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FX Options and Structured Products

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1 FX Options and Structured Products Uwe Wystup 7 April

3 Contents 0 Preface Scope of this Book The Readership About the Author Acknowledgments Foreign Exchange Options A Journey through the History Of Options Technical Issues for Vanilla Options Value A Note on the Forward Greeks Identities Homogeneity based Relationships Quotation Strike in Terms of Delta Volatility in Terms of Delta Volatility and Delta for a Given Strike Greeks in Terms of Deltas Volatility Historic Volatility Historic Correlation Volatility Smile At-The-Money Volatility Interpolation Volatility Smile Conventions At-The-Money Definition Interpolation of the Volatility on Maturity Pillars Interpolation of the Volatility Spread between Maturity Pillars Volatility Sources Volatility Cones Stochastic Volatility

4 4 Wystup Exercises Basic Strategies containing Vanilla Options Call and Put Spread Risk Reversal Risk Reversal Flip Straddle Strangle Butterfly Seagull Exercises First Generation Exotics Barrier Options Digital Options, Touch Options and Rebates Compound and Instalment Asian Options Lookback Options Forward Start, Ratchet and Cliquet Options Power Options Quanto Options Exercises Second Generation Exotics Corridors Faders Exotic Barrier Options Pay-Later Options Step up and Step down Options Spread and Exchange Options Baskets Best-of and Worst-of Options Options and Forwards on the Harmonic Average Variance and Volatility Swaps Exercises Structured Products Forward Products Outright Forward Participating Forward Fade-In Forward Knock-Out Forward Shark Forward Fader Shark Forward

5 FX Options and Structured Products Butterfly Forward Range Forward Range Accrual Forward Accumulative Forward Boomerang Forward Amortizing Forward Auto-Renewal Forward Double Shark Forward Forward Start Chooser Forward Free Style Forward Boosted Spot/Forward Time Option Exercises Series of Strategies Shark Forward Series Collar Extra Series Exercises Deposits and Loans Dual Currency Deposit/Loan Performance Linked Deposits Tunnel Deposit/Loan Corridor Deposit/Loan Turbo Deposit/Loan Tower Deposit/Loan Exercises Interest Rate and Cross Currency Swaps Cross Currency Swap Hanseatic Swap Turbo Cross Currency Swap Buffered Cross Currency Swap Flip Swap Corridor Swap Double-No-Touch linked Swap Range Reset Swap Basket Spread Swap Exercises Participation Notes Gold Participation Note Basket-linked Note Issuer Swap Moving Strike Turbo Spot Unlimited

6 6 Wystup 2.6 Hybrid FX Products Practical Matters The Traders Rule of Thumb Cost of Vanna and Volga Observations Consistency check Abbreviations for First Generation Exotics Adjustment Factor Volatility for Risk Reversals, Butterflies and Theoretical Value Pricing Barrier Options Pricing Double Barrier Options Pricing Double-No-Touch Options Pricing European Style Options No-Touch Probability The Cost of Trading and its Implication on the Market Price of Onetouch Options Example Further Applications Exercises Bid Ask Spreads One Touch Spreads Vanilla Spreads Spreads for First Generation Exotics Minimal Bid Ask Spread Bid Ask Prices Exercises Settlement The Black-Scholes Model for the Actual Spot Cash Settlement Delivery Settlement Options with Deferred Delivery Exercises On the Cost of Delayed Fixing Announcements The Currency Fixing of the European Central Bank Model and Payoff Analysis Procedure Error Estimation Analysis of EUR-USD Conclusion

7 FX Options and Structured Products 7 4 Hedge Accounting under IAS Introduction Financial Instruments Overview General Definition Financial Assets Financial Liabilities Offsetting of Financial Assets and Financial Liabilities Equity Instruments Compound Financial Instruments Derivatives Embedded Derivatives Classification of Financial Instruments Evaluation of Financial Instruments Initial Recognition Initial Measurement Subsequent Measurement Derecognition Hedge Accounting Overview Types of Hedges Basic Requirements Stopping Hedge Accounting Methods for Testing Hedge Effectiveness Fair Value Hedge Cash Flow Hedge Testing for Effectiveness – A Case Study of the Forward Plus Simulation of Exchange Rates Calculation of the Forward Plus Value Calculation of the Forward Rates Calculation of the Forecast Transaction s Value Dollar-Offset Ratio – Prospective Test for Effectiveness Variance Reduction Measure – Prospective Test for Effectiveness Regression Analysis – Prospective Test for Effectiveness Result Retrospective Test for Effectiveness Conclusion Relevant Original Sources for Accounting Standards Exercises

8 8 Wystup 5 Foreign Exchange Markets A Tour through the Market Statement by GFI Group (Fenics), 25 October Interview with ICY Software, 14 October Interview with Bloomberg, 12 October Interview with Murex, 8 November Interview with SuperDerivatives, 17 October Interview with Lucht Probst Associates, 27 February Software and System Requirements Fenics Position Keeping Pricing Straight Through Processing Disclaimers Trading and Sales Proprietary Trading Sales-Driven Trading Inter Bank Sales Branch Sales Institutional Sales Corporate Sales Private Banking Listed FX Options Trading Floor Joke

9 Chapter 0 Preface 0.1 Scope of this Book Treasury management of international corporates involves dealing with cash flows in different currencies. Therefore the natural service of an investment bank consists of a variety of money market and foreign exchange products. This book explains the most popular products and strategies with a focus on everything beyond vanilla options. It explains all the FX options, common structures and tailor-made solutions in examples with a special focus on the application with views from traders and sales as well as from a corporate client perspective. It contains actually traded deals with corresponding motivations explaining why the structures have been traded. This way the reader gets a feeling how to build new structures to suit clients needs. The exercises are meant to practice the material. Several of them are actually difficult to solve and can serve as incentives to further research and testing. Solutions to the exercises are not part of this book, however they will be published on the web page of the book, The Readership Prerequisite is some basic knowledge of FX markets as for example taken from the Book Foreign Exchange Primer by Shami Shamah, Wiley 2003, see [90]. The target readers are Graduate students and Faculty of Financial Engineering Programs, who can use this book as a textbook for a course named structured products or exotic currency options. 9

10 10 Wystup Traders, Trainee Structurers, Product Developers, Sales and Quants with interest in the FX product line. For them it can serve as a source of ideas and as well as a reference guide. Treasurers of corporates interested in managing their books. With this book at hand they can structure their solutions themselves. The readers more interested in the quantitative and modeling aspects are recommended to read Foreign Exchange Risk by J. Hakala and U. Wystup, Risk Publications, London, 2002, see [50]. This book explains several exotic FX options with a special focus on the underlying models and mathematics, but does not contain any structures or corporate clients or investors view. 0.3 About the Author Figure 1: Uwe Wystup, professor of Quantitative Finance at HfB Business School of Finance and Management in Frankfurt, Germany. Uwe Wystup is also CEO of MathFinance AG, a global network of quants specializing in Quantitative Finance, Exotic Options advisory and Front Office Software Production. Previously he was a Financial Engineer and Structurer in the FX Options Trading Team at Commerzbank. Before that he worked for Deutsche Bank, Citibank, UBS and Sal. Oppenheim jr. & Cie. He is founder and manager of the web site and the MathFinance Newsletter. Uwe holds a PhD in mathematical finance from Carnegie Mellon University. He also lectures on mathematical finance for Goethe University Frankfurt, organizes the Frankfurt MathFinance Colloquium and is founding director of the Frankfurt MathFinance Institute. He has given several seminars on exotic options, computational finance and volatility modeling. His area of specialization are the quantitative aspects and the design of structured products of foreign

11 FX Options and Structured Products 11 exchange markets. He published a book on Foreign Exchange Risk and articles in Finance and Stochastics and the Journal of Derivatives. Uwe has given many presentations at both universities and banks around the world. Further information on his curriculum vitae and a detailed publication list is available at Acknowledgments I would like to thank my former colleagues on the trading floor, most of all Gustave Rieunier, Behnouch Mostachfi, Noel Speake, Roman Stauss, Tamás Korchmáros, Michael Braun, Andreas Weber, Tino Senge, Jürgen Hakala, and all my colleagues and co-authors, specially Christoph Becker, Susanne Griebsch, Christoph Kühn, Sebastian Krug, Marion Linck, Wolfgang Schmidt and Robert Tompkins. Chris Swain, Rachael Wilkie and many others of Wiley publications deserve respect as they were dealing with my rather slow speed in completing this book. Nicole van de Locht and Choon Peng Toh deserve a medal for serious detailed proof reading.

