devastating natural disaster
Issuer receives funding (“payout”) from the bond ONLY if a devastating event triggers the bond
in that case, there is NO OBLIGATION to pay interest or the principal (it’s either deferred or completely forgiven)
bondholders (investors) = Institutional Investors (Hedge funds, pension funds)
want diversification benefits, since the bonds are uncorrelated with the general market
Characteristics:
> High yield debt instrument ==> riskier than traditional investment grade bonds ==> higher coupons
> short maturities (3-5 years)
> can be paid monthly
Mechanics:
> Insurance company (via special company called “Sponsor”) ISSUES CAT bond, receives principal from investors
> principal is put into a “secure collateral account” (“SPECIAL PURPOSE VEHICLE” or SPV), where the funds can then be INVESTED in low risk securities (safe, liquid collateral, e.g. US T Bills)
> Sponsor make premium payments to SPV
> Issuer (via SPV) makes INTEREST PAYMENTS (from the account) to investors, usually at a HIGHER rate
> During the life of the bond the investors receive interest on their bonds, and assuming that a catastrophe did not occur, then they received their investment back when the bonds matured.
> if a devastating event happens, payout is triggered: money in the secure collateral account goes to the insurance company
Investors may lose their principal if costs exceed money in the account, otherwise, they get their principal upon maturity
Ex: World Bank issued CAT bonds with the Phillipines Gov’t in 2019
2
Q
Pandemic Bonds
A
> bonds launched by the World Bank to provide financial support to countries facing who need help containing a pandemic. So, they are linked to countries with high risk of having a pandemic
use a facility called the “Pandemic Emergency Financing Facility” to provide funding to these countries
covers 6 viruses most likely to cause a pandemic, like coronaviruses
Triggers for bond payments vary from tranche (Class A and Class B):
- At least 12 weeks after start of event
- At least 2 countries affected, each with minimum 20 deaths
- Outbreak occuring in at least 1 IBRD/IDA country
- Rolling 12-week confirmed IBRD/IDA cases to be at least 250
- Confirmed IBRD/IDA deaths to be at least 250
Case growth rate above zero for 2 week period containing day when all other criteria met - Confirmation ratio at least 20% for 2-week period containing day when all other criteria met
> investors receive high interest payments IN RETURN for taking on risk for losing money if a pandemic occurs
> however, the bond has STRICT trigger points such that it is designed NOT to e be triggered aka no money directed to affected countries
> was not triggered by ebola, and has delayed triggering for covid-19
> Regional outbreak = 2-7 countries meet criteria
Global outbreak = 8+ countries meet criteria
3
Q
CFs for “selling” a bond
A
“Issuing a bond”
T = 0
> RECEIVE money (equal to the bond’s price, which could be equal to FV, or sold at a discount or premium)
In between 0 and maturity
> pay interest in the form of coupon payments
T = maturity
> PAY back principal (equal to FV) plus interest
4
Q
What is YTM?
A
YTM is AVERAGE RATE OF RETURN to an investor who purchases a bond and holds it until maturity
> once received, coupons are reinvested at YTM
(recall if you don’t reinvest at YTM, you will get a different realized yield)
Po * (1 + ytm)^n = Future Value (par value + reinvested coupons)
5
Q
GLOBAL Bond Market (Debt Market)
> what is the biggest COMPONENT of the bond market (in terms of outstanding amount)?
(different than trading)
A
Biggest component = Private Non-financial sector, aka companies
Then, financial sector and Government
6
Q
Bond Market
> Where is the bulk of daily TRADING concentrated in?
A
Treasury
Then, Agency followed by corporate debt
7
Q
Are stocks or bonds more liquid?
A
Stocks
Bonds are traded OTC and have a larger size per issue than stocks
8
Q
Why do investors invest in bonds?
A
- Bonds are EASIER TO PRICE
> certainty in coupons
> certainty in maturity date
> certainty in par value - Bonds ENHANCE risk-return performance of a portfolio
> offer diversification since bonds have LOW correlation with stocks (e.g. 0.3)
> bonds also had reasonably good returns for substantially LESS RISK
9
Q
Features of bonds (found in bond prospectuses)
Indenture provision
A
“Indenture” refers to the WRITTEN bond contract between the issuer and bondholder, specifying “legal” requirements
> benefits both issuer and bondholder
10
Q
Features of bonds (found in bond prospectuses)
Nonrefunding provision
A
Prohibits the issuer from prematurely retiring a bond by using proceeds from another bond issue (“refunding”)
> benefits bondholder
11
Q
Features of bonds (found in bond prospectuses)
Sinking fund
A
Specifies that a bond must be PAID OFF systematically OVER ITS LIFE (e.g. periodic principal payments) rather than only at maturity
> helps ease the issuer’s burden to repay
benefits bondholder
12
Q
Features of bonds (found in bond prospectuses)
Callable bonds
> higher or lower coupon rate? YTM?
Puttable bond
A
Bonds that enable the ISSUER to pay back its principal early, usually because the issuer can REFINANCE AT A LOWER INTEREST RATE
> to compensate investors for this added risk, callable bonds have HIGHER COUPON RATES and YTM
The opposite is a Puttable Bond, which gives the RIGHT to RECALL to the BONDHOLDER (e.g. right to demand early payment)
13
Q
Features of bonds (found in bond prospectuses)
Secured versus Unsecured bonds
A
Secured bonds are BACKED BY ASSETS (collateral). Secured bondholders get paid first in the event of a bankruptcy or issuer default
> more senior debt
Unsecured bonds are merely backed by a promise and general credit of the issuer
14
Q
Bonds by issuer type
Gov’t Treasury Bonds (“Treasury”)
A
Bonds issued by the NATION’s GOVERNMENT
15
Q
Bonds by issuer type
Gov’t Agency Bonds (“Agency”)
A
Bonds issued by political SUBDIVISIONS of the GOVERNMENT
> better return than Treasury, but slightly more risk
16
Q
Bonds by issuer type
Municipal Bonds
A
Bonds issued by municapls, like states, provinces, city governments, towns, districts
> higher risk than treasury
17
Q
Bonds by issuer type
Corporate Bonds
A
Bonds issued by companies to raise funds
> risk widely ranges from AAA to junk bonds (7% to 30+%)
18
Q
Bonds by issuer type
International Bonds:
- Foreign Bonds
- Eurobonds
A
- Foreign Bonds are bonds issued by foreign entities in LOCAL currency
> Yankee Bonds = any bond issued in the US
> Samurai Bonds = any bond issued in Japan
> Bulldog Bonds = any bond issued in UK - Eurobond are bonds issued in FOREIGN CURRENCY (or issued outside of own country but still in its own currency)
19
Q
Nominal Yield?
