Radcliff had listened with interest and had challenged Jo on several points that she was pleased to have been able to defend. A subsequent offer and attaining top grades in all her school exams had gained Jo a place at Jesus College, Cambridge, to study Mathematics. It was only two weeks into her first term as an undergraduate that she realized that the ‘advanced theories’ she had been expounding to Radcliff were, in fact, considered basic on her new course.
As the train edged into Cambridge station, Jo eased her thoughts back into the present. Jo’s mind started to race again as she grappled with her sticking point in Bray’s theory. She felt nervousness mingled with anticipation. For all his habitual warmth of manner, Jo was aware that Radcliff was distinctly cold when dealing with any lack of preparedness on the part of his students.
Jo took a taxi from the station to Jesus College. The route took her past familiar haunts including pubs, restaurants and the shop from where she had rented her graduation gown. The driver then turned down the side of Parker’s Piece, the common which had been the backdrop to her first collage break-up after the May Ball in her second year.
Once out of the cab, Jo made her way down the Chimney, a long walled walkway that marked the entrance to the college, and which was lined with students’ bicycles all the way to the porters’ lodge.
She was greeted by the Head Porter. Jo recalled memories of him chasing her over the college lawns after she had misappropriated a traffic sign as part of a scavenger hunt.
“Well, hello, Madam,” greeted Clive Brown in mock formality.
They were interrupted by a chattering crew of Jesus College Boat Club members heading off to the race on the river. Jo didn’t recognize any of them and concluded that they must be a first year undergraduate novice crew. Jo marveled that she must have looked that young when she first arrived.
The porter handed Jo the key to the college room she would be staying in overnight. She dropped off her bag in the monastic room, and immediately set off to the river for the Fairbairn Cup races.
Throngs of crews and supporters from all the different colleges were also tracing the same path on foot and bicycle, each college member wearing their distinct colors. Jo followed the red and black kit of the Jesus crews to their college boathouse.
She got immediately caught up in the atmosphere, greeting old rowing friends and catching up with the gruff college boatman, who remained fiercely proud of his teams through the passing decades. Jo began to wish she could don her kit and take part in the grueling but exhilarating race. She ran her fingers over the calluses on her palms that still remained after her three years of undergraduate rowing.
Jo walked down the river and settled herself on one of the bends with a good view of approaching crews and the finish line. As the first boats came into sight, the noise level rose like an impending tidal wave. Jo braced herself in the midst of blaring horns and yelling coaches and supporters. A tangle of bicycles followed the crews, each jostling for position precariously close to the river bank edge. The race was timed with teams setting off at intervals. The fact that the results wouldn’t be posted until later did not, however, dampen victorious cries at the race’s end.
The women’s first crew was particularly satisfied with their performance and when Jo rejoined them at the boathouse, cheap champagne was already flowing.
“Have a swig!” urged Bridget, the women’s captain, as she proffered a bottle.
“Maybe later. Certainly later,” promised Jo. “Excellent race, girls.” She wanted to be clear-headed for her meeting with Radcliff that was scheduled to take place in an hour’s time.
Back at Jesus College, Jo gathered the books she needed from her room. Checking the time, she decided she just has time to run and indulge in a huge baguette sandwich and delectable flapjack from her favorite sandwich shop in Cambridge, Natalia’s Patisserie.
With her stomach full, she hurried down the Chimney again and arrived back at the college at five minutes to one. Her habitual ten minutes of tardiness would never be acceptable for a meeting with the Professor. Jo resolutely ascended the narrow, worn stone staircase to Radcliff’s study to find his door slightly ajar. She knocked and heard an “Enter!”
Jo crossed the threshold into the quintessential Cambridge professor’s study with its leaded glass windows, wooden floor, worn rugs, and oversized desk. The stone fireplace was flanked by faded armchairs, and a large mobile blackboard completed the room’s academic credentials.
Jo also noticed the piles of papers stacked on every surface and on the floor, recalling that despite the seemingly random filing system, it never prevented Radcliff from quickly locating anything he wanted.
Radcliff looked up from his desk where he was grading papers. Peering over his glasses, he gave a broad smile and rose to come around his desk and warmly embrace Jo.
The Professor had a full requisite of salt and pepper color hair, with the salt encroaching a little more every year, and paired with light blue eyes and an athletic frame. He emanated an outdoor ruggedness, while always succeeding in looking poised and distinguished at any formal event.
Jo, like most female students, had had to overcome any romantic fantasies about the brilliant but elusive older professor. Radcliff’s own life had been a solitary one for the most part. He had never married and, as far as anyone knew, had only been involved in one long term relationship several decades earlier with an Italian concert pianist. From the relationship he had a daughter, Isabella, on whom he doted.
Isabella was now in her late twenties, and an art school graduate as well as a formidable free spirit. Father and daughter shared passions for sailing, travel and humanitarian causes.
Radcliff had become a strong mentor figure to Jo, offering fatherly support in a very empathetic manner, while also challenging her to realize her full academic potential. As she felt herself slipping back into a familiar role, the sensation of being back in this environment reminded Jo that, in many ways this was also her home, where she had experienced the confidence that came from the right mix of acceptance and encouragement. For a brief moment, Jo wished that she could crawl back into the cocoon of this world.