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13 Chapter 1 Foreign Exchange Options FX Structured Products are tailor-made linear combinations of FX Options including both vanilla and exotic options. We recommend the book by Shamah [90] as a source to learn about FX Markets with a focus on market conventions, spot, forward and swap contracts, vanilla options. For pricing and modeling of exotic FX options we suggest Hakala and Wystup [50] or Lipton [71] as useful companions to this book. The market for structured products is restricted to the market of the necessary ingredients. Hence, typically there are mostly structured products traded the currency pairs that can be formed between USD, JPY, EUR, CHF, GBP, CAD and AUD. In this chapter we start with a brief history of options, followed by a technical section on vanilla options and volatility, and deal with commonly used linear combinations of vanilla options. Then we will illustrated the most important ingredients for FX structured products: the first and second generation exotics. 1.1 A Journey through the History Of Options The very first options and futures were traded in ancient Greece, when olives were sold before they had reached ripeness. Thereafter the market evolved in the following way. 16th century Ever since the 15th century tulips, which were liked for their exotic appearance, were grown in Turkey. The head of the royal medical gardens in Vienna, Austria, was the first to cultivate those Turkish tulips successfully in Europe. When he fled to Holland because of religious persecution, he took the bulbs along. As the new head of the botanical gardens of Leiden, Netherlands, he cultivated several new strains. It was from these gardens that avaricious traders stole the bulbs to commercialize them, because tulips were a great status symbol. 17th century The first futures on tulips were traded in As of 1634, people could 13

14 14 Wystup buy special tulip strains by the weight of their bulbs, for the bulbs the same value was chosen as for gold. Along with the regular trading, speculators entered the market and the prices skyrocketed. A bulb of the strain Semper Octavian was worth two wagonloads of wheat, four loads of rye, four fat oxen, eight fat swine, twelve fat sheep, two hogsheads of wine, four barrels of beer, two barrels of butter, 1,000 pounds of cheese, one marriage bed with linen and one sizable wagon. People left their families, sold all their belongings, and even borrowed money to become tulip traders. When in 1637, this supposedly risk-free market crashed, traders as well as private individuals went bankrupt. The government prohibited speculative trading; the period became famous as Tulipmania. 18th century In 1728, the Royal West-Indian and Guinea Company, the monopolist in trading with the Caribbean Islands and the African coast issued the first stock options. Those were options on the purchase of the French Island of Ste. Croix, on which sugar plantings were planned. The project was realized in 1733 and paper stocks were issued in Along with the stock, people purchased a relative share of the island and the valuables, as well as the privileges and the rights of the company. 19th century In 1848, 82 businessmen founded the Chicago Board of Trade (CBOT). Today it is the biggest and oldest futures market in the entire world. Most written documents were lost in the great fire of 1871, however, it is commonly believed that the first standardized futures were traded as of CBOT now trades several futures and forwards, not only T-bonds and treasury bonds, but also options and gold. In 1870, the New York Cotton Exchange was founded. In 1880, the gold standard was introduced. 20th century In 1914, the gold standard was abandoned because of the war. In 1919, the Chicago Produce Exchange, in charge of trading agricultural products was renamed to Chicago Mercantile Exchange. Today it is the most important futures market for Eurodollar, foreign exchange, and livestock. In 1944, the Bretton Woods System was implemented in an attempt to stabilize the currency system. In 1970, the Bretton Woods System was abandoned for several reasons. In 1971, the Smithsonian Agreement on fixed exchange rates was introduced. In 1972, the International Monetary Market (IMM) traded futures on coins, currencies and precious metal.

15 FX Options and Structured Products 15 21th century In 1973, the CBOE (Chicago Board of Exchange) firstly traded call options; four years later also put options. The Smithsonian Agreement was abandoned; the currencies followed managed floating. In 1975, the CBOT sold the first interest rate future, the first future with no real underlying asset. In 1978, the Dutch stock market traded the first standardized financial derivatives. In 1979, the European Currency System was implemented, and the European Currency Unit (ECU) was introduced. In 1991, the Maastricht Treaty on a common currency and economic policy in Europe was signed. In 1999, the Euro was introduced, but the countries still used cash of their old currencies, while the exchange rates were kept fixed. In 2002, the Euro was introduced as new money in the form of cash. 1.2 Technical Issues for Vanilla Options We consider the model geometric Brownian motion ds t = (r d r f )S t dt + σs t dw t (1.1) for the underlying exchange rate quoted in FOR-DOM (foreign-domestic), which means that one unit of the foreign currency costs FOR-DOM units of the domestic currency. In case of EUR-USD with a spot of , this means that the price of one EUR is USD. The notion of foreign and domestic do not refer the location of the trading entity, but only to this quotation convention. We denote the (continuous) foreign interest rate by r f and the (continuous) domestic interest rate by r d. In an equity scenario, r f would represent a continuous dividend rate. The volatility is denoted by σ, and W t is a standard Brownian motion. The sample paths are displayed in Figure 1.1. We consider this standard model, not because it reflects the statistical properties of the exchange rate (in fact, it doesn t), but because it is widely used in practice and front office systems and mainly serves as a tool to communicate prices in FX options. These prices are generally quoted in terms of volatility in the sense of this model. Applying Itô s rule to ln S t yields the following solution for the process S t S t = S 0 exp <(r d r f 12 >σ2 )t + σw t, (1.2) which shows that S t is log-normally distributed, more precisely, ln S t is normal with mean ln S 0 + (r d r f 1 2 σ2 )t and variance σ 2 t. Further model assumptions are

16 16 Wystup Figure 1.1: Simulated paths of a geometric Brownian motion. The distribution of the spot S T at time T is log-normal. 1. There is no arbitrage 2. Trading is frictionless, no transaction costs 3. Any position can be taken at any time, short, long, arbitrary fraction, no liquidity constraints The payoff for a vanilla option (European put or call) is given by F = [φ(s T K)] +, (1.3) where the contractual parameters are the strike K, the expiration time T and the type φ, a binary variable which takes the value +1 in the case of a call and 1 in the case of a put. The symbol x + denotes the positive part of x, i.e., x + = max(0, x) = 0 x Value In the Black-Scholes model the value of the payoff F at time t if the spot is at x is denoted by v(t, x) and can be computed either as the solution of the Black-Scholes partial differential

17 FX Options and Structured Products 17 equation v t r d v + (r d r f )xv x σ2 x 2 v xx = 0, (1.4) v(t, x) = F. (1.5) or equivalently (Feynman-Kac-Theorem) as the discounted expected value of the payofffunction, v(x, K, T, t, σ, r d, r f, φ) = e r dτ IE[F ]. (1.6) This is the reason why basic financial engineering is mostly concerned with solving partial differential equations or computing expectations (numerical integration). The result is the Black-Scholes formula We abbreviate v(x, K, T, t, σ, r d, r f, φ) = φe r dτ [fn (φd + ) KN (φd )]. (1.7) x: current price of the underlying τ = T t: time to maturity f = IE[S T S t = x] = xe (r d r f )τ : forward price of the underlying θ ± = r d r f σ ± σ 2 d ± = ln x K +σθ ±τ σ τ = ln f K ± σ 2 2 τ σ τ n(t) = 1 2π e 1 2 t2 = n( t) N (x) = x n(t) dt = 1 N ( x) The Black-Scholes formula can be derived using the integral representation of Equation (1.6) v = e r dτ IE[F ] = e rdτ IE[[φ(S T K)] + ] + [ ( = e r dτ φ xe (r d r f 1 2 σ2 )τ+σ + τy K)] n(y) dy. (1.8) Next one has to deal with the positive part and then complete the square to get the Black- Scholes formula. A derivation based on the partial differential equation can be done using results about the well-studied heat-equation.