A
Coupon rate of the bond
> “nominal” since we usually issue bonds at YTM equal to Coupon rate
20
Q
Yield To Call
A
> applies to Callable Bonds, which are bonds that can be REDEEMED by its issuer BEFORE stated maturity date at a Call Price
happens when IR falls
Call Price is the price at which the issuer buys back the bonds at
(theoretical max price = call price when IR = 0)
To calculate Yield to Call: > replace FV with Call Price > replace Time until Maturity with Time Until Call (N) > SAME price of the bond > Coupons remain the SAME too
Use calculator
21
Q
Current Yield
A
Coupon $ / Current Price
22
Q
Realized Yield
What is the term for actual IR?
A
Can be different from Yield to Maturity due to “surprises” or “REINVESTMENT RISK” (i.e. not knowing what rate coupons will be reinvested at)
Actual IR = “Ex-post” IR
- Calculate the Future value after you reinvest coupons at prevailing 1 year rates with balances rolling forward
> first coupon is reinvested at the END OF YEAR 1 @ rate between 1 and 2
> there is no reinvestment of the last coupon - Bo = price you bought it at
Future Value = what you get
so
Bo = Future Value / (1 + realized yield) ^N
23
Q
When IR decreases and approaches 0, what does the bond price approach?
A
YTM => 0
So, bond price simply approaches the SUM of Coupons and Face Value
24
Q
What is the yield curve?
How can we use yield curves to price bonds?
A
Y axis: YTM
X axis: Maturity
> each point on the yield curve represents a distinct BOND that share SIMILAR CHARACTERISTICS (just differing maturities)
> we use the yield curve for ZERO COUPON BONDS to discount CFs back to 0
The Price of a coupon paying bond can be viewed as a PORTFOLIO of zero coupon bonds
25
What do the shape of yield curves tell you?
Can infer whether short rates are rising or falling
This is because (ignoring inflation and liquidity premiums) when the short rate (aka 1 year forward rate) is GREATER than the spot rates (yn), the next year's spot rate will increase
Fn+1 > Yn
e.g. forward rate for 3 > spot rate for 2
26
Spot rates versus short rates versus forward rates
Does the actual interest rate need to equal the forward rate? Why or why not?
Spot rates = rates prevailing TODAY
> we know what the n-year interest rate will be today
Short rates are 1 year forward rate
> you can determine the EXPECTED future short rate
NO
> the actual interest rate in the future DOES NOT need to equal the forward rate (expected short rate)
> known as REINVESTMENT RISK
27
What are the rates or return in the following strategy:
Buying and holding a 2 year bond versus buying a 1 year bond and reinvesting proceeds in another 1 year bond
SAME Holding Period Return
PROOF:
1. Bo = 1000/(1 + spot)^n
2. B1 = 1000/(1 + f)
3. HPR = (B1 - Bo + 0)/Bo
HPR of buy and hold strategy will give you the SAME return as the roll over strategy (r1 = HPR)
28
Expectations Hypothesis
Forward rate = market expectation of future short rate
> an investor earns the SAME amount if he invests in two consecutive 1 year zero-coupon bonds or invests in one 2 year zero-coupon bond today
> zero liquidity premium
> Long Term Rate is a GEOMETRIC AVERAGE of current and future short term rates over the maturity
i.e.
(1 + r5)^5 = (1 + r1)*(1 + f2)*(1+f3)*(1+f4)*(1+f5)
> therefore, if the yield curve were upward sloping, then this signals that LT rates are higher than ST rates, meaning that ST rates are expected to rise in the future
(which will cause LT rates to increase)
29
Liquidity Preference Theory
> Short Term investors demand a LIQUIDITY PREMIUM for holding LONGER TERM BONDS
> Longer Term Yields are higher than Short Term Yields
> the premium INCREASES with maturity
f2 > E(r2)
f2 = E(r2) + Liquidity Premium
Why?
> Reinvestment risk creates uncertainty about the price of the bond (future actual IR is not known)
> less liquid since you're locking in money for longer time period
Empirical support available
30
Segmented Market Hypothesis
Bonds with DIFFERENT MATURITIES should be viewed SEPARATELY (their markets are separate)
> thus, LT and ST interest rates are NOT related to one another
Weak empirical support, mostly used by practioners
31
Stock Index Futures
Type of settlement
Contract Size in Dollars
> cash settlement
> underlying asset is INDEX
> futures price expressed as index value
E.g. 1,400
So we need to convert from index to $ when calculating PROFITS
> Dollar Value of Index Futures Contract = Contract Size = Value of Index * $ Multiplier
aka $ worth of stock per futures contract
e.g. $250 * 1,400 index level = $350,000 worth of stock
So if I have $140 million to invest, I can purchase 140 million/350 000 = 400 futures contracts
> SP 500's multiplier is $250
32
Index arbitrage
Buy low, sell high
Trying to profit from MISPRICINGS between futures price and theoretically correct parity value
E.g. if futures price is too high:
> Short Futures contract
> Buy stocks in the index
33
Index Futures to Hedge Systematic or Market Risk
PURPOSE:
> costly to rebalance your portfolio to respond to market changes
> so you use futures to hedge your market exposure
Given:
> SP 500 Index current level
> New level of SP 500
> Portfolio Beta
When the SP 500 drops, you expect your portfolio value to drop by beta*% decrease in SP 500
Translate this into dollar terms: % change in port, value * current port. value
To hedge this risk, you can SHORT STOCK INDEX FUTURES (since you are long stocks right now)
> when your portfolio falls in value along with broad market, the futures contract will provide offsetting profit
H = Change in Port. Value/ Change in dollar value of 1 futures contract
34
Hedging Interest rate risk
Perfect hedge?
