exchange risk of the principal amount, which is exchanged only at final settlement. Projected credit exposure of a forward also slopes continually upward, as there is no exchange of payments before settlement.
6. James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of Economic Studies26/1 (February 1958), 65–86.
7. J. R. Hicks, “Liquidity,” Economic Journal72 (December 1962), 787–802.
8. Ibid.
9. J. Marschak, “Money and the Theory of Assets,” Econometrica6 (1938), 311–325.
10. Ibid., 314.
11. James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of Economic Studies26/1 (February 1958), 65–86.
12. William F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance19/3 (September 1964), 425–442; John Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Economics and Statistics47/1 (February 1965), 13–37.
13. Johnann von Neumann and Oskar Morgenstern, “Theory of Games and Economic Behavior,” 3d ed., Princeton, NJ: Princeton University Press, 1967 (1st ed., 1944).
14. J. B. Williams, The Theory of Investment Value,Cambridge, MA: Harvard University Press, 1938.
15. J. L. Farrell, “The Dividend Discount Model: A Primer,” Financial Analysts Journal41 (November–December 1985), 16–19, 22–25.
16. D. H. Leavens, “Diversification of Investments,” Trusts and Estates80 (May 1945), 469–473.
17. Harry M. Markowitz, “Portfolio Selection (1),” Journal of Finance7 (March 1952), 77–91.
18. A. D. Roy, “Safety First and the Holding of Assets,” Econometrica20/3 (July 1952), 431–449.
19. Harry M. Markowitz, “The Optimization of a Quadratic Function Subject to Linear Constraints,” Naval Research Logistics Quarterly3 (1956), 111–133;
Portfolio Selection—Efficient Diversification of Investments,New York: John Wiley & Sons, 1959; Mean-Variance Analysis in Portfolio Choice and Capital Markets,Oxford, U.K.: Basil Blackwell, 1987.
20. Harry M. Markowitz, Portfolio Selection (2),2d ed., Oxford, U.K.: Basil Blackwell, 1992, p. 154ff.
21. James Tobin, “Liquidity Preference as Behavior Towards Risk,” Review of Economic Studies26/1 (February 1958), 65–86.
22. William F. Sharpe, “Capital Asset Prices, A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance19/3 (September 1964), 425–442.
23. John Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Economics and Statistics47/1 (February 1965), 13–37; “Security Prices, Risk, and Maximal Gains from Diversification,” Journal of Finance20 (1965), 587–615.
Market Risk 121
24. Jan Mossin, “Equilibrium in a Capital Asset Market,” Econometrica35/4 (October 1966), 768–783.
25. Diana R. Harrington, Modern Portfolio Theory, the Capital Asset Pricing Model and Arbitrage Pricing Theory: A User’s Guide, 2d ed., Englewood Cliffs, NJ:
Prentice-Hall, 1987, p. 35.
26. For a detailed discussion, see Christoph Aukenthaler, “Trust Banking, Theorie und Praxis des Anlagegeschäftes,” PhD thesis, University of Zurich, Haupt, Bern, 1991, 244ff., or Pirmin Hotz, “Das Capital Asset Pricing Model und die Markteffizienzhypothese unter besonderer Berücksichtigung der empirisch beobachteten ‘Anomalien’ in den amerikanischen und anderen internationalen Aktienmärkten,” PhD thesis, University St. Gall, Victor Hotz AG, Baar, 1989, p. 43ff.
27. Eugene Fama, “Efficient Capital Market: A Review of Theory and Empirical Work,” Journal of Finance3 (1970), 383–417.
28. Thomas Vock and Heinz Zimmermann, “Risiken und Renditen
schweizerischer Aktien,” Schweizerzische Zeitschrift für Volkwirtschaft und Statistik4 (1984), 547–576.