18 18 Wystup A Note on the Forward The forward price f is the strike which makes the time zero value of the forward contract F = S T f (1.9) equal to zero. It follows that f = IE[S T ] = xe (r d r f )T, i.e. the forward price is the expected price of the underlying at time T in a risk-neutral setup (drift of the geometric Brownian motion is equal to cost of carry r d r f ). The situation r d > r f is called contango, and the situation r d 19 FX Options and Structured Products 19 Speed. 3 v x 3 = e r f τ n(d +) x 2 σ τ ( ) d+ σ τ + 1 (1.14) Theta. v t = e r f τ n(d +)xσ 2 τ + φ[r f xe r f τ N (φd + ) r d Ke rdτ N (φd )] (1.15) Charm. 2 v x τ = φr f e r f τ N (φd + ) + φe r f τ n(d + ) 2(r d r f )τ d σ τ 2τσ τ (1.16) Color. 3 v x 2 τ = e r f τ n(d + ) 2xτσ τ [ 2r f τ (r d r f )τ d σ ] τ 2τσ d + τ (1.17) Vega. v σ = xe r f τ τn(d + ) (1.18) Volga. 2 v σ = 2 xe r f τ τn(d + ) d +d σ (1.19) Volga is also sometimes called vomma or volgamma. Vanna. 2 v σ x = e r f τ n(d + ) d σ (1.20) Rho. v r d = φkτe rdτ N (φd ) (1.21) v r f = φxτe r f τ N (φd + ) (1.22)

20 20 Wystup Dual Delta. Dual Gamma. v K = φe r dτ N (φd ) (1.23) 2 v = e r dτ n(d ) K 2 Kσ τ (1.24) Dual Theta. v T = v t (1.25) Identities The put-call-parity is the relationship d ± = d (1.26) σ σ d ± τ = (1.27) r d σ d ± τ = (1.28) r f σ xe r f τ n(d + ) = Ke rdτ n(d ). (1.29) N (φd ) = IP [φs T φk] (1.30) N (φd + ) = IP [φs T φ f ] 2 (1.31) K v(x, K, T, t, σ, r d, r f, +1) v(x, K, T, t, σ, r d, r f, 1) = xe r f τ Ke r dτ, (1.32) which is just a more complicated way to write the trivial equation x = x + x. The put-call delta parity is v(x, K, T, t, σ, r d, r f, +1) x v(x, K, T, t, σ, r d, r f, 1) x = e r f τ. (1.33) In particular, we learn that the absolute value of a put delta and a call delta are not exactly adding up to one, but only to a positive number e r f τ. They add up to one approximately if either the time to expiration τ is short or if the foreign interest rate r f is close to zero.

21 FX Options and Structured Products 21 Whereas the choice K = f produces identical values for call and put, we seek the deltasymmetric strike Ǩ which produces absolutely identical deltas (spot, forward or driftless). This condition implies d + = 0 and thus Ǩ = fe σ2 2 T, (1.34) in which case the absolute delta is e r f τ /2. In particular, we learn, that always Ǩ > f, i.e., there can t be a put and a call with identical values and deltas. Note that the strike Ǩ is usually chosen as the middle strike when trading a straddle or a butterfly. Similarly the dual-delta-symmetric strike ˆK = fe σ2 2 T can be derived from the condition d = Homogeneity based Relationships We may wish to measure the value of the underlying in a different unit. This will obviously effect the option pricing formula as follows. av(x, K, T, t, σ, r d, r f, φ) = v(ax, ak, T, t, σ, r d, r f, φ) for all a > 0. (1.35) Differentiating both sides with respect to a and then setting a = 1 yields v = xv x + Kv K. (1.36) Comparing the coefficients of x and K in Equations (1.7) and (1.36) leads to suggestive results for the delta v x and dual delta v K. This space-homogeneity is the reason behind the simplicity of the delta formulas, whose tedious computation can be saved this way. We can perform a similar computation for the time-affected parameters and obtain the obvious equation v(x, K, T, t, σ, r d, r f, φ) = v(x, K, T a, t a, aσ, ar d, ar f, φ) for all a > 0. (1.37) Differentiating both sides with respect to a and then setting a = 1 yields 0 = τv t σv σ + r d v rd + r f v rf. (1.38) Of course, this can also be verified by direct computation. The overall use of such equations is to generate double checking benchmarks when computing Greeks. These homogeneity methods can easily be extended to other more complex options. By put-call symmetry we understand the relationship (see [6], [7],[16] and [19]) v(x, K, T, t, σ, r d, r f, +1) = K f v(x, f 2 K, T, t, σ, r d, r f, 1). (1.39)

22 22 Wystup The strike of the put and the strike of the call result in a geometric mean equal to the forward f. The forward can be interpreted as a geometric mirror reflecting a call into a certain number of puts. Note that for at-the-money options (K = f) the put-call symmetry coincides with the special case of the put-call parity where the call and the put have the same value. Direct computation shows that the rates symmetry v + v = τv (1.40) r d r f holds for vanilla options. This relationship, in fact, holds for all European options and a wide class of path-dependent options as shown in [84]. One can directly verify the relationship the foreign-domestic symmetry 1 x v(x, K, T, t, σ, r d, r f, φ) = Kv( 1 x, 1 K, T, t, σ, r f, r d, φ). (1.41) This equality can be viewed as one of the faces of put-call symmetry. The reason is that the value of an option can be computed both in a domestic as well as in a foreign scenario. We consider the example of S t modeling the exchange rate of EUR/USD. In New York, the call option (S T K) + costs v(x, K, T, t, σ, r usd, r eur, 1) USD and hence v(x, K, T, t, σ, r usd, r eur, 1)/x ( ) 1 +. EUR. This EUR-call option can also be viewed as a USD-put option with payoff K 1 K S T This option costs Kv( 1, 1, T, t, σ, r x K eur, r usd, 1) EUR in Frankfurt, because S t and 1 S t have the same volatility. Of course, the New York value and the Frankfurt value must agree, which leads to (1.41). We will also learn later, that this symmetry is just one possible result based on change of numeraire Quotation Quotation of the Underlying Exchange Rate Equation (1.1) is a model for the exchange rate. The quotation is a permanently confusing issue, so let us clarify this here. The exchange rate means how much of the domestic currency are needed to buy one unit of foreign currency. For example, if we take EUR/USD as an exchange rate, then the default quotation is EUR-USD, where USD is the domestic currency and EUR is the foreign currency. The term domestic is in no way related to the location of the trader or any country. It merely means the numeraire currency. The terms domestic, numeraire or base currency are synonyms as are foreign and underlying. Throughout this book we denote with the slash (/) the currency pair and with a dash (-) the quotation. The slash (/) does not mean a division. For instance, EUR/USD can also be quoted in either EUR-USD, which then means how many USD are needed to buy one EUR, or in USD-EUR, which then means how many EUR are needed to buy one USD. There are certain market standard quotations listed in Table 1.1.

23 FX Options and Structured Products 23 currency pair default quotation sample quote GBP/USD GPB-USD GBP/CHF GBP-CHF EUR/USD EUR-USD EUR/GBP EUR-GBP EUR/JPY EUR-JPY EUR/CHF EUR-CHF USD/JPY USD-JPY USD/CHF USD-CHF Table 1.1: Standard market quotation of major currency pairs with sample spot prices Trading Floor Language We call one million a buck, one billion a yard. This is because a billion is called milliarde in French, German and other languages. For the British Pound one million is also often called a quid. Certain currency pairs have names. For instance, GBP/USD is called cable, because the exchange rate information used to be sent through a cable in the Atlantic ocean between America and England. EUR/JPY is called the cross, because it is the cross rate of the more liquidly traded USD/JPY and EUR/USD. Certain currencies also have names, e.g. the New Zealand Dollar NZD is called a kiwi, the Australian Dollar AUD is called Aussie, the Scandinavian currencies DKR, NOK and SEK are called Scandies. Exchange rates are generally quoted up to five relevant figures, e.g. in EUR-USD we could observe a quote of The last digit 5 is called the pip, the middle digit 3 is called the big figure, as exchange rates are often displayed in trading floors and the big figure, which is displayed in bigger size, is the most relevant information. The digits left to the big figure are known anyway, the pips right of the big figure are often negligible. To make it clear, a rise of USD-JPY by 20 pips will be and a rise by 2 big figures will be Quotation of Option Prices Values and prices of vanilla options may be quoted in the six ways explained in Table 1.2.