What is the interest rate exposure of the position after hedging?
Slippage?
> used by fixed-income managers
> hedge interest rate risk and uncertainty from movements in the entire structure of interest rates
> rises in interest rates will cause capital losses
Purpose:
> costly to rebalance your portfolio
> want to lock in yield
Use: Price Value of a Basis Point (PVBP)
> sensitivity of the dollar value of the portfolio to 1 change in basis point
= Change in Port. Value / Change in Basis Points
How to Hedge?
> take offsetting position in INTEREST RATE FUTURES CONTRACT / Bond Futures / Treasury Bond Futures
> has its own modified duration
> has its own futures price which has the same % change as bond price (from - D* x change y)
(assumes T-bond futures contract and bond portfolio move perfectly in unison aka perfect hedge)
> then, you can calculate PVBP = Change in Futures Price / Change in Basis Points
H = PVBP of Port / PVBP of hedge vehicle
= # of futures contracts
*the hedged fixed-income position has a duration or a PVBP = 0 (market neutral)
Slippage happens when the yield spread between the T bond futures and underlying bond is NON-CONSTANT
Therefore, most hedging activity is "cross-hedging" (a hedge vehicle is a different asset than the one to be hedged)
35
Sources Risks of the bonds
What is the credit rating for a junk bond?
> Default risk or counterparty risk (as measured by credit ratings)
BB or B- bond is JUNK BOND
> Interest rate risk (when IR changes, price of bond changes)
> inflation risk
> Reinvestment risk
> call risk (bondholders risk having bonds paid back earlier)
> exchange rate risk (converting foreign currencies back to local currency)
> liquidity risk (from holding longer maturity bonds)
36
Expected Return of a Bond?
Why do we need to split risk free rate into __ and ___
Expected Return of Bond = Real Rf + Inflation Rate + Risk Premium
Recall: Nominal Rate = Real Rate + Inflation
We split the risk free rate into INFLATION RATE and REAL RISK FREE RATE
> equity markets uses "nominal risk free rate" (free of all risk except inflation risk)
Why?
> Bonds have instruments that PROTECT US from inflation risk e.g. treasury bills
> do so by ADJUSTING COUPONS
> higher inflation leads to higher coupons
37
CF signs for creating a "synthetic loan" to LEND
First CF = NEGATIVE
| Second CF = POSITIVE
38
CF signs for creating a "synthetic loan" to BORROW
First CF = POSITIVE
| Second CF = NEGATIVE
39
Determinants of real interest rates?
Supply of capital and Demand of money
SUPPLY driven by: Households and Governments
DEMAND driven by: Businesses and Government
40
What is the magnitude of changes in the bond price from interest rate changes for:
1. Different Maturities
Increasing or decreasing rate of price change?
2. Different Coupons
3. Decrease or increase in IR
4. Different YTM
MORE SENSITIVE = GREATER MAGNITUDE of Price Changes
1. Bonds with LONGER MATURITIES are MORE SENSITIVE to interest rate changes
(get principal back more slowly)
> however, percentage price change increases at a decreasing rate of change
e. g. Impact of 1% interest rate increase on a 10 year versus 20 year versus 30 year bond
- 21% > -26% > -28%
2. SMALL coupons are MORE SENSITIVE to interest rate changes
(get principal back more slowly)
**3. Draw price curve
> IR decreases result in GREATER PRICE INCREASES than equivalent IR increases
4. LOWER YTM leads to HIGHER SENSITIVITY
(inverse relationship between YTM and sensitivity too)
41
Trading Strategies for bondholders / investors facing IR changes (general, not talking about duration or convexity yet)
If you expect IR to fall?
If you expect IR to rise?
*If you expect IR to fall:
> This is GOOD since bond prices will increase
> so we want to maximize bond price appreciation, want bonds that are more sensitive
> Lower coupons (close to 0), longer maturity
If you expect IR to rise:
> BAD because bond prices will fall
> so you want to max protection, want bonds that are less sensitive
> higher coupons, shorter maturity
42
What is Duration?
What is modified duration?
> D refers to Macaulay's duration
> units = years
> measures the weighted average TIME UNTIL payment
(before a bondholder receives the bond's cash flows)
> also a measure of SENSITIVITY (higher duration, greater price change)
(you can think of duration as the balance point of a see saw)
```
t = time of payment (e.g. 0.5, 1)
n = period (for discounting) (e.g. 1, 2)
y = yield per period
```
Modified Duration (D*) = D/(1 + y per period)
43
Rules for Duration
1. What is the duration of a zero coupon bond?
Holding other factors constant...
2. When coupon rate is lower, what happens to duration?
1. Duration of zero-coupon bond equals maturity
2. When coupon rate is lower, weight placed more on the last CF
> therefore to "balance", duration is HIGHER
> akin to lower coupon, increase price sensitivity
44
Rules for Duration (continued)
3. When time to maturity increases, what happens to duration?
4. When YTM decreases, what happens to duration?
3. When time to maturity increases, "board" elongates
> therefore to "balance", duration is 'generally' is HIGHER
> akin to longer term maturity, increase price sensitivity
Caveat: except fo extremely DISCOUNT bonds, where YTM exceeds coupon rate by a low
> duration decreases with maturity
4. When YTM decreases (due to inverse relationship), duration increases
> based on Duration formula (1 + y at the denomin)
45
Trading Strategies for bondholders/investors facing IR changes (duration involved)
If you expect IR to fall?
If you expect IR to rise?
If you expect IR to fall:
> means price will increase, which is GOOD
> max price appreciation, want more sensitive or higher (longer) duration bonds
If you expect IR to rise:
> price will fall, which is BAD
> want to minimize losses or max protection, want less sensitive or shorter duration bonds
46
What is convexity? Why do we need convexity? Does the duration rule under or over estimate what?
Convexity refers to the CURVATURE in the shape of the price-yield curve (bond price as a function of bond yields)
> it is NOT a linear relationship (as approximated by the duration rule)
> when IR decreases, price increases more and more (progressively greater increases in bond price)
> when IR increases, price falls by less and less (progressively smaller decreases in bond price)
> duration rule only works for small changes in YTM, as it tends to UNDERSTATE the value of the bond (overestimate price decreases and underestimate price increases)
47
How does convexity change with:
1. Coupons
2. Maturity
3. YTM
SAME direction as duration!