29. Eugene Fama, Foundations of Finance,New York: Basic Books, 1976, p. 25ff.
30. Stanley J. Kon, “Models of Stock Returns—A Comparison,” Journal of Finance 39 (1984), 147–165.
31. Randolph Westerfield, “An Examination of Foreign Exchange Risk and Fixed and Floating Exchange Rate Regimes,” Journal of International Economics7 (1977), 181–200.
32. Walter Wasserfallen and Heinz Zimmermann, “The Behaviour of Interdaily Exchange Rates,” Journal of Banking and Finance9 (1985), 55–72.
33. Heinz Zimmermann, “Zeithorizont, Risiko und Performance, eine Übersicht,” Finanzmarkt und Portfolio Management2 (1991), 169.
34. Fischer Black, “Capital Market Equilibrium with Restricted Borrowing,”
Journal of Business7, 444–454.
35. For a detailed analysis see Fischer Black, Michael C. Jensen, and Myron Scholes, “The Capital Asset Pricing Model: Some Empirical Tests,” in Michael Jensen, Studies in the Theory of Capital Markets,New York: Praeger, 1972.
36. Eugene Fama, “Efficient Capital Market: A Review of Theory and Empirical Work,” Journal of Finance3 (1970), 383–417; Fischer Black, Michael C. Jensen, and Myron Scholes, “The Capital Asset Pricing Model: Some Empirical Tests,” in Michael Jensen, Studies in the Theory of Capital Markets,New York:
Praeger, 1972; Eugene Fama and James MacBeth, “Risk, Return and Equilibrium: Empirical Tests,” Journal of Political Economy9 (1973), 601–636.
37. Stephen A. Ross, “The Arbitrage Theory of Capital Asset Pricing,” Journal of Economic Theory13 (1976), 341–360.
38. Louis Bachelier, “Theorie de la Speculation,” Annales de l’Ecole Normale Superieure17 (1900), 21–86. English translation by A.J. Boness in Paul H.
Cootner (ed.), The Random Character of Stock Market Prices,Cambridge, MA:
MIT Press, 1967, pp. 17–78.
39. C. Sprenkle, “Warrant Prices as Indicators of Expectations and Preferences,”
Yale Economic Essays1 (1961), 172–231; P. Samuelson, “Rational Theory of Warrant Pricing,” Industrial Management Review10 (1965), 15–31.
40. Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy81 (May–June 1973), 637–654; R. C.
Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science4/1 ( June 1974), 141–183.
41. Ibid., Black and Scholes.
42. Ibid., Merton.
43. Fischer Black, “The Pricing of Commodity Contracts,” Journal of Financial Economics3 (1976), 167–179.
44. M. Asay, “A Note on the Design of Commodity Option Contracts,” Journal of Finance2 (1982), 1–8.
45. M. Garman and S. Kohlhagen, “Foreign Currency Option Values,” Journal of International Money and Finance2 (1983), 231–238.
46. R. Geske, “The Valuation of Compound Options,” Journal of Financial Economics7 (1979), 63–81.
47. Richard Roll, “An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends,” Journal of Financial
Economics5 (1977), 251–258; R. Geske, “A Note on an Analytical Formula for Unprotected American Call Options on Stocks with Known Dividends,”
Journal of Financial Economics7 (1979), 375–380; R. Whaley, “On the Valuation of American Call Options on Stocks with Known Dividends,” Journal of Financial Economics9 (1981), 207–211.
48. M. Rubinstein, “Pay Now, Choose Later,” Risk(February 1991), 13.
49. S. Gray and R. Whaley, “Valuing S&P 500 Bear Market Warrants with a Periodic Reset,” Journal of Derivatives5 (1997), 99–106.
50. B. Goldman, H. Sosin, and M. Gatto, “Path Dependent Options: Buy at the Low, Sell at the High,” Journal of Finance34 (1979), 1111–1127.