24 24 Wystup name symbol value in units of example domestic cash d DOM 29,148 USD foreign cash f FOR 24,290 EUR % domestic % d DOM per unit of DOM % USD % foreign % f FOR per unit of FOR % EUR domestic pips d pips DOM per unit of FOR USD pips per EUR foreign pips f pips FOR per unit of DOM EUR pips per USD Table 1.2: Standard market quotation types for option values. In the example we take FOR=EUR, DOM=USD, S 0 = , r d = 3.0%, r f = 2.5%, σ = 10%, K = , T = 1 year, φ = +1 (call), notional = 1, 000, 000 EUR = 1, 250, 000 USD. For the pips, the quotation USD pips per EUR is also sometimes stated as % USD per 1 EUR. Similarly, the EUR pips per USD can also be quoted as % EUR per 1 USD. The Black-Scholes formula quotes d pips. The others can be computed using the following instruction. d pips 1 S 0 S 0 1 %f K S %d 0 S f pips 0 K d pips (1.42) Delta and Premium Convention The spot delta of a European option without premium is well known. It will be called raw spot delta δ raw now. It can be quoted in either of the two currencies involved. The relationship is δ reverse raw = δ raw S K. (1.43) The delta is used to buy or sell spot in the corresponding amount in order to hedge the option up to first order. For consistency the premium needs to be incorporated into the delta hedge, since a premium in foreign currency will already hedge part of the option s delta risk. To make this clear, let us consider EUR-USD. In the standard arbitrage theory, v(x) denotes the value or premium in USD of an option with 1 EUR notional, if the spot is at x, and the raw delta v x denotes the number of EUR to buy for the delta hedge. Therefore, xv x is the number of USD to sell. If now the premium is paid in EUR rather than in USD, then we already have v x EUR, and the number of EUR to buy has to be reduced by this amount, i.e. if EUR is the premium currency, we need to buy v x v x EUR for the delta hedge or equivalently sell xv x v USD.

25 FX Options and Structured Products 25 The entire FX quotation story becomes generally a mess, because we need to first sort out which currency is domestic, which is foreign, what is the notional currency of the option, and what is the premium currency. Unfortunately this is not symmetric, since the counterpart might have another notion of domestic currency for a given currency pair. Hence in the professional inter bank market there is one notion of delta per currency pair. Normally it is the left hand side delta of the Fenics screen if the option is traded in left hand side premium, which is normally the standard and right hand side delta if it is traded with right hand side premium, e.g. EUR/USD lhs, USD/JPY lhs, EUR/JPY lhs, AUD/USD rhs, etc. Since OTM options are traded most of time the difference is not huge and hence does not create a huge spot risk. Additionally the standard delta per currency pair [left hand side delta in Fenics for most cases] is used to quote options in volatility. This has to be specified by currency. This standard inter bank notion must be adapted to the real delta-risk of the bank for an automated trading system. For currencies where the risk free currency of the bank is the base currency of the currency it is clear that the delta is the raw delta of the option and for risky premium this premium must be included. In the opposite case the risky premium and the market value must be taken into account for the base currency premium, such that these offset each other. And for premium in underlying currency of the contract the market-value needs to be taken into account. In that way the delta hedge is invariant with respect to the risky currency notion of the bank, e.g. the delta is the same for a USD-based bank and a EUR-based bank. Example We consider two examples in Table 1.3 and 1.4 to compare the various versions of deltas that are used in practice. delta ccy prem ccy Fenics formula delta % EUR EUR lhs δ raw P % EUR USD rhs δ raw % USD EUR rhs [flip F4] (δ raw P )S/K % USD USD lhs [flip F4] (δ raw )S/K Table 1.3: 1y EUR call USD put strike K = for a EUR based bank. Market data: spot S = , volatility σ = 12%, EUR rate r f = 3.96%, USD rate r d = 3.57%. The raw delta is 49.15%EUR and the value is 4.427%EUR.

26 26 Wystup delta ccy prem ccy Fenics formula delta % EUR EUR lhs δ raw P % EUR USD rhs δ raw % USD EUR rhs [flip F4] (δ raw P )S/K % USD USD lhs [flip F4] δ raw S/K Table 1.4: 1y call EUR call USD put strike K = for a EUR based bank. Market data: spot S = , volatility σ = 12%, EUR rate r f = 3.96%, USD rate r d = 3.57%. The raw delta is 94.82%EUR and the value is 21.88%EUR Strike in Terms of Delta Since v x = = φe r f τ N (φd + ) we can retrieve the strike as K = x exp < φn 1 (φ e r f τ )σ τ + σθ + τ >. (1.44) Volatility in Terms of Delta The mapping σ = φe r f τ N (φd + ) is not one-to-one. The two solutions are given by σ ± = 1 <φn 1 (φ e r f τ ) ± (N 1 (φ e r f τ )) 2 σ >τ(d + + d ). (1.45) τ Thus using just the delta to retrieve the volatility of an option is not advisable Volatility and Delta for a Given Strike The determination of the volatility and the delta for a given strike is an iterative process involving the determination of the delta for the option using at-the-money volatilities in a first step and then using the determined volatility to re determine the delta and to continuously iterate the delta and volatility until the volatility does not change more than ɛ = 0.001% between iterations. More precisely, one can perform the following algorithm. Let the given strike be K. 1. Choose σ 0 = at-the-money volatility from the volatility matrix. 2. Calculate n+1 = (Call(K, σ n )). 3. Take σ n+1 = σ( n+1 ) from the volatility matrix, possibly via a suitable interpolation. 4. If σ n+1 σ n 27 FX Options and Structured Products 27 In order to prove the convergence of this algorithm we need to establish convergence of the recursion n+1 = e r f τ N (d + ( n )) (1.46) ( = e r f ln(s/k) + τ (rd r f + 1 ) 2 N σ2 ( n ))τ σ( n ) τ for sufficiently large σ( n ) and a sufficiently smooth volatility smile surface. We must show that the sequence of these n converges to a fixed point [0, 1] with a fixed volatility σ = σ( ). This proof has been carried out in [15] and works like this. We consider the derivative The term n+1 = e r f τ n(d + ( n )) d ( n ) n σ( n ) σ( n ). (1.47) n e r f τ n(d + ( n )) d ( n ) σ( n ) converges rapidly to zero for very small and very large spots, being an argument of the standard normal density n. For sufficiently large σ( n ) and a sufficiently smooth volatility surface in the sense that n σ( n ) is sufficiently small, we obtain σ( n ) n = q 28 28 Wystup which we assume to be given. From these we can retrieve Interpretation of Dual Delta d + = φn 1 (φe r f τ + ), (1.52) d = φn 1 ( φe r dτ ). (1.53) The dual delta introduced in (1.23) as the sensitivity with respect to strike has another – more practical – interpretation in a foreign exchange setup. We have seen in Section that the domestic value v(x, K, τ, σ, r d, r f, φ) (1.54) corresponds to a foreign value v( 1 x, 1 K, τ, σ, r f, r d, φ) (1.55) up to an adjustment of the nominal amount by the factor xk. From a foreign viewpoint the delta is thus given by ( ) φe rdτ N φ ln( K ) + (r x f r d σ2 τ) σ τ = ( φe rdτ N φ ln( x ) + (r K d r f 1 ) 2 σ2 τ) σ τ =, (1.56) which means the dual delta is the delta from the foreign viewpoint. We will see below that foreign rho, vega and gamma do not require to know the dual delta. We will now state the Greeks in terms of x, +,, r d, r f, τ, φ. Value. (Spot) Delta. v(x, +,, r d, r f, τ, φ) = x + + x e r f τ n(d + ) e r dτ n(d ) (1.57) Forward Delta. v f v x = + (1.58) = e (r f r d )τ + (1.59)

29 FX Options and Structured Products 29 Gamma. 2 v = e r f τ n(d + ) x 2 x(d + d ) (1.60) Taking a trader s gamma (change of delta if spot moves by 1%) additionally removes the spot dependence, because Γ trader = x 2 v = e r f τ n(d + ) 100 x 2 100(d + d ) (1.61) Speed. 3 v = e r f τ n(d + ) x 3 x 2 (d + d ) (2d 2 + d ) (1.62) Theta. 1 v x t = e r f τ n(d +)(d + d ) [ 2τ ] e r f τ n(d + ) + r f + + r d e r dτ n(d ) (1.63) Charm. Color. Vega. Volga. 2 v x τ 3 v x 2 τ = φr f e r f τ N (φd + ) + φe r f τ n(d + ) 2(r d r f )τ d (d + d ) 2τ(d + d ) (1.64) [ = e r f τ n(d + ) 2r f τ (r ] d r f )τ d (d + d ) d + 2xτ(d + d ) 2τ(d + d ) (1.65) v σ = xe r f τ τn(d + ) (1.66) 2 v σ 2 = xe r f τ τn(d + ) d +d d + d (1.67)