48
Convexity trading strategy
If you expect IR to FLUCTUATE?
If you expect IR to STABILIZE?
If you expect IR to fluctuate:
> GOOD because convexity results in greater price increases when IR fall and smaller price decreases when IR rise
> buy HIGH convexity bonds to max gain from volatility
If you expect IR to stabilize:
> buy low convexity bonds to minimize price volatility
> also, convexity is costly (accept lower Exp. returns, YTM or pay higher prices)
49
Special negative convexity bonds: Callable bonds
Max price of call bond?
> recall curve (region of negative convexity)
> cannot use duration rule to approximate
> so, we use EFFECTIVE DURATION
= – ( Change in P/P) / Change R
Where:
Change R = Change in Market IR from shift in term structure
= Assumed Increase in rates - assumed decrease in rates
Change P = Price @ increase in rates - Price @ decrease in rates
Max Price of a callable bond = call price
> when IR fall, this increase likelihood of calling it
> price ceiling on price = call price
50
What is negative convexity?
Unattractive asymmetry
> when IR decrease, price don't increase as much
> when IR increase, price fall too much
IR increases causes larger P decreases than equal increase decrease
51
Special negative convexity bonds: Mortgage-backed securities
Max price of mortgage-backed security?
> CFs passed from borrower (homeowner) to lender to federal agency to purchaser of mortgage-back securities
> Cash flows from the underlying MORTGAGE POOL are divided among to TRANCHES
> Tranche A gets the best payment - short pay class
> Tranche B gets next payment - intermediate pay class
> Tranche C gets paid last - long pay class
> when IR drop, homeowners can pay back their loans by issuing new loan at lower IR = REFINANCING their loans
> Therefore, mortgage-backed securities are viewed as a PORTFOLIO of callable, amortizing loans
> Call Price = Remaining Principal Balance
> however, since NOT every homeowner will immediately refinance their loans when IR drop ("inertia effect"), there is no fixed price ceiling like callable bonds
> thus, price of these securities can exceed Call Price (remaining principal balance)
52
What are the bond investment strategies?
1. Passive Investment Strategies (see market prices as correct, however, they differ in the level of risk)
A) Stratification (indexing)
B) Immunization and rebalancing immunized portfolio when yield curve shifts
2. Active Investment strategies - buy low, sell high
53
Bond Indexing (Stratification)
Risk level? Tracking Error?
> try to follow the Bond Index
> it is difficult to fully replicate the bond index (due to there being THOUSANDS of securities and changing composition as bonds MATURE/Turn over)
> therefore, bond index funds hold a "representative SAMPLE" of bonds in the actual index
> known as Stratification
How it works:
> bonds in each subclass (strata) are HOMOGENOUS (similar characteristics, such as sector, time to maturity, credit risk, coupon rate etc.)
> determine PERCENTAGES of bonds in index within each strata
> create bond portfolio with same percentages
> Risk Level = same as bond market index
> performances should also match
> High tracking errors since not purely replicating bond index
54
Immunization
General gist of it
What organizations use immunization strategies?
> seek to establish a ZERO-RISK portfolio (zero interest risk)
> duration of assets match duration (D) of liabilities
> this means that any IR movements have NO impact on firm value
(e.g. questions where term structure increase and decrease and you see impact on net position = PV Assets - PV liabilities)
Immunization strategies used by:
A. Banks - want NET WORTH
B. Pension funds - have a future obligation (liability), so they need to ensure they have sufficient funds to pay off that liability (via assets!)
55
Immunization
What's a GIC?
Guaranteed Investment Contract
> like a zero coupon bond
> issued by insurance company to its customers
> liability for insurance company
56
Rebalancing immunized portfolio?
> rebalancing occurs when there is a change in interest rates, or passage of time (decrease in time to maturity)
> affects duration
Is the position still immunized?
> check new PV of obligation and assets
= PV (1 + interest rate)
Do the weights need to change? (likely since duration changed)
1. find new duration of obligation
2. find new durations of assets (could be zero coupon bonds or perpetuities or other)
3. solve for new weights
4. find new amounts that need to be invested (PV)
* incur transaction costs
57
Active Bond Investment
> goal is to OUTPERFORM the market (e.g. better predict interest rate movements and IDENTIFY MISPRICINGS between 2 bonds or portfolios)
> idea is to BUY LOW, SELL HIGH
Include:
1. Substitution swap
2. Intermarket swap
3. Rate anticipation swap
4. Pure yield pickup
5. Tax swap
58
Active Bond Investment:
Substitution Swap
E.g. 6% coupon Toyota bond with YTM of 6.05% (same maturity)
6% coupon Honda bond with YTM of 6.15% (same maturity)
Belief that the market has temporarily MISPRICED the two bonds ($ or YTM)
> involves buying low priced bonds, and selling high priced bonds
> exchange one bond for a nearly IDENTICAL SUBSTITUTE
(equal coupon, maturity, quality, call features, sinking fund provisions, credit risk etc.)
E.g.
Honda bond has higher YTM and LOWER PRICE
So, you buy Honda bond, sell Toyota bond
59
Active Bond Investment:
Intermarket Spread Swap
E.g. Yield Spread between 10-year Treasury bonds and 10-year Baa-rated corporate bonds is NOW 3%. Historical spread has been 2%.