“So how was your journey from the big metropolis this morning? Smooth I hope?” asked Radcliff.
“Yes, early but uneventful.”
“Early?” Radcliff smiled and shook his head. “Surely you hot shot trader types are used to being up at the crack of dawn? No more slothful student lie-ins. Worth coming down to see our crews’ performance though. Quite a good showing. Tea?” he asked brandishing a kettle.
Jo nodded assent. “I think there’ll be some celebrating tonight.”
Radcliff put the kettle on and removed the piles of papers from the armchairs by the fire. He motioned for Jo to sit down. As Jo settled herself, she noticed a prestigious award being used as a paper weight for a stack of journals on the floor. The Professor had always been self-effacing with regard to formal acclaim, but maintaining that it was the price of being able to fund his department and pursue his work.
A couple of minutes later, Henry Radcliff produced the English answer to all situations; a large teapot of steaming tea and two mugs.
Stirring in milk, there was a glint of humor in Radcliff’s eyes as he addressed Jo. “So, I haven’t had the opportunity to offer my congratulations.”
Jo looked quizzical.
“The job. Butterfly Investments?” prompted Radcliff.
“Oh, yes,” Jo answered. She felt slightly awkward, as if faced with a reminder that she has sold out. There had been some discussion of her returning to study for her PhD, but Jo had never committed herself and Radcliff was not one to press.
“They were very impressed with you when they visited. The Butterfly recruiters, I mean.”
“But I never met them here.”
“No, not knowingly. Their snooping was all very covert. Quite amusing really. I thought it was all pretty harmless otherwise I would have let you in on it. Don’t worry, I didn’t rev
eal anything compromising, like how you only just scraped a 1st in your second year exams,” Radcliff teased. He then added sincerely, “But no, I’m happy for you.”
Jo remained silent, staring at her tea. There was a long pause before Radcliff dipped his head to meet her gaze.
“Are you happy for you?” he asked.
“Of course,” replied Jo breezily. She changed the subject, refusing to dwell on her choices, “But I’m a little stuck. I hope you don’t mind.”
Jo opened her bag and took out the photocopied pages from Bray’s book. She handed them to Radcliff.
Radcliff replaced his reading glasses and took the papers. Jo watched for any reaction to the author’s name, but saw none. She watched him scanning the pages, his eyes moving quickly over the complicated formulas with no pause.
Jo took small sips of the hot tea as she became aware of the rain that had begun to fall outside. The only other sound was the ticking clock on the mantle. Jo curled up her feet and savored the quietude.
Jo wasn’t sure whether she had been lost in thought or a light sleep when she felt the pages being placed on her lap. The Professor rose and refilled their mugs from the teapot. Jo could not contain her eagerness.
“So, what do you think?”
“Interesting, very interesting. Some of his best work, no doubt.”
Jo noticed that the reference to Bray was indirect.
“His application of neural network theory to predictive market analysis is brilliant. There’s no other word for it. Highly innovative.” Radcliff trailed off and then laughed. “He should publish this.”
Jo smiled ruefully, “I don’t think that’s going to happen. You’re looking at the goose that lays their golden eggs.”
“You’re also looking at the settling of a long standing score.”
Jo immediately wondered if it had anything to do with Radcliff’s department, making Radcliff’s next question unexpected.
“Are you familiar with Bray’s father?”
“No,” admitted Jo.
“Well that’s the root of the issue. Not many people know of him. Edward Bray was a stockbroker in New York and seemingly a very successful one until, one day, at the peak of his career he made a radical change in course and went back to college in the US to get a PhD in economics. Armed with his new degree he then immersed himself in theoretical research, specifically expounding the theory that stock price movements were not random, but could be predicted based on analyzing and processing enough information.”
“What kind of information?”
“A whole range of data. Obvious statistics like past stock prices, company financial data, interest rate movements, economic growth, but also less logical figures such as weather trends, the political climate, demographic movements.”
“Was he right?” asked Jo.
“Impossible to say one way or the other. It was just a mathematical theory. A kind of sophisticated iterative process that claimed that the more information you added, the greater was the predictive value of the model. The problem at the time was that computing power was both very slow and very expensive. Dr. Bray Senior never had the resources to put his theories to the test.”
“Were they accepted anyway?”
“Not by the establishment that mattered to him. Edward Bray was already wealthy from his days in finance. He wasn’t looking for a way to make more money. What he wanted was academic acclaim. Unfortunately for him, his university career coincided with the time when a small group of influential Ivy League scholars dominated economic thinking when it came to market analysis. Specifically, they said that all predictive models were useless. Instead they preached that market movements, to the extent they took any path, followed a random walk pattern. They also firmly established the Efficient Market Theory, which …”
“States that all information is already priced into securities,” finished Jo. “Yes, I had already gathered that Bray isn’t a big proponent of this.”
