Department of Statistics, DH2086 Comments on Models for Investors in Real World Markets June 30, 2002 General Comments. "For we have not followed cunningly devised fables..." 2 Peter 1.16 KJV a. It is a pleasure to read another book by these cogent authors. They are irreverent toward the orthodox fictions, and honor the truth. Since the last Findlay book I read was Investment Analysis, his perspective is refreshing. The level of state-of-the-art review is thorough, and astute analysis is found throughout. b. Anecdotes, operational examples, quotations and analogies are well-placed. The writing is consistent, persuasive, and of high calibre. Any remarks made suggesting correction or improvement do not detract from the conclusions, discoveries, choice of examples or excellence in writing or presentation. c. Need to reconcile use of the term "table" vs. "figure" for tables of numbers. Some chapters use "figure" to refer to tables of numbers, while other chapters use "table," and reserve "figure" for what hard science normally terms "figures." Specific Comments by Chapter. a. Chapter 1. 1. Footnote 2, page 17. "limited order book" should read "limit order book." 2. Reduced or negligible commission, top of page 19. (a) It should be noted that there is a price for these "cheap" market orders, and that is the additional spread the unsuspecting investor is subjected to. In the industry this is called "payment for order flow." The deep-discount broker is happy to quote a commission of $20 or less, and then route the orders to its market-making trading arm to match against other customers' orders, routinely costing a quarter point or more. This practice is exposed in the trade press (see [1], [2], [3]). (b) Regarding "unlimited free trading", called a "wrap fee" in the industry, you can be sure if you really trade with an activity level such that the average commission is less than some trigger amount, the brokerage will revoke the wrap privileges, citing "foregone commission cost" to them, and the wrap agreement is such that if it is revoked, the client is still responsible for the wrap fees for the balance of the contract performance period, IN ADDITION TO paying the renegotiated commission structure. b. Chapter 2. 1. Utils vs. Utiles. Having done all MBA homework in utils, it appears the use of utiles vs. utils is a personal choice, although a search of 3 American economics textbooks at this location reveals utils in all; utiles seems to be the continental usage. A WWW search on "keynes utiles" vs. "keynes utils" favors utiles 847:6; "irving fisher utiles" favors 27:15, and "modigliani utiles" 247:6. Most of these sites are European. Overall, "'utility theory' utils" favors utils 81:50. 2. Footnote 4, page 6. Equation reference (2.9) should be (2.10)? 3. Max dollar range $1,000,000. It would be helpful if this were increased to $3M or $10M, but I can see why the examples use $1M. 4. Scenario C, page 13. Replace $490,000 and $890,000 (in the root) with $810,000. 5. Infinite expectation not seen, top of page. 16. Sippose one considers (-1)*loss of one's life = infinity; this has been realized numerous times by investors who have suffered losses and taken their lives; I believe the remark could tastefully be made. 6. Line before fig. 2.5, page 17. "Market" should read "markets." Although the book limits itself to the equity market, the truth is that al the markets tend not to provide the infinite expectation. Given the book's title, a single use of "markets" here would be appropriate. 7. Writing, page 26. Fix the phrase "it is interesting to note" used twice in 4 lines, paragraphs 1 and 2. (NOTE: we make very few of these type comments.) 8. Writing, 2nd paragraph, page 27. Second ":" should be ",". c. Chapter 3. 1. Figure 3.6, page 9. The ordinate, abscissa and certain graph labels should be made larger. 2. Reference correction, page 14. Lintner[11] should be Lintner[17] or [18]. 3. Equation 3,10, page 14. Suggest dropping the 4 extra "mu =" and replacing with just "=". d. Chapter 4. 1. Note on Thematic Coherence. In chapters 3 and 4, caveats should be provided when referring or alluding to the "risk = sigma" paradigm. The review of CML, SML, and Sharpe diagonalization is excellent, and this standard equation is expected. A good disclaimer is made in the middle of first full paragraph on page 8. But without caveats at the outset, the reader will wonder about statements like those at the bottom of pages 2 and 5, etc. 2. Illustration constants, page 6. In calculations for mu and sigma, constant b2 should be 2.0, not 0.2; the numerical results (i.e. 1.32) indicate b2=2.0; using b2=0.2 gives different results. 3. Formatting or first illustration constants, page 6. Suggest inserting a tab after the semicolons to better separate the Sigma_c_i declarations. 