> Discrepancy in yield spread between two SECTORS of the bond market
> buy low price, sell high price
> spread is different than HISTORICAL levels (either wider or narrower)
> eventually the spread will RETURN to HISTORICAL LEVELS
e.g. corporate and government bond yield spread
> shift from one bond sector to another sector
Higher Yield - Lower Yield (safer bond) = Yield Spread
Ex:
> spread is WIDER than historical levels and will eventually narrow
Baa-rated yield - Treasury = 3%
> profit from this movement
> buy higher yield or Baa-rated @ lower price (expect yield to fall or price to rise)
> sell Treasury
60
Active Bond Investment:
Rate anticipation swap
> swap is pegged to IR forecasting
> if Investors believe IR will FALL, they will swap into LONGER DURATION BONDS of same credit risk
(when IR fall, want to max price appreciation, so want greater sensitivity to IR or longer duration)
> if Investors believe IR will RISE, they want to max protection, so they will want less sensitive, and swap into shorter duration bonds
61
Active Bond Investment:
Pure yield pickup
> not pursued in response to perceived mispricing
> swap to increase return by HOLDING HIGHER YIELD BONDS
When yield curve is upward sloping, move into LONGER TERM BONDS
> want premium
> willing to bear IR risk
> earn higher rate of return as long as yield curve does not shift up during holding period
62
Active Bond Investment:
Tax Swap
> swap to exploit TAX ADVANTAGE
> e.g. realization of capital losses if advantageous for tax purposes
63
Forward contracts versus Futures contracts
Differences?
Similarities?
1. Liquidity
> Forward contracts are traded OTC
> Futures contract are traded on an exchange, and are more liquid
2. Customization
> Forward contracts are highly customized and between two parties (in terms of quality, quantity/contract size, delivery date)
> Futures contracts are standardized
3. Counterparty or default risk
> Forward contracts have high counterparty risk
> Futures contracts have zero counterparty risk (since both parties have to put up collateral or margin, and there is a clearinghouse)
4. Delivery date
> Forward contracts have 1 delivery date (settlement at maturity)
> Futures contracts have multiple delivery dates (daily settlement called Marking to Market) - settlement prior to maturity
5. Delivery
> Forward contracts involve delivery of the asset or final cash
> Futures contracts involve closing out position
6. Time Value of Money
> futures contracts have a component of time value of money
SIMILARITIES:
> no money changes hands at time 0 (just entering into commitment)
> initial "value" of the contract is zero
> derivatives is a ZERO SUM GAME (one party profits when price changes, one party suffers loss)
64
What is the meaning of:
Long Forward
Short Forward
Buying Bond
Selling Bond
Buying Loan Contract
Selling Loan Contract
Long Forward:
> obligation to ACCEPT DELIVERY of asset at time T
> pay delivery price in exchange for asset
> purpose is to hedge against rise in asset prices
Short Forward:
> obligation to DELIVER asset at time T
> receive delivery price in exchange for asset
> purpose is to hedge against fall in asset prices
```
Buying BOND (like selling a loan): investor
> initial CF = negative (to purchase bond)
> terminal CF = positive (receive principal)
```
```
Selling BOND (like buying a loan): borrower
> initial CF = positive (inflow)
> terminal CF = negative (return principal and interest)
```
Buying LOAN Contract: Borrower
(e.g. buying forward loan contract)
> initial CF = positive
> terminal CF = negative
Selling LOAN Contract: Investor
> initial CF = negative (lending out)
> terminal CF = positive
65
Examples of Futures contracts that are listed and traded
```
CBT (exchange)
(fixed-income, agriculture)
> 30-year U.S. treasury
> 10-year U.S. treasury
> municipal bond index
> corn
> soybeans
> wheat
```
('B' comes before 'M')
```
CME (exchange)
(stocks, currency)
> SP 500 index
> NASDAQ 100 index
> Eurodollars
> Nikkei 225
> Pork bellies
> Heating and cooling degree-days
> Japanese Yen
```
```
NYMEX
(natural resources, minerals)
> crude oil
> natural gas
> heating oil
> gasoline
> gold
> copper
> electricity
```
66
Futures: Marking to Market (daily settlement)
```
Time 0?
Day 1?
Day 2?
Day T?
Net Long Position?
Net Short Position?
```
What is the relationship between the futures price and spot price at maturity?
Time 0:
> set F0,T
(as futures prices change, profits accrue daily - either credit margin account or debit/take away from margin account)
Day 1:
> Short Party gets: Fo,T - F1,T
> Long Party get: F1,T - Fo,T
Day 2:
> Short Party gets F1,T - F2,T
> Long Party gets F2,T - F1,T
...
Day T: CASH SETTLEMENT (closing out)
> Short Party gets F(T-1,T) - ST
> Long Party gets ST - (FT-1,T)
**On the contract maturity date, the futures price will EQUAL the spot price of the asset (since a MATURING contract calls for immediate delivery, the futures price on that day must equal the spot price).
> called Convergence Property
> basis risk (F - Spot) = 0
NET LONG POSITION
= ST - F(o,T)
NET SHORT POSITION
= F(o,T) - ST
> Sum of Daily Gains/Losses = Cumulative Gains/Losses = (FT - Fo)*# of Assets
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Manufacturing Forward Contract (long)
"Synthetic forward"
Time 0: Borrow and buy
> Borrow $ (+)
> use borrowed money to Buy Asset (-)
Net CF = 0
Time T:
> Asset worth ST (+)
> Pay back loan (-)
*similar CFs to entering in long forward contract
> 0 CF at time 0
> Take delivery of asset at T, while paying delivery price EQUAL TO LOAN
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Manufacturing Forward Contract (short)
"Synthetic forward"
Time 0: Short and invest
> Short asset (+)
> Invest proceeds in MM account (-)
Net CF = 0
Time T:
> liquidate MM account (+)
> buy back stock @ ST (-)
> return stock to broker
*similar CFs to entering in short forward contract
> 0 CF at time 0
> receive delivery price EQUAL to investment, deliver asset at T
69
Arbitrage using forward and futures
1. Quoted Forward price is LOWER than equilibrium Forward price
2. Quoted Forward Price is HIGHER than equilibrium Forward price
General principle: Buy Low, Sell High
Mispricing from forward price (or differences in spot or futures MARKET)
Strategy 1: Buy Forward, Sell Synthetic Forward
> Buy forward contract
> Sell manufactured or synthetic forward
Strategy 2: Sell Forward, Buy Synthetic Forward
> Sell Forward
> Buy manufactured version
70
Hedging for Underlying Asset Position with Forward:
What is hedging?