30 30 Wystup Vanna. 2 v σ x = e r f τ τd n(d + ) (1.68) d + d Rho. Dual Delta. v e rf τ n(d + ) = xτ (1.69) r d e r dτ n(d ) v = xτ + (1.70) r f v K = (1.71) Dual Gamma. K 2 2 v K 2 = x 2 2 v x 2 (1.72) Dual Theta. v T = v t (1.73) As an important example we consider vega. Vega in Terms of Delta The mapping v σ = xe r f τ τn(n 1 (e r f τ )) is important for trading vanilla options. Observe that this function does not depend on r d or σ, just on r f. Quoting vega in % foreign will additionally remove the spot dependence. This means that for a moderately stable foreign term structure curve, traders will be able to use a moderately stable vega matrix. For r f = 3% the vega matrix is presented in Table Volatility Volatility is the annualized standard deviation of the log-returns. It is the crucial input parameter to determine the value of an option. Hence, the crucial question is where to derive the volatility from. If no active option market is present, the only source of information is estimating the historic volatility. This would give some clue about the past. In liquid currency

31 FX Options and Structured Products 31 Mat/ 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 1D W W M M M M M Y Y Y Table 1.5: Vega in terms of Delta for the standard maturity labels and various deltas. It shows that one can vega hedge a long 9M 35 delta call with 4 short 1M 20 delta puts. pairs volatility is often a traded quantity on its own, which is quoted by traders, brokers and real-time data pages. These quotes reflect views of market participants about the future. Since volatility normally does not stay constant, option traders are highly concerned with hedging their volatility exposure. Hedging vanilla options vega is comparatively easy, because vanilla options have convex payoffs, whence the vega is always positive, i.e. the higher the volatility, the higher the price. Let us take for example a EUR-USD market with spot , USD- and EUR rate at 2.5%. A 3-month at-the-money call with 1 million EUR notional would cost 29,000 USD at at volatility of 12%. If the volatility now drops to a value of 8%, then the value of the call would be only 19,000 USD. This monotone dependence is not guaranteed for non-convex payoffs as we illustrate in Figure Historic Volatility We briefly describe how to compute the historic volatility of a time series S 0, S 1. S N (1.74)

32 32 Wystup Figure 1.2: Dependence of a vanilla call and a reverse knock-out call on volatility. The vanilla value is monotone in the volatility, whereas the barrier value is not. The reason is that as the spot gets closer to the upper knock-out barrier, an increasing volatility would increase the chance of knock-out and hence decrease the value. of daily data. First, we create the sequence of log-returns Then, we compute the average log-return r i = ln S i S i 1, i = 1. N. (1.75) r = 1 N N r i, (1.76) i=1

33 FX Options and Structured Products 33 their variance and their standard deviation ˆσ 2 = 1 N 1 N (r i r) 2, (1.77) i=1 ˆσ = 1 N (r i r) N 1 2. (1.78) The annualized standard deviation, which is the volatility, is then given by ˆσ a = B N (r i r) N 1 2, (1.79) where the annualization factor B is given by i=1 i=1 B = N d, (1.80) k and k denotes the number of calendar days within the time series and d denotes the number of calendar days per year. The is done to press the trading days into the calendar days. Assuming normally distributed log-returns, we know that ˆσ 2 is χ 2 -distributed. Therefore, given a confidence level of p and a corresponding error probability α = 1 p, the p-confidence interval is given by [ ] N 1 N 1 ˆσ a, ˆσ χ 2 a, (1.81) N 1;1 χ 2 α N 1; α 2 2 where χ 2 n;p denotes the p-quantile of a χ 2 -distribution 1 with n degrees of freedom. As an example let us take the 256 ECB-fixings of EUR-USD from 4 March 2003 to 3 March 2004 displayed in Figure 1.3. We get N = 255 log-returns. Taking k = d = 365, we obtain r = 1 N r i = , N i=1 ˆσ a = B N (r i r) N 1 2 = 10.85%, i=1 and a 95% confidence interval of [9.99%, 11.89%]. 1 values and quantiles of the χ 2 -distribution and other distributions can be computed on the internet, e.g. at

34 34 Wystup EUR/USD Fixings ECB Exchange Rate /4/03 4/4/03 5/4/03 6/4/03 7/4/03 8/4/03 9/4/03 Date 10/4/03 11/4/03 12/4/03 1/4/04 2/4/04 Figure 1.3: ECB-fixings of EUR-USD from 4 March 2003 to 3 March 2004 and the line of average growth Historic Correlation As in the preceding section we briefly describe how to compute the historic correlation of two time series x 0, x 1. x N, y 0, y 1. y N, of daily data. First, we create the sequences of log-returns Then, we compute the average log-returns X i = ln x i x i 1, i = 1. N, Y i = ln y i y i 1, i = 1. N. (1.82) X = 1 N Ȳ = 1 N N X i, i=1 N Y i, (1.83) i=1

35 FX Options and Structured Products 35 their variances and covariance ˆσ X 2 = ˆσ Y 2 = ˆσ XY = and their standard deviations ˆσ X = ˆσ Y = 1 N 1 1 N 1 1 N 1 N (X i X) 2, (1.84) i=1 N (Y i Ȳ )2, (1.85) i=1 N (X i X)(Y i Ȳ ), (1.86) i=1 1 N (X i N 1 X) 2, (1.87) i=1 1 N (Y i N 1 Ȳ )2. (1.88) i=1 The estimate for the correlation of the log-returns is given by ˆρ = ˆσ XY ˆσ X ˆσ Y. (1.89) This correlation estimate is often not very stable, but on the other hand, often the only available information. More recent work by Jäkel [37] treats robust estimation of correlation. We will revisit FX correlation risk in Section Volatility Smile The Black-Scholes model assumes a constant volatility throughout. However, market prices of traded options imply different volatilities for different maturities and different deltas. We start with some technical issues how to imply the volatility from vanilla options. Retrieving the Volatility from Vanilla Options Given the value of an option. Recall the Black-Scholes formula in Equation (1.7). We now look at the function v(σ), whose derivative (vega) is The function σ v(σ) is v (σ) = xe r f T T n(d + ). (1.90)

36 36 Wystup 1. strictly increasing, 2. concave up for σ [0, 2 ln F ln K /T ), 3. concave down for σ ( 2 ln F ln K /T, ) and also satisfies v(0) = [φ(xe r f T Ke r dt )] +, (1.91) v(, φ = 1) = xe r f T, (1.92) v(σ =, φ = 1) = Ke r dt, (1.93) v (0) = xe r f T T / 2πII , (1.94) In particular the mapping σ v(σ) is invertible. However, the starting guess for employing Newton s method should be chosen with care, because the mapping σ v(σ) has a saddle point at ( < ( ) ( )>) 2 T ln F K, φe r dt F N φ 2T [ln FK ]+ KN φ 2T [ln KF ]+, (1.95) as illustrated in Figure 1.4. To ensure convergence of Newton s method, we are advised to use initial guesses for σ on the same side of the saddle point as the desired implied volatility. The danger is that a large initial guess could lead to a negative successive guess for σ. Therefore one should start with small initial guesses at or below the saddle point. For at-the-money options, the saddle point is degenerate for a zero volatility and small volatilities serve as good initial guesses. Visual Basic Source Code Function VanillaVolRetriever(spot As Double, rd As Double, rf As Double, strike As Double, T As Double, type As Integer, GivenValue As Double) As Double Dim func As Double Dim dfunc As Double Dim maxit As Integer maximum number of iterations Dim j As Integer Dim s As Double first check if a volatility exists, otherwise set result to zero If GivenValue spot * Exp(-rf * T)) Or (type = -1 And GivenValue > strike * Exp(-rd * T)) Then

37 FX Options and Structured Products 37 Figure 1.4: Value of a European call in terms of volatility with parameters x = 1, K = 0.9, T = 1, r d = 6%, r f = 5%. The saddle point is at σ = 48%. VanillaVolRetriever = 0 Else there exists a volatility yielding the given value, now use Newton s method: the mapping vol to value has a saddle point. First compute this saddle point: saddle = Sqr(2 / T * Abs(Log(spot / strike) + (rd – rf) * T))

Which is the best strategy for day trading, a price action or a technical indicator?