4. Writing, verb tense agreement, section 4.4, page 7. In sentence beginning "Most of the published research...," watch "posses" vs. "possessed" 5. First sentence, page 10. In mentioning lack of arbitrage, how can one not mention that the reason equilibrium is reached is due in large part to the efficient operation of the professional arbitragers?! Textbook examples include put/call parity, futures fair value, program trading, etc. 6. Equation (4.10), page 10. Unless I'm mistaken, the delta_i tilde in the b_i1*delta_i tilde term should be delta_1 tilde, 7. Penultimate sentence, page 12. "Expectations" should be "expectation." e. Chapter 5. Cannot mention anything here without commenting on the brilliant review of the development of the university business school industry. 1. Footnote 4, page 5. This should be referred to as a tenet, and elevated from footnote status, perhaps as a short paragraph before "Some years later..." 2. Acronym usage, page 6. National Science Foundation (NSF) should be spelled out, especially since it is not used again in this chapter. 3. Short Sale Constraints, page 8. (a) Additionally, most brokers do not permit retail clients to earn interest on the short sale proceeds; if one has $500,000 in margin debt, and is short $300,000 stock, he is charged margin interest on the $500,000! (b) An accessible survey of short sale constraints is found in [4] and its references. 4. Victor Niederhoffer, page 12. "Neederhoffer" is "Niederhoffer." It is unclear whether he completed all his PhD requirements, although he was published with MFM Osborne in JASA (61, 897-916), and in Ops Rch (13) and J. Bus (39). Due to the "7-sigma" market crash of 1997, his $500M trading fund was crushed by the power of the brokers when forced to liquidate to meet margin calls on his short S&P futures puts, which would have been fine the following day, had he been cut a little slack, which no-one is. His book [5] was published before the debacle, so it makes for heady reading. His brother still trades OPM (other people's money), and Victor has probably resumed trading. In the trade, one refers to "pulling a Niederhoffer." Continuing his line of thought on the Fama, et al stairway encounter [5, pg 270], he says: Each of them...has served as a partner...to uncov[er] inefficiencies. .... All the anomalies that have appeared in the published literature that, in turn, has formed the basis of the professors' reformulations are mere ephemera designed to lure the unwary followers of professorial authority into ruin. [5, p270, cont'd] 5. Section 5.8, Harry Roberts, page 13. As your reference (Cootner 1964, p2) noted, Robert's observation was based on Bachelier's 1900 theory and H. Working's conclusion (Stanford Univ, c. 1920-1934) that realizations of GBM resembles the stock indices. Roberts' paper was pivotal for the "modern" era, but the ball was started in the commodities field with Holbrook Working (Fellow, ASA and Deming Award honoree) [6]. 6. Finite variance and subsequent writers, page 15. And shortly after people noticed normality fails, the infinite variance models appeared (Mandlebrot), and stable paretian distribution (discussed laster in the book), etc. 7. Bear Jump patches, page 16. Accounting for both up AND down "5-sigma" events is required for a market model in which symmetric market participants trade. Option sellers, for example, have very bad months when tradeables move up OR down by too much more than the models allow (e.g, OAT, NOC after 9/11, takeovers, futures limit days, and dozens of other examples of LEVEL SHIFTS in the process). This is applicable to the covered call program discussed in chapter 11 (page 13). Referring to these jumps as "bear" jumps is almost surely from the perspective of a single trading methodology, long or buy/hold. This trading system is most likely employed by most readers, however, so we will not raise the point again. 8. Acronym usage, page 23. Need to spell out Last-In- First-Out (LIFO), investment tax credit (ITC), etc., since the true EMH investors are disciplined to not pursue any fundamental analysis, where they would have encountered these terms. 9. Footnote 12, page 26. Playing this casino in this manner is an embedded "passport option," which trade OTC. f. Chapter 6. 1. Typos, pages 3 and 4. (a) "solve for u" should be "solve for mu" on page 3. (b) On page 4, t(0) should be t0 or t=0, unless t is function of t! (c) In-line equation references (2.1) thru (2.4) should be (6.1) thru (6.4). 2. Equation 6.10, page 11. "i" should be "r" 3. Algorithm, step 3, page 14. "i" should be "r" 4. Algorithm, step 10, page 15. "i" should be "r" 5. Ordinary income vs. capital gain, page 17. Include STCG (subject to acronym usage) in the list "(dividends, interest, ..." 6. 10% LTCG rate, page 17. Lose the 10% rate, nobody who can afford this textbook will be in the 10% LTCG bracket. 7. Transaction Cost, page 18. The quote for transaction costs of $.03/share assumes a lot size of 1000 shares. Although those with, say, 700 utils to play would trade this size, those with 300 utils might trade in simple 100 lots, in which case the cost is 3/8. In option trading scenarios, commissions are higher. Suppose a retail client has a negotiated one-way commission of $75, regardless of size. 10-lot option trades then cost more than 1/16; this cost greatly influences decision to close out trades in which little premium was received. Round- trip commission on a 10-lot equal .15, more than 1/8th; if the trade was selling options for .15 to begin with, closing out the trade becomes unprofitable. A business' fundamental trading scheme can change based on imposition of these costs. See comment a2(b) on wrap fees above. 