Examples of hedging with derivatives
Hedging is about eliminating or reducing risk exposure from price movements (e.g. unknown ST, IR) by taking the OPPOSITE position
> e.g. decrease in prices for sellers would generate a PROFIT on futures contracts that offset lower sales
> therefore, you are LOCKING in selling or purchasing price
> total hedging involves "flat" payoff graph, so position doesn't get affected by changes in underlying source of risk
1. Total Hedging
2. Partial Hedging
3. Hedging Systematic Risk
4. Hedging Interest Rate Risk
71
Total Hedging
> FULLY or EXACTLY able to hedge away risk
> futures written on SAME underlying asset
> therefore, you are LOCKING in selling or purchasing price (it doesn't matter whether prices increase or decrease, your combined position will result in the same profit in any scenario)
Involves:
T = 0
> buy asset
> short futures
Final payoff is KNOWN at time T = Fo,T, which is INDEPENDENT OF ST
PT + (Fo - Pt) = Fo
** Sellers are LONG assets, so they go SHORT in the forward or futures contract (protect against price declines)
Buyers are SHORT assets, so they go LONG in the forward or futures contract (protect against price rises)
72
Partial hedging
What does H mean in this case?
"Cross hedging"
> hedging a position using futures on ANOTHER ASSET
> imperfect hedge
> find contracts with high CORRELATION with underlying asset to establish hedge
Hedge Ratio = NOT # of contracts (in this case!)
> "optimal hedge ratio" = "minimum variance hedge ratio"
> ratio of futures position relative to spot position that MINIMIZES the variance of the position
> also the SLOPE of the regression line between spot position returns and future position returns
"h percent of size of spot position should be hedged= size of futures position"
H = [ STD(delta S) / STD(delta F) ] x p
STD of change in spot price
STD of change in futures price
p is the correlation coefficient between changes in spot price and changes in futures price
THEN:
of Contracts = h* x (size of underlying portfolio in units / size of 1 futures contract in units)
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Hedge Ratio (H) ***
Slightly different terminology in forward/futures versus options
FORWARDS/FUTURES:
Numerator = How much is your underlying EXPOSURE to Risk (e.g. portfolio, stock)
Denominator = How much PROTECTION forward/futures provides
H = how many CONTRACTS you need to buy or short
1. Optimal Hedge (cross hedging/partial hedging)
> % of risk exposure that should be optimally hedged
> e.g. H = 0.6 means 60% of spot position size should be hedged
2. Hedging systematic risk
> e.g. H = # of index futures contracts
> round up or down, resulting in over- or under- hedge
3. Hedging IR risk
> e.g. H = # of bond futures contracts
> round up or down, resulting in over- or under- hedge
OPTIONS:
H = how much protection do you get
> almost like the reciprocal of forward/futures (underlying exposure is in denim)
4. H = N(d1) = Change in Option Price when underlying asset increases by $1
H = Delta = Change in Value of Option/Change in Value of Stock
= % of Stock that needs to get bought or sold
= % of protection offered by option (will be less than 100%)
Then, you need to purchase more than one option in order to be delta neutral
H * # of options = 1
> positive for calls
> negative for puts
> Portfolio Insurance
> Delta neutral/Delta Hedging
74
Hedging Systematic Risk with Stock Index Futures
Basic idea?
What is the goal?
Basic Idea:
> portfolio has systematic risk (non-zero beta)
> when the index (market) changes in value, the portfolio also changes
(increase in index value increases port value, decrease in index value decreases port value)
> therefore, use stock index futures to hedge
Goal: find # of futures contracts to hedge position (either short or long)
> when index changes by x%, portfolio value will change by Beta*x%
**converting index level to dollar value = multiply level by $250 for SP 500
75
Hedging IR risk with Bond Futures (and other IR futures)
Basic Idea?
Risk after hedge?
Difference between Hedging with Bond Futures and Immunization with bonds?
Basic Idea:
> worried about IR risk - either increasing or decreasing (more so fearful of IR Increases)
> If IR INCREASES, causes bond PRICES to decrease
How to hedge?
> use IR futures like T Bond futures contract
> need to know PVBP (Price Value of a Basis Point) = Dollar Change in Portfolio value per change in basis point
> drive IR exposure to 0 => "Market Neutral Strategy"
> However in practice, this will be an IMPERFECT HEDGE due to SLIPPAGE (non-constant yield spread between T-Bond and Underlying Bond Asset)
Difference?
> Immunization involves the use of another bond to hedge IR risk of a particular bond
> Bonds Futures is a derivative on any underlying bond portfolio
76
Call and Put Options - Holder versus Writer
Call Option:
> option holder has the RIGHT to PURCHASE underlying asset @ strike price (quoted per share) at future point in time (on or after maturity, depends on whether it's an American or European option)
> holder purchases a call option @premium (option value) to protect against price increases
> Writer receives premium and has opposite payoff structure to call option holder
Put Option:
> option holder has the RIGHT to SELL underlying asset @ strike price (quoted per share) at future point in time (on or after maturity)
> holder purchases put option @premium (option value) to protect against price decreases
> Writer receives premium and has opposite payoff structure to put option holder
*Writer has the OBLIGATION to take the other side of the transaction if the holder exercises the option
> Writer is the "seller" of the options
> Holder is the "purchaser" of the options
77
Which are more expensive: American or European options
American -> holder has the flexibility to exercise at any point before or on maturity
78
Where are options traded?
| Types of underlying assets of options? (or the different types of options)
> Centralized exchanges
```
Types of underlying assets tend to be FINANCIAL SECURITIES rather than commodities and physical assets, such as:
> index
> stocks
> futures
> foreign currency
> IR
```
79
What is the Put Call Parity?
> shows the relationship between call and put prices on the SAME underlying asset, having the same strike and expiration date
> both sides of the relationship show "protective put"
Call + T bill with Future Value equal to Strike
Put + Underlying Asset
80
Option Pricing = Premium = Value
What are sources of option's value?
1. Intrinsic Value
> immediate exercise value
> Call IV = ST - K
> Put iV = K - ST
2. Time Value
> Difference between Option Price and Intrinsic Value
> "Volatility value"
> With greater time to expiration, more probability for stock price to move in the desired direction
> at expiration, time value = 0
81
Black Scholes Option Pricing for European Options
You know the formula - what does the output give you?
How do you scale?
What else does the formula show you?
Output of the BSM formulas is the option price PER SHARE
Scaling?