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Full disclosure: I am a trader. It’s how I make my living. I wake up in the morning, do some strength training at the gym, make breakfast for the family, shower and put on a suit and then walk downstairs into my home office and spend 12–16 hours a day trading and monitoring and learning.

That’s how I pay our mortgage, pay for my truck, my wifes car, our health insurance, put food on teh table, etc etc.

I love it. My God, I almost lost everything to get to where I am, but I love it. It was the most horrible and near suicidal experience of my life to become profitable, but I love it. Anyone who.

Hi. Price and using technical indicators are quite propelled and denial too..

Well according to me the theory based on price action is completely subjective. On a chart you just have understand what price is trying to reveal the direction..

Nowadays on YouTube and some other platforms.. many giants are claiming they could read the price action and they are not using any techical support.. well It sounds like a plan .. for me stock Market is a place where you can earn enormous amount of money and loose too.. so if somebody could predict price action he must be awarded then and he must be the r.

Profits Without Prosperity

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September 2020 Issue

Executive Summary

Though corporate profits are high, and the stock market is booming, most Americans are not sharing in the economic recovery. While the top 0.1% of income recipients reap almost all the income gains, good jobs keep disappearing, and new ones tend to be insecure and underpaid.

One of the major causes: Instead of investing their profits in growth opportunities, corporations are using them for stock repurchases. Take the 449 firms in the S&P 500 that were publicly listed from 2003 through 2020. During that period, they used 54% of their earnings—a total of $2.4 trillion—to buy back their own stock. Dividends absorbed an extra 37% of their earnings. That left little to fund productive capabilities or better incomes for workers.

Why are such massive resources dedicated to stock buybacks? Because stock-based instruments make up the majority of executives’ pay, and buybacks drive up short-term stock prices. Buybacks contribute to runaway executive compensation and economic inequality in a major way. Because they extract value rather than create it, their overuse undermines the economy’s health. To restore true prosperity to the country, government and business leaders must take steps to rein them in.

Five years after the official end of the Great Recession, corporate profits are high, and the stock market is booming. Yet most Americans are not sharing in the recovery. While the top 0.1% of income recipients—which include most of the highest-ranking corporate executives—reap almost all the income gains, good jobs keep disappearing, and new employment opportunities tend to be insecure and underpaid. Corporate profitability is not translating into widespread economic prosperity.

The allocation of corporate profits to stock buybacks deserves much of the blame. Consider the 449 companies in the S&P 500 index that were publicly listed from 2003 through 2020. During that period those companies used 54% of their earnings—a total of $2.4 trillion—to buy back their own stock, almost all through purchases on the open market. Dividends absorbed an additional 37% of their earnings. That left very little for investments in productive capabilities or higher incomes for employees.

The buyback wave has gotten so big, in fact, that even shareholders—the presumed beneficiaries of all this corporate largesse—are getting worried. “It concerns us that, in the wake of the financial crisis, many companies have shied away from investing in the future growth of their companies,” Laurence Fink, the chairman and CEO of BlackRock, the world’s largest asset manager, wrote in an open letter to corporate America in March. “Too many companies have cut capital expenditure and even increased debt to boost dividends and increase share buybacks.”

Why are such massive resources being devoted to stock repurchases? Corporate executives give several reasons, which I will discuss later. But none of them has close to the explanatory power of this simple truth: Stock-based instruments make up the majority of their pay, and in the short term buybacks drive up stock prices. In 2020 the 500 highest-paid executives named in proxy statements of U.S. public companies received, on average, $30.3 million each; 42% of their compensation came from stock options and 41% from stock awards. By increasing the demand for a company’s shares, open-market buybacks automatically lift its stock price, even if only temporarily, and can enable the company to hit quarterly earnings per share (EPS) targets.

As a result, the very people we rely on to make investments in the productive capabilities that will increase our shared prosperity are instead devoting most of their companies’ profits to uses that will increase their own prosperity—with unsurprising results. Even when adjusted for inflation, the compensation of top U.S. executives has doubled or tripled since the first half of the 1990s, when it was already widely viewed as excessive. Meanwhile, overall U.S. economic performance has faltered.

If the U.S. is to achieve growth that distributes income equitably and provides stable employment, government and business leaders must take steps to bring both stock buybacks and executive pay under control. The nation’s economic health depends on it.

From Value Creation to Value Extraction

For three decades I’ve been studying how the resource allocation decisions of major U.S. corporations influence the relationship between value creation and value extraction, and how that relationship affects the U.S. economy. From the end of World War II until the late 1970s, a retain-and-reinvest approach to resource allocation prevailed at major U.S. corporations. They retained earnings and reinvested them in increasing their capabilities, first and foremost in the employees who helped make firms more competitive. They provided workers with higher incomes and greater job security, thus contributing to equitable, stable economic growth—what I call “sustainable prosperity.”

This pattern began to break down in the late 1970s, giving way to a downsize-and-distribute regime of reducing costs and then distributing the freed-up cash to financial interests, particularly shareholders. By favoring value extraction over value creation, this approach has contributed to employment instability and income inequality.

As documented by the economists Thomas Piketty and Emmanuel Saez, the richest 0.1% of U.S. households collected a record 12.3% of all U.S. income in 2007, surpassing their 11.5% share in 1928, on the eve of the Great Depression. In the financial crisis of 2008–2009, their share fell sharply, but it has since rebounded, hitting 11.3% in 2020.

Since the late 1980s, the largest component of the income of the top 0.1% has been compensation, driven by stock-based pay. Meanwhile, the growth of workers’ wages has been slow and sporadic, except during the internet boom of 1998–2000, the only time in the past 46 years when real wages rose by 2% or more for three years running. Since the late 1970s, average growth in real wages has increasingly lagged productivity growth. (See the exhibit “When Productivity and Wages Parted Ways.”)

When Productivity and Wages Parted Ways

From 1948 to the mid-1970s, increases in productivity and wages went hand in hand. Then a gap opened between the two.

Not coincidentally, U.S. employment relations have undergone a transformation in the past three decades. Mass plant closings eliminated millions of unionized blue-collar jobs. The norm of a white-collar worker’s spending his or her entire career with one company disappeared. And the seismic shift toward offshoring left all members of the U.S. labor force—even those with advanced education and substantial work experience—vulnerable to displacement.

To some extent these structural changes could be justified initially as necessary responses to changes in technology and competition. In the early 1980s permanent plant closings were triggered by the inroads superior Japanese manufacturers had made in consumer-durable and capital-goods industries. In the early 1990s one-company careers fell by the wayside in the IT sector because the open-systems architecture of the microelectronics revolution devalued the skills of older employees versed in proprietary technologies. And in the early 2000s the offshoring of more-routine tasks, such as writing unsophisticated software and manning customer call centers, sped up as a capable labor force emerged in low-wage developing economies and communications costs plunged, allowing U.S. companies to focus their domestic employees on higher-value-added work.

These practices chipped away at the loyalty and dampened the spending power of American workers, and often gave away key competitive capabilities of U.S. companies. Attracted by the quick financial gains they produced, many executives ignored the long-term effects and kept pursuing them well past the time they could be justified.

A turning point was the wave of hostile takeovers that swept the country in the 1980s. Corporate raiders often claimed that the complacent leaders of the targeted companies were failing to maximize returns to shareholders. That criticism prompted boards of directors to try to align the interests of management and shareholders by making stock-based pay a much bigger component of executive compensation.

Given incentives to maximize shareholder value and meet Wall Street’s expectations for ever higher quarterly EPS, top executives turned to massive stock repurchases, which helped them “manage” stock prices. The result: Trillions of dollars that could have been spent on innovation and job creation in the U.S. economy over the past three decades have instead been used to buy back shares for what is effectively stock-price manipulation.

