An Arbitrage Guide to Financial Markets By Robert Dubil

An Arbitrage Guide to Financial Markets
By Robert Dubil

Sample Pages

Contents

1 The Purpose and Structure of Financial Markets 1
1.1 Overview 1
1.2 Risk sharing 2
1.3 The structure of financial markets 8
1.4 Arbitrage: Pure vs. relative value 12
1.5 Financial institutions: Asset transformers and broker-dealers 16
1.6 Primary and secondary markets 18
1.7 Market players: Hedgers vs. speculators 20
1.8 Preview of the book 22

Part One SPOT 25
2 Financial Math I—Spot 27
2.1 Interest-rate basics 28
Present value 28
Compounding 29
Day-count conventions 30
Rates vs. yields 31
2.2 Zero, coupon and amortizing rates 32
Zero-coupon rates 32
Coupon rates 33
Yield to maturity 35
Amortizing rates 38
Floating-rate bonds 39
2.3 The term structure of interest rates 40
Discounting coupon cash flows with zero rates 42
Constructing the zero curve by bootstrapping 44
2.4 Interest-rate risk 49
Duration 51
Portfolio duration 56
Convexity 57
Other risk measures 58
2.5 Equity markets math 58
A dividend discount model 60
Beware of P/E ratios 63
2.6 Currency markets 64

3 Fixed Income Securities 67
3.1 Money markets 67
U.S. Treasury bills 68
Federal agency discount notes 69
Short-term munis 69
Fed Funds (U.S.) and bank overnight refinancing (Europe) 70
Repos (RPs) 71
Eurodollars and Eurocurrencies 72
Negotiable CDs 74
Bankers’ acceptances (BAs) 74
Commercial paper (CP) 74
3.2 Capital markets: Bonds 79
U.S. government and agency bonds 83
Government bonds in Europe and Asia 86
Corporates 87
Munis 88
3.3 Interest-rate swaps 90
3.4 Mortgage securities 94
3.5 Asset-backed securities 96

4 Equities, Currencies, and Commodities 101
4.1 Equity markets 101
Secondary markets for individual equities in the U.S. 102
Secondary markets for individual equities in Europe and Asia 103
Depositary receipts and cross-listing 104
Stock market trading mechanics 105
Stock indexes 106
Exchange-traded funds (ETFs) 107
Custom baskets 107
The role of secondary equity markets in the economy 108
4.2 Currency markets 109
4.3 Commodity markets 111

5 Spot Relative Value Trades 113
5.1 Fixed-income strategies 113
Zero-coupon stripping and coupon replication 113
Duration-matched trades 116
Example: Bullet–barbell 116
Example: Twos vs. tens 117
Negative convexity in mortgages 118
Spread strategies in corporate bonds 121
Example: Corporate spread widening/narrowing trade 121
Example: Corporate yield curve trades 123
Example: Relative spread trade for high and low grades 124
5.2 Equity portfolio strategies 125
Example: A non-diversified portfolio and benchmarking 126
Example: Sector plays 128
5.3 Spot currency arbitrage 129
5.4 Commodity basis trades 131

Part Two FORWARDS 133
6 Financial Math II—Futures and Forwards 135
6.1 Commodity futures mechanics 138
6.2 Interest-rate futures and forwards 141
Overview 141
Eurocurrency deposits 142
Eurodollar futures 142
Certainty equivalence of ED futures 146
Forward-rate agreements (FRAs) 147
Certainty equivalence of FRAs 149
6.3 Stock index futures 149
Locking in a forward price of the index 150
Fair value of futures 150
Fair value with dividends 152
Single stock futures 153
6.4 Currency forwards and futures 154
Fair value of currency forwards 155
Covered interest-rate parity 156
Currency futures 158
6.5 Convenience assets—backwardation and contango 159
6.6 Commodity futures 161
6.7 Spot–Forward arbitrage in interest rates 162
Synthetic LIBOR forwards 163
Synthetic zeros 164
Floating-rate bonds 165
Synthetic equivalence guaranteed by arbitrage 166
6.8 Constructing the zero curve from forwards 167
6.9 Recovering forwards from the yield curve 170
The valuation of a floating-rate bond 171
Including repo rates in computing forwards 171
6.10 Energy forwards and futures 173