1 Option Contract = x # of shares
So, Option Contract Costs = Option Value by BSM * # of Shares per contract
> most contracts represent 100 shares
Then, figure out how many contracts you need based on how many shares you own
Positive drift in prices over time
82
What is N(d1)?
What is N(d2)?
Hedge Ratio
> Change in the Option Price when Underlying Asset Increases by $1
> Call options have positive H
> Put option have negative H (when stock increases by $1, decreases put option's value, so lower price)
N(d2) = probability that the option is exercised
83
Comparative Statistics for Options:
When ST increases, what happens to C0 and P0?
> C0 increases
> P0 decreases
(think about payoff formula, ST - K or K - ST)
84
Comparative Statistics for Options:
When X increases, what happens to C0 and P0?
> C0 decreases
| > P0 increases
85
Comparative Statistics for Options:
When risk free rate increases, what happens to C0 and P0?
> Call: PV(X) decreases, so C0 increases
| > Put: PV(X) decreases, so P0 decreases
86
Comparative Statistics for Options:
When time to maturity increases, what happens to C0 and P0?
> Call:
1. PV(X) decreases, so C0 Increases
2. Greater % to move in desired direction
> C0 increases
> Put:
1. PV(X) decreases, so P0 decreases
2. Greater % to move in desired direction
> CONFLICTING FORCES, P0 UNSURE
87
Comparative Statistics for Options:
When volatility increases, what happens to C0 and P0?
Both C0 and P0 increase (more opportunity to move in desired direction)
88
Finding Intrinsic Value of Equity using BSM
Basic Idea?
> Firm's equity is valued as a CALL OPTION (only get payoff after firm's debtholders are paid)
> Face Value of Debt = strike
> T = duration
> So = Firm Value or Asset's Market Value
> vol = portfolio equation
89
Arbitrage with Options
Basic idea?
Mispricing from put-call parity
What do you do if put-call parity is VIOLATED:
> buy low cost COMBO
> sell high cost COMBO
By COMBO I mean the Call + Rf and Put + Stock
> at T, payoffs in EITHER SCENARIO (ST greater or less than strike) equal 0 => No RISK!
90
(Delta) Hedging with Options
Portfolio Insurance
Limitations of trying to insure a portfolio of stocks?
Delta Hedging
Portfolio Insurance - limiting the worst case portfolio rate of return by establishing a protective put position
> Long position in both put and stock creates a protective put
> unlimited upside potential, minimum downside protection
> guaranteed payoff = Put option's exercise price (X)
(you are holding a stock and the put contract gives you the right to sell the stock @ X)
> investor's max loss = when put is not exercised = cost of put
Limitations:
> imperfect match creates tracking error (e.g. index puts are used for non-indexed portfolio)
> maturities of put options may be too short for the investors horizon
> hedge ratios or deltas CHANGE as stock value changes -> dynamic rebalancing needed
91
(Delta) Hedging with Options
Delta Neutral?
Delta Neutral is a POSITION where the delta equals 0
> the position is HEDGED AGAINST fluctuations in the price of the underlying asset via use of options
> however, when underlying asset price changes, delta changes => need adjustments to portfolio
For put options, each option will PROTECT H units of the underlying asset
92
(Delta) Hedging with Options
Synthetic and actual protect put positions?
> have the same payoff (equal returns)
> synthetic protective position involves selling H units of stock and placing proceeds in cash equivalents, like T bills which are risk free and don't change
93
(Delta) Hedging with Options
Cross Option Speculation (another example of arbitrage)
> two CALL options with different K are priced differently
> based on the K, T, So, and option prices, you can determine each option's implied vol
> e.g one is at 27% and the other is at 33%
> if the equilibrium vol is 30%, there is clearly a discrepancy = opportunity for ARBITRAGE
Strategy: Buy low priced (27% vol) and sell high priced (33% vol)
Question becomes: how much of each option do you sell in order to also establish a delta neutral position?
> the 33% vol call option has a lower N(d1) or protection, so you need MORE of this option to create delta neutral position
H = how many 33% vol call options to sell = Delta of call option you long / Delta of call option you short
= N(d1) / N(d1)
*for puts, I think it's N(d1) - 1 / N(d1) - 1
Ans: X units of shorted call option for every 1 option you long
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Cases
Understand case
> what did we discuss in class
> interesting points we brought up
95
General picture of Singapore's investment
environment
Overview of investable assets?
1. Equities
> stocks, funds (mutual funds, unit trusts, ETFs, REITs)
> other OTC products (structured deposits, traded life policies, investment linked insurance policies)
2. Bonds
> T bills, Gov't Bonds (Singapore Government Securities, SGS)
> Gov't agency Bonds (quasi-government bonds)
> Corporate Bonds
> Bond ETFs (allow people to buy more DIVERSIFIED BOND portfolios)
3. Derivatives
> Futures
> Options
> OTC interest rate swaps
96
General picture of Singapore's investment
environment
Singapore's Stock Market capitalization relative to G20 countries and rest of Asia?
Cap relative to G20:
> not the smallest nor the largest (larger than Italy, Russia, Indonesia, Turkey, Mexico, Saudi Arabia, and Argentina)
> biggest equity markets are US by a long shot, China, then Japan
Cap relative to Asia:
> #5 largest among ASEAN countries
(behind China, Japan, Hong Kong, and South Korea)
97
General picture of Singapore's investment
Singapore's Bond Market trend in Outstanding Amount
> largest to smallest components
> increasing or decreasing?
```
Outstanding Amount:
> Largest Size (aka biggest component) = Non-SGD Corp
> Then, SGD Corp
> Then SGS or Gov't Bonds
> Then T-Bills
```
Trends:
> Non SGD Corp bonds has been INCREASING over time (more companies coming to Singapore to raise debt)
> Gov't Bond sector is stable
> DECLINE in outstanding amount of T-bills (saw a rise during 2008 financial crisis, then decline)
98
General picture of Singapore's investment
```
Singapore's Financial Innovations: Singapore Savings Bond
> minimum denomination?
> Max investment size
> how does it work?
> max maturity?
> secondary market trading?
> great for which types of investors?