Good Buybacks and Bad

Not all buybacks undermine shared prosperity. There are two major types: tender offers and open-market repurchases. With the former, a company contacts shareholders and offers to buy back their shares at a stipulated price by a certain near-term date, and then shareholders who find the price agreeable tender their shares to the company. Tender offers can be a way for executives who have substantial ownership stakes and care about a company’s long-term competitiveness to take advantage of a low stock price and concentrate ownership in their own hands. This can, among other things, free them from Wall Street’s pressure to maximize short-term profits and allow them to invest in the business. Henry Singleton was known for using tender offers in this way at Teledyne in the 1970s, and Warren Buffett for using them at GEICO in the 1980s. (GEICO became wholly owned by Buffett’s holding company, Berkshire Hathaway, in 1996.) As Buffett has noted, this kind of tender offer should be made when the share price is below the intrinsic value of the productive capabilities of the company and the company is profitable enough to repurchase the shares without impeding its real investment plans.

But tender offers constitute only a small portion of modern buybacks. Most are now done on the open market, and my research shows that they often come at the expense of investment in productive capabilities and, consequently, aren’t great for long-term shareholders.

Companies have been allowed to repurchase their shares on the open market with virtually no regulatory limits since 1982, when the SEC instituted Rule 10b-18 of the Securities Exchange Act. Under the rule, a corporation’s board of directors can authorize senior executives to repurchase up to a certain dollar amount of stock over a specified or open-ended period of time, and the company must publicly announce the buyback program. After that, management can buy a large number of the company’s shares on any given business day without fear that the SEC will charge it with stock-price manipulation—provided, among other things, that the amount does not exceed a “safe harbor” of 25% of the previous four weeks’ average daily trading volume. The SEC requires companies to report total quarterly repurchases but not daily ones, meaning that it cannot determine whether a company has breached the 25% limit without a special investigation.

Further Reading

The Price of Wall Street’s Power

Despite the escalation in buybacks over the past three decades, the SEC has only rarely launched proceedings against a company for using them to manipulate its stock price. And even within the 25% limit, companies can still make huge purchases: Exxon Mobil, by far the biggest stock repurchaser from 2003 to 2020, can buy back about $300 million worth of shares a day, and Apple up to $1.5 billion a day. In essence, Rule 10b-18 legalized stock market manipulation through open-market repurchases.

The rule was a major departure from the agency’s original mandate, laid out in the Securities Exchange Act in 1934. The act was a reaction to a host of unscrupulous activities that had fueled speculation in the Roaring ’20s, leading to the stock market crash of 1929 and the Great Depression. To prevent such shenanigans, the act gave the SEC broad powers to issue rules and regulations.

During the Reagan years, the SEC began to roll back those rules. The commission’s chairman from 1981 to 1987 was John Shad, a former vice chairman of E.F. Hutton and the first Wall Street insider to lead the commission in 50 years. He believed that the deregulation of securities markets would channel savings into economic investments more efficiently and that the isolated cases of fraud and manipulation that might go undetected did not justify onerous disclosure requirements for companies. The SEC’s adoption of Rule 10b-18 reflected that point of view.

Debunking the Justifications for Buybacks

Executives give three main justifications for open-market repurchases. Let’s examine them one by one:

1. Buybacks are investments in our undervalued shares that signal our confidence in the company’s future.

This makes some sense. But the reality is that over the past two decades major U.S. companies have tended to do buybacks in bull markets and cut back on them, often sharply, in bear markets. (See the exhibit “Where Did the Money from Productivity Increases Go?”) They buy high and, if they sell at all, sell low. Research by the Academic-Industry Research Network, a nonprofit I cofounded and lead, shows that companies that do buybacks never resell the shares at higher prices.

Where Did the Money from Productivity Increases Go?

Buybacks—as well as dividends—have skyrocketed in the past 20 years. (Note that these data are for the 251 companies that were in the S&P 500 in January 2020 and were public from 1981 through 2020. Inclusion of firms that went public after 1981, such as Microsoft, Cisco, Amgen, Oracle, and Dell, would make the increase in buybacks even more marked.) Though executives say they repurchase only undervalued stocks, buybacks increased when the stock market boomed, casting doubt on that claim.

Once in a while a company that bought high in a boom has been forced to sell low in a bust to alleviate financial distress. GE, for example, spent $3.2 billion on buybacks in the first three quarters of 2008, paying an average price of $31.84 per share. Then, in the last quarter, as the financial crisis brought about losses at GE Capital, the company did a $12 billion stock issue at an average share price of $22.25, in a failed attempt to protect its triple-A credit rating.

In general, when a company buys back shares at what turn out to be high prices, it eventually reduces the value of the stock held by continuing shareholders. “The continuing shareholder is penalized by repurchases above intrinsic value,” Warren Buffett wrote in his 1999 letter to Berkshire Hathaway shareholders. “Buying dollar bills for $1.10 is not good business for those who stick around.”

2. Buybacks are necessary to offset the dilution of earnings per share when employees exercise stock options.

Calculations that I have done for high-tech companies with broad-based stock option programs reveal that the volume of open-market repurchases is generally a multiple of the volume of options that employees exercise. In any case, there’s no logical economic rationale for doing repurchases to offset dilution from the exercise of employee stock options. Options are meant to motivate employees to work harder now to produce higher future returns for the company. Therefore, rather than using corporate cash to boost EPS immediately, executives should be willing to wait for the incentive to work. If the company generates higher earnings, employees can exercise their options at higher stock prices, and the company can allocate the increased earnings to investment in the next round of innovation.

3. Our company is mature and has run out of profitable investment opportunities; therefore, we should return its unneeded cash to shareholders.

Some people used to argue that buybacks were a more tax-efficient means of distributing money to shareholders than dividends. But that has not been the case since 2003, when the tax rates on long-term capital gains and qualified dividends were made the same. Much more important issues remain, however: What is the CEO’s main role and his or her responsibility to shareholders?

Companies that have built up productive capabilities over long periods typically have huge organizational and financial advantages when they enter related markets. One of the chief functions of top executives is to discover new opportunities for those capabilities. When they opt to do large open-market repurchases instead, it raises the question of whether these executives are doing their jobs.

A related issue is the notion that the CEO’s main obligation is to shareholders. It’s based on a misconception of the shareholders’ role in the modern corporation. The philosophical justification for giving them all excess corporate profits is that they are best positioned to allocate resources because they have the most interest in ensuring that capital generates the highest returns. This proposition is central to the “maximizing shareholder value” (MSV) arguments espoused over the years, most notably by Michael C. Jensen. The MSV school also posits that companies’ so-called free cash flow should be distributed to shareholders because only they make investments without a guaranteed return—and hence bear risk.

Why Money for Reinvestment Has Dried Up

Since the early 1980s, when restrictions on open-market buybacks were greatly eased, distributions to shareholders have absorbed a huge portion of net income, leaving much less for reinvestment in companies.

But the MSV school ignores other participants in the economy who bear risk by investing without a guaranteed return. Taxpayers take on such risk through government agencies that invest in infrastructure and knowledge creation. And workers take it on by investing in the development of their capabilities at the firms that employ them. As risk bearers, taxpayers, whose dollars support business enterprises, and workers, whose efforts generate productivity improvements, have claims on profits that are at least as strong as the shareholders’.

The irony of MSV is that public-company shareholders typically never invest in the value-creating capabilities of the company at all. Rather, they invest in outstanding shares in the hope that the stock price will rise. And a prime way in which corporate executives fuel that hope is by doing buybacks to manipulate the market. The only money that Apple ever raised from public shareholders was $97 million at its IPO in 1980. Yet in recent years, hedge fund activists such as David Einhorn and Carl Icahn—who played absolutely no role in the company’s success over the decades—have purchased large amounts of Apple stock and then pressured the company to announce some of the largest buyback programs in history.

The past decade’s huge increase in repurchases, in addition to high levels of dividends, have come at a time when U.S. industrial companies face new competitive challenges. This raises questions about how much of corporate cash flow is really “free” to be distributed to shareholders. Many academics—for example, Gary P. Pisano and Willy C. Shih of Harvard Business School, in their 2009 HBR article “Restoring American Competitiveness” and their book Producing Prosperity —have warned that if U.S. companies don’t start investing much more in research and manufacturing capabilities, they cannot expect to remain competitive in a range of advanced technology industries.

Retained earnings have always been the foundation for investments in innovation. Executives who subscribe to MSV are thus copping out of their responsibility to invest broadly and deeply in the productive capabilities their organizations need to continually innovate. MSV as commonly understood is a theory of value extraction, not value creation.

Executives Are Serving Their Own Interests

As I noted earlier, there is a simple, much more plausible explanation for the increase in open-market repurchases: the rise of stock-based pay. Combined with pressure from Wall Street, stock-based incentives make senior executives extremely motivated to do buybacks on a colossal and systemic scale.