7 Spot–Forward Arbitrage 175
7.1 Currency arbitrage 176
7.2 Stock index arbitrage and program trading 182
7.3 Bond futures arbitrage 187
7.4 Spot–Forward arbitrage in fixed-income markets 189
Zero–Forward trades 189
Coupon–Forward trades 191
7.5 Dynamic hedging with a Euro strip 193
7.6 Dynamic duration hedge 197

8 Swap Markets 199
8.1 Swap-driven finance 199
Fixed-for-fixed currency swap 200
Fixed-for-floating interest-rate swap 203
Off-market swaps 205
8.2 The anatomy of swaps as packages of forwards 207
Fixed-for-fixed currency swap 208
Fixed-for-floating interest-rate swap 209
Other swaps 210
Swap book running 210
8.3 The pricing and hedging of swaps 211
8.4 Swap spread risk 217
8.5 Structured finance 218
Inverse floater 219
Leveraged inverse floater 220
Capped floater 221
Callable 221
Range 222
Index principal swap 222
8.6 Equity swaps 223
8.7 Commodity and other swaps 224
8.8 Swap market statistics 225

Part Three OPTIONS 231
9 Financial Math III—Options 233
9.1 Call and put payoffs at expiry 235
9.2 Composite payoffs at expiry 236
Straddles and strangles 236
Spreads and combinations 237
Binary options 240
9.3 Option values prior to expiry 240
9.4 Options, forwards and risk-sharing 241
9.5 Currency options 242
9.6 Options on non-price variables 243
9.7 Binomial options pricing 244
One-step examples 244
A multi-step example 251
Black–Scholes 256
Dividends 257
9.8 Residual risk of options: Volatility 258
Implied volatility 260
Volatility smiles and skews 261
9.9 Interest-rate options, caps, and floors 264
Options on bond prices 265
Caps and floors 265
Relationship to FRAs and swaps 267
An application 268
9.10 Swaptions 269
Options to cancel 270
Relationship to forward swaps 270
9.11 Exotic options 272
Periodic caps 272
Constant maturity options (CMT or CMS) 273
Digitals and ranges 273
Quantos 274

10 Option Arbitrage 275
10.1 Cash-and-carry static arbitrage 275
Borrowing against the box 275
Index arbitrage with options 277
Warrant arbitrage 278
10.2 Running an option book: Volatility arbitrage 279
Hedging with options on the same underlying 279
Volatility skew 282
Options with different maturities 284
10.3 Portfolios of options on different underlyings 284
Index volatility vs. individual stocks 285
Interest-rate caps and floors 286
Caps and swaptions 287
Explicit correlation bets 288
10.4 Options spanning asset classes 289
Convertible bonds 289
Quantos and dual-currency bonds with fixed conversion rates 290
Dual-currency callable bonds 291
10.5 Option-adjusted spread (OAS) 291
10.6 Insurance 292
Long-dated commodity options 293
Options on energy prices 294
Options on economic variables 294
A final word 294

Appendix CREDIT RISK 295

11 Default Risk (Financial Math IV) and Credit Derivatives 297
11.1 A constant default probability model 298
11.2 A credit migration model 300
11.3 Alternative models 301
11.4 Credit exposure calculations for derivatives 302
11.5 Credit derivatives 305
Basics 306
Credit default swap 306
Total-rate-of-return swap 307
Credit-linked note 308
Credit spread options 308
11.6 Implicit credit arbitrage plays 310
Credit arbitrage with swaps 310
Callable bonds 310
11.7 Corporate bond trading 310

Index 313

1 The Purpose and Structure of Financial Markets

1.1 OVERVIEW

Financial markets play a major role in allocating wealth and excess savings to productive ventures in the global economy. This extremely desirable process takes on various forms. Commercial banks solicit depositors’ funds in order to lend them out to businesses that invest in manufacturing and services or to home buyers who finance new construction or redevelopment. Investment banks bring to market offerings of equity and debt from newly formed or expanding corporations. Governments issue short- and long-term bonds to finance construction of new roads, schools, and transportation networks. Investors-bank depositors and securities buyers-supply their funds in order to shift their consumption into the future by earning interest, dividends, and capital gains.

The process of transferring savings into investment involves various market participants: individuals, pension and mutual funds, banks, governments, insurance companies, industrial corporations, stock exchanges, over-the-counter dealer networks, and others. All these agents can at different times serve as demanders and suppliers of funds, and as transfer facilitators.