51. M. Rubinstein and E. Reiner, “Breaking Down the Barriers,” Risk(September 1991), 31–35.
52. J. Cox, S. Ross, and M. Rubinstein, “Option Pricing: A Simplified Approach,”
Journal of Financial Economics7 (1979), 229–264; R. Rendleman Jr. and B.
Bartter, “Two-State Option Pricing,” Journal of Finance34 (1979), 1093–1110.
53. P. Boyle, J. Evnine, and S. Gibbs, “Numerical Evaluation of Multivariate Contingent Claims,” Review of Financial Studies2 (1989), 241–250.
54. P. Boyle, “A Lattice Framework for Option Pricing with Two State Variables,” Journal of Financial and Quantitative Analysis23 (1988), 1–12.
55. E. Schwartz, “The Valuation of Warrants: Implementing a New Approach,”
Journal of Financial Economics4 (1977), 79–93; M. Brennen and E. Schwartz, “The Valuation of American Put Options,” Journal of Finance32 (1977), 449–462.
56. P. Boyle, “Options: A Monte Carlo Approach,” Journal of Financial Economics 4 (1977), 323–338.
Market Risk 123
57. R. Geske and H. Johnson, “The American Put Valued Analytically,” Journal of Finance39 (1984), 1511–1524.
58. G. Barone-Adesi and R. Whaley, “Efficient Analytic Approximation of American Option Values,” Journal of Finance42 (1987), 301–320.
59. L. MacMillan, “Analytic Approximation for the American Put Option,”
Advances in Futures and Options Research1 (1986), 119–139.
60. R. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science4/1 (1973), 141–183.
61. J. Cox and S. Ross, “The Valuation of Options for Alternative Stochastic Processes,” Journal of Financial Economics3 (1976), 145–166.
62. E. Derman and I. Kani, “Riding on the Smile,” Risk(July 1994), 32–39;
D. Dupire, “Pricing with a Smile,” Risk(July 1994), 18–20; M. Rubinstein and E. Reiner, “Implied Binomial Trees,” Journal of Finance49 (1994), 771–818.
63. R. C. Merton, “Option Pricing when Underlying Stock Returns are Discontinuous,” Journal of Financial Economics3 (1976), 125–143.
64. J. Hull and A. White, “The Pricing of Options and Assets with Stochastic Volatilities,” Journal of Finance42 (1987), 281–300.
65. L. Scott, “Option Pricing when the Variance Changes Randomly: Theory Estimation, and an Application,” Journal of Financial and Quantitative Analysis 22 (1987), 419–438; J. Wiggins, “Option Values Under Stochastic Volatility:
Theory and Empirical Estimates,” Journal of Financial Economics19 (1987), 351–372.
66. D. Bates, “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in PHLX Deutschemark Options,” Review of Financial Studies9 (1996), 69–108.
67. Alan Greenspan, “Measuring Financial Risk in the Twenty-First Century,”
remarks before a conference sponsored by the Office of the Comptroller of the Currency, Washington, D.C., October 14, 1999.
68. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards,Basel, Switzerland: Bank for International Settlement, July 1988.
69. See U.S. General Accounting Office, Long-Term Capital Management, Regulators Need to Focus Greater Attention on Systemic Risk,Washington, DC:
General Accounting Office, October 1999.
70. See the analysis and recommendations in Commodity Futures Trading Commission (CFTC), Hedge Funds, Leverage, and the Lessons of Long-Term Capital Management: Report of the President’s Working Group on Financial Markets, Washington, DC: Commodity Futures Trading Commission, April 1999, www.cftc.gov/tm/hedgefundreport.html, accessed May 19, 2000.
71. Financial Times,“Greenspan Hits Out at Way Banks Treat Risk” (October 12, 1999), 10.
72. The Basel Committee’s members are representatives of the central banks and local regulatory organizations of the Group of Ten (G-10) countries:
Belgium, Canada, France, Germany, Italy, Japan, the Netherlands, Sweden, the United Kingdom, and the United States, plus Luxembourg and
Switzerland. The committee meets four times a year, usually in Basel, Switzerland, under the chairmanship of the Bank for International Settlement, where the permanent secretariat of the committee is located.
73. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards,Basel, Switzerland: Bank for International Settlement, July 1988.
74. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Prudential Supervision of Banks’ Derivatives Activities,Basel, Switzerland: Bank for International Settlement, December 1994; Amendment to the Capital Accord of July 1988,Basel, Switzerland: Bank for International Settlement, July 1994; Basel Capital Accord: The Treatment of the Credit Risk Associated with Certain Off-Balance-Sheet Items,Basel, Switzerland: Bank for International Settlement, July 1994.
75. The U.S. banking industry regulators consist of the Federal Reserve Board, the Office of the Comptroller of the Currency, and the Federal Deposit Insurance Corporation.
76. The Basel Committee has extended the add-ons on equities, precious metals, and commodities contracts and increased the add-ons in general for longer maturities. See Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Treatment of Potential Exposure for Off-Balance-Sheet Items, Basel, Switzerland: Bank for International Settlement, April 1995. See as well the discussion of the Basel Committee’s 1994 and 1995 modifications in Section 2.8. See also the regulations issued in Bank for International
Settlement (BIS), Basel Committee on Banking Supervision, Interpretation of the Capital Accord for the Multilateral Netting of Forward Value Foreign Exchange Transactions,Basel, Switzerland: Bank for International Settlement, April 1996;
and Survey of Disclosures About Trading and Derivatives Activities of Banks and Securities Firms: Joint Report by the Basel Committee on Banking Supervision and the Technical Committee of the International Organisation of Securities Commission, Basel, Switzerland: Bank for International Settlement, November 1996.
77. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Amendment to the Capital Accord to Incorporate Market Risks, Basel, Switzerland: Bank for International Settlement, January 1996, modified in September 1997.
78. Ibid.
79. Committee members who are also members of the European Union regard this definition as being consistent with (albeit less detailed than) the definition of the trading book in the EU’s Capital Adequacy Directive.
80. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Amendment to the Capital Accord to Incorporate Market Risks, Basel, Switzerland: Bank for International Settlement, January 1996, modified September 1997.
81. Ibid., para. II.a.
82. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Market Risk 125
Comment by 31 May 2001,Basel, Switzerland: Bank for International Settlement, January 2001, part 2I, para. 20.
83. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Amendment to the Capital Accord to Incorporate Market Risks, Basel, Switzerland: Bank for International Settlement, January 1996, modified September 1997, para. 7.
84. Switzerland Federal Banking Commission, “Guidelines Governing Capital Adequacy Requirements to Support Market Risks,” EG-FBC Circular No.
97/1, October 22, 1997.
85. See comments in Reto R. Gallati, “De-Minimis-Regel diskriminiert,”
Schweizer Bank(Zurich), 9 (1998), 41–43.
86. See definition of specific risk in Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Amendment to the Capital Accord to Incorporate Market Risks,Basel, Switzerland: Bank for International
Settlement, January 1996, modified September 1997, para. I.b, footnote 5.
87. See Bank for International Settlement (BIS), Basel Committee on Banking Supervision, International Convergence of Capital Measurement and Capital Standards,Basel, Switzerland: Bank for International Settlement, July 1988.
88. Traded mortgage securities and mortgage derivative products possess unique characteristics because of the risk of prepayment. Accordingly, for the time being, no common treatment applies to these securities, which are dealt with at national discretion. A security that is the subject of a
repurchase or securities-lending agreement will be treated as if it were still owned by the lender of the security—i.e., it will be treated in the same manner as other securities positions.
89. This includes the delta-equivalent value of options. The delta equivalent of the legs arising out of the treatment of caps and floors can also be offset against each other under the rules laid down in this paragraph.