Consider the 10 largest repurchasers, which spent a combined $859 billion on buybacks, an amount equal to 68% of their combined net income, from 2003 through 2020. (See the exhibit “The Top 10 Stock Repurchasers.”) During the same decade, their CEOs received, on average, a total of $168 million each in compensation. On average, 34% of their compensation was in the form of stock options and 24% in stock awards. At these companies the next four highest-paid senior executives each received, on average, $77 million in compensation during the 10 years—27% of it in stock options and 29% in stock awards. Yet since 2003 only three of the 10 largest repurchasers—Exxon Mobil, IBM, and Procter & Gamble—have outperformed the S&P 500 Index.

The Top 10 Stock Repurchasers 2003–2020

At most of the leading U.S. companies below, distributions to shareholders were well in excess of net income. These distributions came at great cost to innovation, employment, and—in cases such as oil refining and pharmaceuticals—customers who had to pay higher prices for products.

Reforming the System

Buybacks have become an unhealthy corporate obsession. Shifting corporations back to a retain-and-reinvest regime that promotes stable and equitable growth will take bold action. Here are three proposals:

Put an end to open-market buybacks.

In a 2003 update to Rule 10b-18, the SEC explained: “It is not appropriate for the safe harbor to be available when the issuer has a heightened incentive to manipulate its share price.” In practice, though, the stock-based pay of the executives who decide to do repurchases provides just this “heightened incentive.” To correct this glaring problem, the SEC should rescind the safe harbor.

A good first step toward that goal would be an extensive SEC study of the possible damage that open-market repurchases have done to capital formation, industrial corporations, and the U.S. economy over the past three decades. For example, during that period the amount of stock taken out of the market has exceeded the amount issued in almost every year; from 2004 through 2020 this net withdrawal averaged $316 billion a year. In aggregate, the stock market is not functioning as a source of funds for corporate investment. As I’ve already noted, retained earnings have always provided the base for such investment. I believe that the practice of tying executive compensation to stock price is undermining the formation of physical and human capital.

Rein in stock-based pay.

Many studies have shown that large companies tend to use the same set of consultants to benchmark executive compensation, and that each consultant recommends that the client pay its CEO well above average. As a result, compensation inevitably ratchets up over time. The studies also show that even declines in stock price increase executive pay: When a company’s stock price falls, the board stuffs even more options and stock awards into top executives’ packages, claiming that it must ensure that they won’t jump ship and will do whatever is necessary to get the stock price back up.

In 1991 the SEC began allowing top executives to keep the gains from immediately selling stock acquired from options. Previously, they had to hold the stock for six months or give up any “short-swing” gains. That decision has only served to reinforce top executives’ overriding personal interest in boosting stock prices. And because corporations aren’t required to disclose daily buyback activity, it gives executives the opportunity to trade, undetected, on inside information about when buybacks are being done. At the very least, the SEC should stop allowing executives to sell stock immediately after options are exercised. Such a rule could help launch a much-needed discussion of meaningful reform that goes beyond the 2020 Dodd-Frank Act’s “Say on Pay”—an ineffectual law that gives shareholders the right to make nonbinding recommendations to the board on compensation issues.

But overall the use of stock-based pay should be severely limited. Incentive compensation should be subject to performance criteria that reflect investment in innovative capabilities, not stock performance.

Transform the boards that determine executive compensation.

Boards are currently dominated by other CEOs, who have a strong bias toward ratifying higher pay packages for their peers. When approving enormous distributions to shareholders and stock-based pay for top executives, these directors believe they’re acting in the interests of shareholders.

Further Reading

Capitalism for the Long Term

That’s a big part of the problem. The vast majority of shareholders are simply investors in outstanding shares who can easily sell their stock when they want to lock in gains or minimize losses. As I argued earlier, the people who truly invest in the productive capabilities of corporations are taxpayers and workers. Taxpayers have an interest in whether a corporation that uses government investments can generate profits that allow it to pay taxes, which constitute the taxpayers’ returns on those investments. Workers have an interest in whether the company will be able to generate profits with which it can provide pay increases and stable career opportunities.

It’s time for the U.S. corporate governance system to enter the 21st century: Taxpayers and workers should have seats on boards. Their representatives would have the insights and incentives to ensure that executives allocate resources to investments in capabilities most likely to generate innovations and value.

Courage in Washington

After the Harvard Law School dean Erwin Griswold published “Are Stock Options Getting out of Hand?” in this magazine in 1960, Senator Albert Gore launched a campaign that persuaded Congress to whittle away special tax advantages for executive stock options. After the Tax Reform Act of 1976, the compensation expert Graef Crystal declared that stock options that qualified for the capital-gains tax rate, “once the most popular of all executive compensation devices…have been given the last rites by Congress.” It also happens that during the 1970s the share of all U.S. income that the top 0.1% of households got was at its lowest point in the past century.

The members of the U.S. Congress should show the courage and independence of their predecessors and go beyond “Say on Pay” to do something about excessive executive compensation. In addition, Congress should fix a broken tax regime that frequently rewards value extractors as if they were value creators and ignores the critical role of government investment in the infrastructure and knowledge that are so crucial to the competitiveness of U.S. business.

Instead, what we have now are corporations that lobby—often successfully—for federal subsidies for research, development, and exploration, while devoting far greater resources to stock buybacks. Here are three examples of such hypocrisy:

Alternative energy.

Exxon Mobil, while receiving about $600 million a year in U.S. government subsidies for oil exploration (according to the Center for American Progress), spends about $21 billion a year on buybacks. It spends virtually no money on alternative energy research.

This article also appears in:

HBR’s 10 Must Reads 2020

Meanwhile, through the American Energy Innovation Council, top executives of Microsoft, GE, and other companies have lobbied the U.S. government to triple its investment in alternative energy research and subsidies, to $16 billion a year. Yet these companies had plenty of funds they could have invested in alternative energy on their own. Over the past decade Microsoft and GE, combined, have spent about that amount annually on buybacks.


Intel executives have long lobbied the U.S. government to increase spending on nanotechnology research. In 2005, Intel’s then-CEO, Craig R. Barrett, argued that “it will take a massive, coordinated U.S. research effort involving academia, industry, and state and federal governments to ensure that America continues to be the world leader in information technology.” Yet from 2001, when the U.S. government launched the National Nanotechnology Initiative (NNI), through 2020 Intel’s expenditures on buybacks were almost four times the total NNI budget.

Pharmaceutical drugs.

In response to complaints that U.S. drug prices are at least twice those in any other country, Pfizer and other U.S. pharmaceutical companies have argued that the profits from these high prices—enabled by a generous intellectual-property regime and lax price regulation—permit more R&D to be done in the United States than elsewhere. Yet from 2003 through 2020, Pfizer funneled an amount equal to 71% of its profits into buybacks, and an amount equal to 75% of its profits into dividends. In other words, it spent more on buybacks and dividends than it earned and tapped its capital reserves to help fund them. The reality is, Americans pay high drug prices so that major pharmaceutical companies can boost their stock prices and pad executive pay. Given the importance of the stock market and corporations to the economy and society, U.S. regulators must step in to check the behavior of those who are unable or unwilling to control themselves. “The mission of the U.S. Securities and Exchange Commission,” the SEC’s website explains, “is to protect investors, maintain fair, orderly, and efficient markets, and facilitate capital formation.” Yet, as we have seen, in its rulings on and monitoring of stock buybacks and executive pay over three decades, the SEC has taken a course of action contrary to those objectives. It has enabled the wealthiest 0.1% of society, including top executives, to capture the lion’s share of the gains of U.S. productivity growth while the vast majority of Americans have been left behind. Rule 10b-18, in particular, has facilitated a rigged stock market that, by permitting the massive distribution of corporate cash to shareholders, has undermined capital formation, including human capital formation.

The corporate resource allocation process is America’s source of economic security or insecurity, as the case may be. If Americans want an economy in which corporate profits result in shared prosperity, the buyback and executive compensation binges will have to end. As with any addiction, there will be withdrawal pains. But the best executives may actually get satisfaction out of being paid a reasonable salary for allocating resources in ways that sustain the enterprise, provide higher standards of living to the workers who make it succeed, and generate tax revenues for the governments that provide it with crucial inputs.

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