Economic theorists design optimal securities and institutions to make the process of transferring savings into investment most efficient. ‘‘Efficient’’ means to produce the best outcomes-lowest cost, least disputes, fastest, etc.-from the perspective of security issuers and investors, as well as for society as a whole. We start this book by addressing briefly some fundamental questions about today’s financial markets. Why do we have things like stocks, bonds, or mortgage-backed securities? Are they outcomes of optimal design or happenstance? Do we really need ‘‘greedy’’ investment bankers, securities dealers, or brokers soliciting us by phone to purchase unit trusts or mutual funds? What role do financial exchanges play in today’s economy? Why do developing nations strive to establish stock exchanges even though often they do not have any stocks to trade on them?

Once we have basic answers to these questions, it will not be difficult to see why almost all the financial markets are organically the same. Like automobiles made by Toyota and Volkswagen which all have an engine, four wheels, a radiator, a steering wheel, etc., all interacting in a predetermined way, all markets, whether for stocks, bonds, commodities, currencies, or any other claims to purchasing power, are built from the same basic elements.

All markets have two separate segments: original-issue and resale. These are characterized by different buyers and sellers, and different intermediaries. They perform different timing functions. The first transfers capital from the suppliers of funds (investors) to the demanders of capital (businesses). The second transfers capital from the suppliers of capital (investors) to other suppliers of capital (investors). The original-issue and resale segments are formally referred to as:

* Primary markets (issuer-to-investor transactions with investment banks as intermediaries in the securities markets, and banks, insurance companies, and others in the loan markets).
* Secondary markets (investor-to-investor transactions with broker-dealers and exchanges as intermediaries in the securities markets, and mostly banks in the loan markets).

Secondary markets play a critical role in allowing investors in the primary markets to transfer the risks of their investments to other market participants.

All markets have the originators, or issuers, of the claims traded in them (the original demanders of funds) and two distinctive groups of agents operating as investors, or suppliers of funds. The two groups of funds suppliers have completely divergent motives. The first group aims to eliminate any undesirable risks of the traded assets and earn money on repackaging risks, the other actively seeks to take on those risks in exchange for uncertain compensation. The two groups are:

* Hedgers (dealers who aim to offset primary risks, be left with short-term or secondary risks, and earn spread from dealing).
* Speculators (investors who hold positions for longer periods without simultaneously holding positions that offset primary risks).

The claims traded in all financial markets can be delivered in three ways. The first is an immediate exchange of an asset for cash. The second is an agreement on the price to be paid with the exchange taking place at a predetermined time in the future. The last is a delivery in the future contingent on an outcome of a financial event (e.g., level of stock price or interest rate), with a fee paid upfront for the right of delivery. The three market segments based on the delivery type are:

* Spot or cash markets (immediate delivery).
* Forwards markets (mandatory future delivery or settlement).
* Options markets (contingent future delivery or settlement).

We focus on these structural distinctions to bring out the fact that all markets not only transfer funds from suppliers to users, but also risk from users to suppliers. They allow risk transfer or risk sharing between investors. The majority of the trading activity in today’s market is motivated by risk transfer with the acquirer of risk receiving some form of sure or contingent compensation. The relative price of risk in the market is governed by a web of relatively simple arbitrage relationships that link all the markets. These allow market participants to assess instantaneously the relative attractiveness of various investments within each market segment or across all of them. Understanding these relationships is mandatory for anyone trying to make sense of the vast and complex web of today’s markets.

1.2 RISK SHARING

All financial contracts, whether in the form of securities or not, can be viewed as bundles, or packages of unit payoff claims (mini-contracts), each for a specific date in the future and a specific set of outcomes. In financial economics, these are referred to as state-contingent claims.

Let us start with the simplest illustration: an insurance contract. A 1-year life insurance policy promising to pay $1,000,000 in the event of the insured’s death can be viewed as a package of 365 daily claims (lottery tickets), each paying $1,000,000 if the holder dies on that day. The value of the policy upfront (the premium) is equal to the sum of the values of all the individual tickets. As the holder of the policy goes through the year, he can discard tickets that did not pay off, and the value of the policy to him diminishes until it reaches zero at the end of the coverage period.