8. 1st full paragraph, page 18. See comment f5 above. We are aware that the holding period used in this book is greater than 1 year; however, the text should hold without loss of generality. (a) In the assumption list, include "a holding period of greater than 1 year." (b) Ordinary income list should read "(dividends, interest, STCG, etc." (c) "20% on capital gains" should read "20% on LT capital gains." g. Chapter 7. 1. Table text size. The reviewer is delighted to find a single volume which provides a concise list of most-used accounting ratios. However, the text is too small. Please make all these tables larger. The problem is similar to the Rice University Office of Development publications; anyone with the ability to substantially gift to Rice is UNABLE to read the print in those documents. 2. 7.1, Introduction. In the teens and 1920's the job title "statistician" was what applied to what we now call "securities analysis." Graham was promoted to fixed-income statistician in 1914. [7, ch 2] 3. Typo, 3rd line, page 2. "Ration" should read "Ratio." 4. Last sentence before equation 7,1, page 22. Since equation 6.1 has been defined previously, suggest changing "by iterating equation (6.1)" to "by reiterating equation (6.1)." 5. Problem 7.1, page 25. The Balance Sheet is labeled Income Statement. The balance sheet probably needs a snapshot date as well. h. Chapter 8. 1. Equation reference, page 8. Equation reference (7.12) should most likely be (8.12). i. Chapter 9. 1. End of big paragraph, page 8. Suggest fixing incomplete sentence, "These are big questions." 2. Section 9.4.2. Should emphasize the different strategy is performed in a TAXABLE ACCOUNT, not tax-deferred, as in the previous example. 3. 2nd paragraph, page 12. Suggest changing "And is downright pleasant" to "And it is downright pleasant." 4. Growth rate alpha, page 19f. It seems mu has been replaced with alpha, should change previous reference or something. 5. Footnote 7, page 23. "..even the advocates..." should be changed to "..even the EMH advocates..." since it is not implicit in the note. 6. Section 9.5.1, first sentence, page 25. Suggest adding after George Bush "and his ideological predecessors." 7. Results, 2nd paragraph, page 25. Consider adding a sentence summarizing the results under the existing SSA plan, with mu less than 1.5%, then index for inflation. 8. Page 28. For completeness, how about resampling 20- year stretches? 9. Section 9.7, conclusions, 2nd paragraph, page 34. Change "ENRON" to "Enron". 10. Broad bear markets, 3rd paragraph, page 34. Suggest changing "2000 and 2001" to "2000 - 2002;" even if the bear market ends this year, it must be said the bottom was in 2002. 11. Problem 9.4, page 35. In the problem statement, change "monthly prices" to "weekly prices." j. Chapter 10. 1. Figure 10,1, page 2. Consider adding another significant digit to the OI/S column so readers will not think the recurring 19% is a misprint. 2. Figure 10.10, page 8. Replace with correct figure for Ameritape stock price. 3. Figure 10.13, page 11. Try to move figure 10.13 a little closer to figure 10.12. 4. Typo, 2nd paragraph, page 17. Correct "portfolio os stocks" to "portfolio of stocks." k. Chapter 11. 1. Definitions, page 1. We are lucky with futures and options, the US Government (CFTC) publishes official definitions, the SEC does not. Most exchanges also publish glossaries. Referring to these, we suggest: (a) Strangle. This is what was meant by "spread," see comment below. The strangle can have either the put or call out of the money (OTM). (b) Spread. A spread is buying and writing the same type of option (call/put) on the same underlying, with different strikes or expiration dates. (c) 2nd paragraph, 2nd half, page 1. Since the option premium is the market price of the option, we suggest replacing the last 3 existing sentences with the following: In this case, the option has an intrinsic arithmetic value, i.e. the difference between the existing stock price and the specified exercise, or strike, price of the option. All options with any time to expiration will, of course, trade at prices above this value, the difference being called its time value. The time value, when added to the intrinsic value, gives the market price, or option premium. 2. 3rd paragraph, page 1. Because the example posits only 6 contracts, suggest adding "suppose there are ..." to "there are six contracts..." 3. Un-numbered table, page 2. What happened to the Oct 02 17.5 put? Either add, or delete the row. 4. UMF and BBMF funds, page 5. One could add another scenario: Around the time of expected FDA approval, Formerly Feckless Trader (FFT) has recently attended an options trading seminar, and observes ten times the usual option volume in the near-term options, and rising implied volatility based on C_m the market price of the options. The trader is a little miffed that the BSOPM/CIR model prices the option at 3.75 with imp. sigma=.66, but the spread is 3.2 by 4.5. FFT buys a straddle for $9.00. Being long the straddle at 9, he thinks this only requires at 20% move with BlahBlah at 50 to break even. The FDA approves the drug, and BlahBlah jumps to 60, the IV collapses, and he sells the spread for 10. The stock made a huge move, and FFT breaks even after commissions, not thinking the market makers had already priced in the expected event. 