90. The separate legs of different swaps may also be matched, subject to the same conditions.
91. Where equities are part of a forward contract, a future, or an option (quantity of equities to be received or to be delivered), any interest rate or foreign currency exposure from the other leg of the contract should be reported.
92. For example, an equity swap, in which a bank receives an amount based on the change in value of one particular equity or stock index, and pays on a different index will be treated as a long position in the former and a short position in the latter. Where one of the legs involves receiving or paying a fixed or floating interest rate, that exposure should be slotted into the appropriate repricing time band for interest-rate-related instruments. The stock index should be covered by the equity treatment.
93. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Amendment to the Capital Accord to Incorporate Market Risks, Basel, Switzerland: Bank for International Settlement, January 1996, modified September 1997, sec. 5.3.1, para. 130.
94. Ibid., sec. 5.3.2.b, para. 96.
95. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Proposal to Issue a Supplement to the Basel Capital Accord to Cover Market Risks,Basel, Switzerland: Bank for International Settlement, April 1995; An Internal Model–Based Approach to Market Risk Capital Requirements, Basel, Switzerland: Bank for International Settlement, 1995.
96. Alan Greenspan, “Risk Management in the Global Financial System—Before the Annual Financial Markets Conference of the Federal Reserve Bank of Atlanta,” Miami Beach, Florida, February 27, 1998.
97. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, Supervisory Framework for the Use of“Backtesting” in Conjunction with the Internal Models Approach to Market Risk Capital Requirements,Basel, Switzerland: Bank for International Settlement, January 1996.
98. P. Kupiec and J. O’Brien, “A Pre-Commitment Approach to Capital Requirements for Market Risk,” FEDS Working Paper no. 95-34, Washington, DC: Federal Reserve Board of Governors, 1995.
99. A typical management response is to cut positions as losses accumulate.
This pattern of trading can be compared to portfolio insurance, which attempts to replicate a put option. Therefore, attempts by management to control losses will create a pattern of payoffs over long horizons that will be asymmetrical, similar to options. The problem is that traditional VaR measures are inadequate with highly nonlinear payoffs.
100. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, The New Basel Capital Accord: Consultative Document, Issued for Comment by 31 May 2001,Basel, Switzerland: Bank for International Settlement, January 2001, 6ff.; Amendment to the Capital Accord to Incorporate Market Risks,Basel, Switzerland: Bank for International Settlement, January 1996, modified September 1997.
101. E. Dimson and R. Marsh, “Capital Requirements for Securities Firms,”
Journal of Finance50 (1995), 821–851.
102. Misconceptions of models are that they are conceptually built for “normal conditions”. See comments from Tim Shepheard-Walwyn and Robert Litterman, “Building a Coherent Risk Measurement and Capital Optimization Model for Financial Firms,” paper presented at the
Conference on Financial Services at the Crossroads: Capital Regulation in the 21st Century, New York, February 26–27, 1998, FRBNY Economic Policy Review(October 1998), 173ff. and Section 5.8 of this book, which discusses misconceptions of models.
103. See Securities and Exchange Commission Item 305 of Regulation S-K and Item 9A of Form 20-F.
104. For a description of the required qualitative market risk disclosures, see Securities and Exchange Commission Item 305(b) of Regulation S-K and Item 9A(b) of Form 20-F.
105. Bank for International Settlement (BIS), Basel Committee on Banking Supervision, The New Basel Capital Accord: Consultative Document, Issued for
Market Risk 127
Comment by 31 May 2001,Basel, Switzerland: Bank for International Settlement, January 2001, paras. 74, 655ff.
106. A market-neutral risk arbitrage book would consist of a series of long and short positions; this hedges out market risk but leaves exposure to firm- specific risk. A trading strategy that eliminates broad market risk (equity, interest rate, foreign exchange, or commodity) leaves only residual risk. For example, a hedge fund manager can hedge the market risk of a U.S. stock portfolio by shorting S&P 500 Stock Index futures, leaving only firm-specific residual risk.
C H A P T E R 3