“Well now you know why. A family grudge. Things became pretty vindictive, with one of the Harvard Professors writing a letter to Edward Bray, using words of only one syllable, informing him of all the perceived flaws in his theories and suggesting he return to the stock market and use the weather forecast to manage old ladies’ retirement funds. Somehow the letter got leaked to the main economic journal of the day.”
“That must have been humiliating.”
“Certainly. Bray pretty much retired from academia. It also didn’t help that the same Harvard Professor was later awarded the Nobel Prize in Economics.”
Jo pointed to the pages still on her lap. “So how does this settle the score as you say?”
“Well nowadays neural network theory is all the rage. It’s a major buzzword and you see it all over academic and finance articles. But it’s basically an extension of what Edward Bray had suggested all along. You come up with a program that can gather and analyze a vast amount of seemingly unrelated data and you shove it through a black box and out spits a bunch of supposedly accurate predictions.”
“What’s in this black box?”
“Those pages that you’re holding. It’s not literally a black box of course. The term refers to a series of processes that appear from the outside to be highly opaque, but are actually the amalgamation of many intricate analytical steps. The model is only as useful as the rules that govern it and that’s what Bray’s model does. It establishes those rules.”
“So Bray took his father’s theory and brought it into the computer age?”
“That’s not the whole story. Edward Bray’s theory is available for anyone who cares to search for it. Our Charles Bray has certainly taken its core and built on it. But knowing where to invest is only half the equation. A consistently successful investor also knows how much to invest. Tell me Jo, are you familiar with the term ‘gambler’s ruin’?”
CHAPTER EIGHTEEN
Jo pondered the beguiling term of ‘gambler’s ruin’ for a moment. “Not specifically,” she answered, “but it sounds like something unfortunate that might befall you at a saloon in the Wild West.”
Radcliff laughed. “In colloquial terms it’s pretty self-explanatory. It’s also a legitimate mathematical term. Imagine a so-called fair bet, where neither side has an advantage.”
“Like a coin toss?”
“Exactly. If you bet the same amount every time, how much would you expect to end up with over a long series of wagers?”
“The same as I started with, I guess.”
“And your expectation would be correct. In the long run you should neither win nor lose, but – and this is the crucial part – it is what happens in the interim that causes many a demise.” With cat like agility, Radcliff leapt up and strode to the blackboard. He drew a long horizontal line followed by a pointed wave form that oscillated above and below the line. As the wave traversed from left to right, its peaks and its troughs increased in magnitude.
“The horizontal line is your original stake and the jagged procession is your wealth over time,” continued Radcliff. “Two things to note. Indeed, the wave crosses the original line at several points meaning your assets are back to their starting level. But also pay attention to the fact that in the interim periods, your wealth at any given time varies considerably, and the swings get wilder the longer you gamble. We’re back at that random walk theory.”
“This is interesting Professor,” hesitated Jo, “but I haven’t witnessed many coin tosses at Butterfly. In fact I get the impression that even intimating that their methods are akin to any form of gambling would be a sacrilege.”
Radcliff laughed. “My apologies. I was forgetting. Arbitrage isn’t it? Look, I’m obviously not on the inside, but if all the firm did was invest based on sure things then you’d all be lounging in the Caribbean and then bursting into a day’s frenetic activity once every two weeks. Those opportunities don’t come along very often. No, the black box may be housing an incredibly sophisticated model, but it’s not hiding an
oracle. A level of speculation is always in play. Although I’m sure that fact is glossed over when luring clients.”
“Actually, Butterfly doesn’t have any clients. Not anymore.” Jo knew that she was probably revealing too much.
“Really?” Radcliff appeared genuinely surprised. “Let me see that model again.”
He gestured for Jo to pass the pages copied from Bray’s book to him again and he scanned the pages toward the end. “I see,” he nodded to himself.
“What is it?” asked Jo, trying to peer over.
“Well,” began Radcliff, and then stopped. “I don’t think it’s relevant to what you need my help with today. It’s just something I had skimmed over,” he trailed off, “now where were we?” he said sitting down again.
“Heads or tails I think,” offered Jo.
“Right. Well Bray’s first passion, as far as I can tell, was to establish the preeminence of his family’s name when it came to predictive modeling in finance. Fortunately for him, his mathematical prowess was matched by his gift for self-promotion.”
Jo looked up. This was the closest she had ever heard to sarcasm coming from the Professor.
“He also had a second passion he was less likely to publicize.”
Jo resisted the urge to suggest fast cars and women, and instead politely raised her eyebrows.
“Gambling,” revealed Radcliff. To this, Jo raised her eyebrows less politely.
“I suppose I should have clarified. I meant in a theoretical sense. He was somewhat fixated with the theory of gambling and particularly what were the optimal stakes a player should risk in order to maximize return while minimizing the risk of ruin.”
“And was this legitimate research or a pastime?”
“Both. Following a default by the Russian government on a large portion of its bonds, Bray published some papers analyzing which funds and banks had invested heavily in the bonds and had suffered irrevocable losses and those that had managed to weather the downturn in portfolio value. Investing in these bonds is akin to high stakes gambling. The most interesting finding from his perspective was that many of those who survived employed an asset allocation methodology based on the same model. The Kelly model.”
The Girl Inside Page 11