> risk compared to banks
```
1. Singapore Savings Bond
> Launched in 2015 (relate back to sudden drop in T-bill issuances)
> works like a gov't bond (SGS bond)
> put money in these bonds (minimum denomination is $500)
> **you earn HIGHER interest the LONGER you hold these bonds
(increasing interest rates rather than constant!)
> max # of years you can hold these bonds is 10 years
> no secondary market trading
> great for retail investors
> max is 50,000 for each of the 4 savings bonds
> total investment cannot exceed $100k
> LOWER RISK compared to investing with bank
99
General picture of Singapore's investment
AUM in Singapore?
Investment of Funds by Asset Classes?
Sources of Funds by Region?
Investment of Funds by Region?
Concluding thoughts?
2014: SGD 2200 b
Investment of Funds by Asset Classes:
1. Equities (50%)
2. Bonds (21%)
Sources of Funds by Region:
1. Asia Pacific (54%)
2. Europe (19%) and NA (18%)
Investment of Funds by Region:
1. Asia Pacific (68%)
2. Europe
3. North America
Conclusion:
> Singapore attracts funds from everywhere, but they aren't staying in Singapore market
> Singapore is a hub that allows professional money managers to manage their funds IN SINGAPORE, but money goes out to rest of Asia Pacific and world
100
General picture of Singapore's investment
Time Trend of Financial Assets:
Market Cap of SGX Equities as a % of GDP?
Why?
Market Cap EXCEEDS Singapore's GDP
2018: 191%
(has varied from 191 to 262% over past five years)
Why?
> GDP is a PER YEAR measurement, whereas market cap reflects PV of future cash flows
> Market Cap could also include FOREIGN COMPANIES
101
General picture of Singapore's investment
Time Trend of Financial Assets:
Total Market Turnover? $ and %?
Why?
Total Market Turnover = Value of Total Shares Traded / Capitalization
= 299,257 million or ~30% turnover (Turnover / market cap)
Why?
> Singapore's equity market is NOT that active
102
General picture of Singapore's investment
Time Trend of Financial Assets: Insights from bonds?
> Singapore's government runs a POSITIVE BUDGET SURPLUS , so they DON'T NEED to issue that many bonds (i.e. don't need to raise debt)
> Singapore's government also has HIGH CAPACITY to pay off outstanding bonds (relative to equity)
> Gov't still issues bonds to set up PRICING BENCHMARK
> SG has more non-SGD denominated corporate bonds (eurobonds) than SGD denominated bonds
103
General picture of Singapore's investment
Singapore's Bond Market trend in Issuance Volume
> increasing or decreasing?
> ratio of Non SGD and SGD debt between Outstanding Amount and Issuance Volume
> T bills saw sharp DECLINE in new issuance after 2008-2011
> Large difference in the ratio of Non SGD and SGD in terms of Outstanding amount and Issuance volume
(2:1 versus 10:1)
> more Non SGD bonds being issued
> a lot of foreign companies issuing SHORT TERM DEBT
104
General picture of Singapore's investment
Singapore's Bond Market
SGD-denominated Debt issuer's Profile
2018:
> Largest came from Government Agency/Statutory Boards such as HDB, PUB (public utilities board), LTA (land transport authority), BCA (building construction authority), GTC
> Then, Financial Institutions
> Then Corporations
(DIFFERENT THAN GLOBAL)
105
General picture of Singapore's investment
Singapore's Bond Market
Non-SGD-denominated Debt issuer's Profile
> LARGELY (80.3%) Financial Institutions
| > then corporations
106
General picture of Singapore's investment
Singapore's Bond Market
Why would Corporations in the PROPERTY sector issue more SGD-denominated bonds than non-SGD bonds?
> Property sector involves building and selling houses IN SINGAPORE
> revenues and costs are all denominated in SGD
> so it makes sense to also issue debt in same currency
107
General picture of Singapore's investment
Credit Ratings of Outstanding SGD Bonds (% between rated and unrated)
% Rated is LESS than % Unrated (40-60)
> costly to get credit rating, so many companies don't have an idea of their credit risk
> despite subsidies, it is still costly to get credit ratings
108
General picture of Singapore's investment
Singapore's Financial Innovations: Green Bond
> Supports environmental friendly projects such as reducing CO2 emissions
> Launched in 2017: Green Bond Grant Scheme
> 2019: size of green bond market SGD 6 billlion
109
General picture of Singapore's investment
Singapore's Financial Innovations: Sustainable Bond Scheme
> what is it?
> two major focuses of MAS and Central Bank?
> 2019: Expanded Green Bond Grant Scheme to include SOCIAL and SUSTAINABILITY bonds
> Renamed as Sustainable Bond Grant Scheme
> will be in place until May 2023
> gives out LARGER SUBSIDIES and LOWER MIN ISSUANCE SIZE to include bonds issued for SOCIAL PROJECTS (e.g. helping underprivileged children and elderly)
Two Main Focuses:
1. Fin Tech
2. Sustainability
110
Two bonds in the same industry, with same risk, different coupon rates, but same maturity
Which one do you choose to maximize your return for x number of years?
Compare YTM
111
Which bond(s) among the given four bonds will you choose if you expect future interest rate to decrease? Why?
Need to pick highest duration bond
112
Long-term treasury bonds are currently selling at YTM = 6%. You EXPECT IR TO FALL. Which bond would you choose to maximize your HPR over the next year if you are correct?
Option 1: A Baa-rated bond with coupon rate 6% and Time to Maturity 20 years?
Option 2: An Aaa-rated bond with coupon rate of 6% and Time to Maturity 20 years
Only difference is riskiness
If you expect IR to fall, choose bonds with greater sensitivity (higher duration, low coupons, longer maturity, low YTM)
Baa-rated bonds have HIGHER YTM
Therefore, choose the Aaa-rated bond because it has LOWER YTM
113
In what ways is owning a corporate bond similar to a writing a put and call opion?
Recall valuing firm and its equity
Call Option:
> bondholders write a call option to equity holders
> equity holders have the right to claim value of firm after B dollar debt
Put Option:
> bondholders write a put option, making them obligated to pay B dollars debt (e.g. having their loans cancelled) in return for a firm worth V
> this happens in cases when the firm's value is lower than B debt
