Jo looked nonplussed. “Don’t worry, you’re not alone. The model is either largely ignored, or, at the other extreme, provokes fervent responses by both its advocates and naysayers. It’s not difficult to understand. In fact it is elegantly simple. Basically, its originator, Kelly, stated that the proportion of your bankroll that you should gamble is the same as the ratio of the edge you believe you have in a wager to the odds offered by the market as a whole. He further stated that the rate of return is proportionate to the bettor’s so called informational advantage.”
Jo let pass the fact that the words ‘elegantly simple’ didn’t immediately come to mind in relation to the Professor’s last sentences.
“So were Bray’s findings well received?” asked Jo.
“Hard to say. They didn’t exactly create a furor. In fact the response is probably best described as lukewarm.”
“Ouch. I bet that hurt.”
“I see you already know Bray quite well,” smiled Radcliff. “Yes, he took it quite personally; as if the ghosts of family academic disparagement had come back to haunt him.”
“So what did he do?” Jo felt like she was being drawn into a tale with pleasingly more drama than was usually warranted by financial theory.
“Well I think he thought that he needed the opportunity to prove his theories in actual trading scenarios. And a university isn’t really the place to pursue that …”, again Radcliff trailed off, no longer looking at Jo.
“So that’s one of the reasons Bray started Butterfly Investments. To prove a point,” suggested Jo.
“You’d have to ask him that. But, the model in your hands is clearly based on the gathering of vast amounts of data and the sophisticated mathematical manipulation of this data to produce an informational advantage, which should then translate into a superior rate of return. And firmly planted on page fifteen, I believe, is the Kelly formula, which determines just how much of the fund’s assets should be allocated to a particular trade based on the firm’s informational advantage.”
“But,” Jo pressed, “if Bray had already established all this theory while he was in your group, why did he disappear for so long before materializing as the co-founder of Butterfly? Why not act immediately?”
“Look Jo,” said Radcliff, shifting in his chair and looking at his watch, “I’m not sure exactly how we digressed onto these subjects, but is there some specific mathematical problem I can help you with?”
Jo was well versed enough in reading her professor’s tone to know that a subject had just been firmly closed. She put her head down and turned the pages of Bray’s model until she located the set of equations that she had failed to understand. She showed the page to Radcliff.
“It starts with this non-linear, multi regression equation. I understand that the network is trying to minimize the final error term by iteratively feeding outputs back through the system. But I don’t get how this series of partial differential equations feeds into the sigmoid function at each node.”
Radcliff scanned the equations for a few seconds and walked again to the chalkboard. He proceeded to go over the steps in the equations, breaking them down into their component parts.
Within a few minutes, under the patient tutelage of the professor, Jo was able to grasp the elements that had previously eluded her. She felt a welcome release of the tension that had built up behind the impasse reached by her comprehension. Radcliff handed the papers back to Jo and she began to thank him for his time.
“Wait,” interrupted Radcliff, “now I’ve shed some light on your questions, maybe you can help with one of mine. Now understand that I only ask this out of curiosity and I’m not fishing for you to disclose any confidential information, but how does your employer manage to achieve these astonishing returns so consistently?”
Jo was confused, having just shared Bray’s seminal work from Butterfly’s deepest enclaves. Radcliff wore an expression of mild anticipation, but Jo felt at a loss at how to satisfy it.
“Well their returns are generated by trading on the recommendations of the model – the one we went through. Weren’t you the one who just said Dr. Bray should publish it?”
“I suppose I should have clarified – I meant as an academic paper. The theory and the algorithms are quite brilliant, as well as the ingenious incorporation of the Kelly formula we discussed. But it appears that in all the hours of study that you’ve clearly spent on this model, you’ve failed to take note of the most important figure.”
Jo’s brows furrowed and Bray motioned for her to hand back the papers. Like the model’s author, Radcliff appeared to attach great importance to the title page. He indicated a line of text at the foot of the paper. The font was so small that Jo had to approach to read it. The Professor’s finger pointed to a copyright symbol followed by Charles Bray’s name and a year five years previous.
“You mean the date?” asked Jo, since this was the only figure on the page.
“Precisely!” exclaimed Radcliff.
“Is it important?”
Radcliff laughed heartily at Jo’s unintended pun. “Jo, my dear, you have a knack for understatement. When Dr. Bray deemed to share the product of his brilliance with you, perhaps there was a recurring theme that he emphasized? The crucial factor that gives a market participant an advantage over their rivals?”
This time Jo didn’t have to hesitate.
“Information,” she replied reflexively.
“Indeed. So the model’s output, its predictive power you might say, is dependent on the information it is fed. And the kind of information that drives market movement changes over time. A status quo might persist for a while and then some factor will come along that the market hadn’t anticipated, like an oil crisis or a political change, and the dynamics of the whole market equation will shift.”
“There is already a vast amount of information fed into the model,” Jo pointed out.
“But is it the relevant information? The factors that are driving the markets today?”