5. Footnote 6, page 8. Since space is not an issue with this footnote, change "agreement about the stat outcomes..." to "agreement about the statistical outcomes..." 6. Footnote 6, page 9. Clarify "derivation of the hedged [portfolio, not] arbitrage..." 7. Risk-neutral probability measure q, page 11. Suggest use of the phrase "...has SOME of the formal properties of a probability." Although Cox-Ingersoll-Ross has undoubtedly established the probability behind this whole martingale-measure thing, I strongly believe counterexamples can be presented which show either the failuer of Q << P on sets with non-zero measure, or one could show that Q may be only finitely additive, which would disqualify it from being a probability measure. 8. Last sentence before section 11.3, page 14. Reading this statement is like watching the bombing down building air vents in TV coverage of the Gulf War. 9. Missing text before table 11.7, page 18. There seems to be a block of missing text introducing the bear jumps into the option price tables. 10. Section 11.5, page 20. Change "(big and frequently false)" to "(a big and frequently false)." 11. 2nd sentence, page 23. Change "vendors of the stock to take note" to "vendors of the option to take note." They are not the same. 12. Last paragraph, page 21. Change "transaction costs are not free" to either "transaction costs exist", or "transaction costs are not zero." 13. Last sentence, page 22. Consider adding: "Everything, that is, except for compound interest." l. Chapter 12. 1. 1st sentence, page 1. For improved parallelism, consider changing "electromagnetic flux" to "electromagnetism", or else change "mechanics" to "mechanical phenomena." 2. 3rd paragraph, page 1. Suggest changing "2000-2001" to "2000-2002." 3. Worldcom merger, page 2. Could add remark about the Clinton Justice Department's decision to attack Microsoft for creating a ubiquitous computing environment. [NOTE: these comments are written in Wordperfect 5.1+ for DOS since the Windows version of Word is unmanageable for paragraph numbering.] 4. 3rd sentence, page 4. Although my dictionaries are not handy, I believe "tact" should be "tack;" but, I never get into English word-choice matches with my thesis advisor. 5. John Meriweather, page 6. The perp's name is spelled Meriweather. m. Appendix A. 1. Figure A.3, page 13. Consider adding continuity dots at the left of each step function. Then there is also room to add remarks like "we note that F(x)-> 0 as x-> -infinity, F(x)-> 1 as x-> infinity, and that the function is right- continuous." 2. Gamma function, after equation A.52. Before "the random variable X" you could insert the generalized factorial factoid since many readers will keep this book on their shelves; for any a, use the Gamma(a+1)=a! representation. 3. Section A.13, W(t) properties, page 25. These three properties (and their necessary implications) are correct as written, but their rigor could be emphasized without additional clutter by replacing "stochastically independent" with "stationary and independent." 4. Equation A.73, page 25. Suggest using "We define a Brownian process with drift S(t) as..." 5. Equation A.74, page 25. mu*t should be mu*dt. 6. Equation A.75, page 26. This should read: dS(t)/S = mu*dt + sigma*dW(t). 7. Item 3, page 28. t = -ln(1-u)/lambda, not +ln... 8. Item 3, page 31. Need a space between normal and observation. 9. Sentence for equation A.102, page 32. Suggest this be: "Then, since sigma_ij = sigma_ji, i.NE.j, we have as our covariance...." 10. Nelder-Mead Algorithm, page 42. PLEASE MAKE LARGER! n. Appendix B. Thank you for including tables in your books. The text is WAY too small. Also, consider drawing a horizontal line every 5 lines to aid readability. References. [1] Bright, Don (2000). "Since You Asked," Technical Analysis of Stocks and Commodities October 2000. [2] Greg Ip (2000). "Role as Big Nasdaq Market Maker Helps Knight/Trimark's Portfolio," The Wall Street Journal, March 3, 2000. [3] Greg Ip and Rebecca Buckman (1999). "Regulators Worry That Online Investors May Be Getting Poor Trade Executions," The Wall Street Journal, April 23, 2000. [4] Harrison G. Hong, and Jeremy C. Stein (rev. 2002). "Differences of Opinion, Short-Sales Constraints and Market Crashes," Review of Financial Studies (accepted), [5] Niederhoffer, Victor (1997). The Education of a Speculator, New York: John Wiley & Sons [6] Dobelman, J (1999). "Contributions of Holbrook Working", Research Report, Statistics Department, Rice University. [7] Janet Lowe (1994). Benjamin Graham on Value Investing: Lessons from the Dean of Wall Street, Chicago: Dearborn Financial Publishing If additional information is needed, please contact John A. Dobelman, at 713 348 3652, or via dobelman@stat.rice.edu.