“Well maybe this paper is just the theory behind the programming and the inputs are adapted as market drivers change,” reasoned Jo.
Radcliff looked doubtful. “Maybe. But for neural networks, changing the inputs, or independent variables, basically requires a new model, a whole new set of mapping equations. Why would Bray waste his time training you on an old version?”
“So what are you implying?” pressed Jo.
“I’m not implying anything in particular,” evaded Radcliff, “I’m merely curious. Don’t forget, I started off as a mathematician and when my interest was drawn toward the economic field, I too thought models were the solution to every seemingly chaotic system. That behind the data lay a perfectly logical set of rules. I was a staunch technician.”
“In what way?”
“I believed that a sufficient volume of past data was all that was required to predict future data. It’s called technical analysis. Let’s just say that many years, and models later, that I don’t agree with the strong version of the efficient market hypothesis, which holds that analysis of past data is completely futile, but I also don’t believe any model can truly be an oracle. Unless of course, the model’s architects consistently have access to information that other market participants don’t.”
Jo didn’t really have anything to say. She had never before doubted anything Professor Radcliff had taught her, but she had been so convinced by Bray’s confidence in his work, and thought it illogical that her boss would spend any of his time that he valued so highly, tutoring her on a model that didn’t work. The reference to exclusive information also reminded her of topics she didn’t wish to delve into.
“My hunch,” continued Radcliff, “is that this model may have functioned very adequately, exceptionally even, when it was first devised. The model itself may even be a victim of its own complexity; in these cases a neural network tends to memorize data rather than extrapolate to make new forecasts. Effectively, the network predicts, with what might be
construed as astonishing accuracy, that past patterns will repeat themselves. But this predictive power will have become obsolete over time.”
“Well that’s not what has happened, according to Bray anyway.”
“So you say. But what also don’t appear to have become obsolete are the profits that Butterfly seems to generate. Their methods may be proprietary, but our Dr. Bray never quite mastered the talent for discretion when it comes to his own achievements.”
Jo was beginning to wonder if Bray’s financial success elicited an element of jealousy in Professor Radcliff. She felt drawn to defend her employer, having, in some way, chosen a side. She also wanted to cling onto the belief that Butterfly’s profits were indeed the product of superior knowledge, not insider information.
“Maybe I’ve misunderstood the importance of the model for Butterfly. Dr. Bray’s Quant Group, the department I’m in, is very adept at identifying individual arbitrage opportunities – market mispricing and the like. They are usually very profitable.”
Bray raised his eyebrows. “Profitable enough for the Bray Foundation to single-handedly sponsor the recent Uffizi exhibit at the National Gallery?”
Jo didn’t have a convincing answer and the fact annoyed her.
“You seem to take a great interest in Dr. Bray and his activities,” she challenged.
“Well, now I have a vested interest,” replied Radcliff, gesturing towards Jo. His tone was contrastingly kind and Jo felt ashamed of her outburst.
Radcliff eyed his watch.
“Much as I’m enjoying our time together, I am expected in the Master’s Lodge in half an hour for Boat Club dinner pre-drinks, and the much anticipated unveiling of the Master’s latest addition to our college’s illustrious collection of modern art artifacts.”
Jo returned his rueful smile. Modern art had certainly proved an enduring passion of the current Master, and the Jesus College lawns were generously adorned with a scattering of sculptures, some more identifiable than others.
“Look Jo,” said Radcliff, rising from his chair and escorting Jo toward the door, “you’ve only been there a few weeks. I’m certain there’s many things you don’t yet know, but I’m sure it will all come clear in the end.”
Jo’s pride felt stung. While she was happy to accept her role as a relative ingénue, she felt that having now graduated she had earned a certain amount of professional respect.
Jo had not come with the intention of confiding in Professor Radcliff since she even avoided mulling over her findings in her own mind. Yet she didn’t want their meeting to end with Professor Radcliff having the impression that she was fulfilling her job requirements in docile naïveté.
“There is something,” she blurted out, “something I came across. I accessed some files that I wasn’t supposed to – by accident – and they had some details about future trades …”
Radcliff put up a hand and Jo was reminded of her brother-in-law’s reaction. The subject appeared to be so toxic that no-one wanted to be anywhere in its vicinity.
“I don’t know what you were going to say, but I don’t think it was the explanation I was hoping for. I thought maybe there was some quirk in the currency markets or some trading legality loophole that Butterfly had figured out, and that even years later, they are still waiting for the market catch onto. Such cases aren’t unknown. It isn’t any secret that Dr. Bray and I have a history, shall we say, but I would like to think the best of him. And perhaps it would be best to delve no further. Or, then again, perhaps I am mistaken and this model of his is more adaptive than it appears.” Radcliff held out his hand. “Here, leave it with me. Maybe I’m the one missing something.”
They both knew this was highly unlikely and Jo knew she shouldn’t be parting with the copies of the sacred tome of the Quantitative Group. Her reluctance was exacerbated by the fact that the photocopiers at Butterfly Investments required each employee to key in a personal code that was then imprinted on to the copies produced. Should the papers go astray, they would be traced directly back to Jo.
Radcliff’s arm remained outstretched. “I have some time so I can look at it tomorrow, and I have a meeting Monday afternoon at Imperial College in London. We could get together for lunch beforehand when I’ll return the papers.”
Jo could not turn down the offer of further insight from Radcliff and she passed him the pages.
Jo enjoyed the riotous atmosphere of the Boat Club dinner, especially since the women’s crew had indeed been victorious in the Fairbairn Cup. There was much cheering and toasting down the lengths of the long wooden tables in the college’s vaulted dining hall. Amidst all the fun, however, Jo sensed that she had already crossed some indefinable line that nudged her away from student frivolity and toward the role of a responsible adult. After downing three glasses of port in rapid succession, she revised her assessment down to semi-responsible adult.
CHAPTER NINETEEN
The following evening, while Jo was still nursing a hangover, glad for once of the thudding distraction, the phone rang at the Bray’s mews residence in Knightsbridge. Laura Bray urged her husband to answer it quickly, lest the noise disturb their sleeping infant.
The pace at which Charles Bray ambled over to the handset was noticeably slower than the rate at which the color then drained from his face.
“Charles? Are you there? I said it’s Henry. Henry Radcliff.”
Bray rallied to regain his composure.
“Henry! Well it’s certainly been a while. To what do I owe this honor?”
“Surely the honor’s all mine given the great forays you’ve made into the business world since we last spoke.”
“It’s true, I’ve had some fortuitous years, but I’m sure you didn’t call to chat. Does the Department need me to fund a new Chair or are you looking for a change in career – want to get in on all this action you’ve been missing?”
Radcliff affably fielded the offers. “No, nothing like that. Our department is very well funded, over funded in fact, and I remain very content in my career choice. I merely called to offer my congratulations.”
“How very kind of you. Is there something I’ve done you consider to be of particularly merit?” inquired Bray, maintaining the façade of polite banter redolent of gentlemanly exchanges two centuries previously.
“Well yes in fact. It appears that you had the great acuity to hire one of my former students.”
“Josephine Lavelle?”
“Indeed.”
“In that case, I am the one who should perhaps be congratulating you. You certainly provided her with an excellent foundation and she is proving very useful to the firm.”
“I am happy I could oblige, although the talent of course is all Jo’s. I regard her as somewhat of a protégée and, if I may be so bold, I think her mathematical talents may have been better employed elsewhere.”
“By ‘elsewhere’ I assume you mean at Cambridge in your department. Well rest assured Jo’s continuing education is in capable hands. The best in the industry in fact.”
“So I’ve heard. Repeatedly, in fact, in the financial press. I must say that Butterfly Investments’ ability to consistently beat the market is astounding. Care to share your secrets with an old colleague – my interest is purely academic of course?”
Bray emitted a dry laugh. “Now if I were paid a pound for each time I’ve been asked that, then my income might even surpass that of my fund. But you’re forgetting one of the main reasons for setting up a private hedge fund – its methods are just that, private.”
“Still,” pressed Radcliff, “it’s quite remarkable. While funds all around you are dropping like flies here is Butterfly scaling even greater heights of financial success – well if you believe the reports.”
“Maybe we shouldn’t believe everything we read.”
“Even if you’re quoted as the source? Nevertheless, you must have the regulatory authorities crawling all over you, suspicious, or perhaps just jealous. But then I hear that Butterfly i
s very well connected. Those irksome investigations are probably only for the minions.”
Bray, already uncomfortable talking to Radcliff, became distinctly uneasy about the direction their conversation was taking.
“Henry, it’s been a pleasure and I’m flattered by your interest in my company and its hiring choices, but it’s getting late.”
“And here I was thinking the markets and its Titans never slept! I’ll keep in touch then. You know, I have a genuine concern for Jo’s future and plan to follow her early career closely – act as mentor.”
“You still speak with her then?”
Radcliff deflected the question. “Well we’re both keen supporters of the Jesus rowing crews, as you used to be I seem to recall. Anyway, I’m happy to fill that role as long as she’d like me to.” Radcliff paused. “The thing is Charles, if I’m honest, I’d hate to see such potential thwarted by any regrettable embroilments or unfortunate associations.”
Bray had been reclining, or attempting to, in an angular Queen Anne chair upholstered in rich purple velvet, but now he rose to his feet.
“Damn it Henry!” Bray exclaimed, unable to keep up the pretense of civility any longer. “What’s all this drivel about ‘regrettable’ and ‘unfortunate’? The girl should be bloody grateful for where she’s at. In fact, call and congratulate her if you feel the need to meddle in her life. But if you’ve got something to say to me, spit it out!”
“I think we both know what I’m saying, but if you’d like me to act the role of your tutor again, let me be plainer. Results such as Butterfly’s are practically unheard of. Achieving recurrent double digit returns on large positions for over half a decade just doesn’t happen, unless… ”
The Girl Inside Page 12