AC437 Financial Econometrics

This is another core module. The first part is taught together with the MSc Econ students, which covers classical econometric theory - linear regression, OLS, MME, MLE, GLS, IVE, hypothesis test framework, Wald, LR, LM, asymptotic theory. The second part focuses on applications to finance - random walk, event studies, CAPM, factor models, PV relations, volatility modelling, GMM.

The paper this morning was not too difficult, but I can kick myself now. I am embarassed to say that I got simple stuff wrong...calculation of power of a test! That's 10% gone! Shit happens. But I'm not the only duck, apparently many people got it wrong too. Other than that, I'll probably be penalised here and there for whatever reasons they might give. Hope I'll scrap through to get a distinction on this one, but not very confident either.

The next paper on Tue is gonna be a killer. The whole class is scared shit. And it happens to be the module I like most.

CAPM tests

Many tests have been carried out to determine if the CAPM holds. CAPM postulates that beta completely captures the cross-sectional variation of expected returns. Now, I am not convinced that this simple relationship can help to predict asset returns, and is evidenced by the many test results over the past few decades. Presence of irrational investors and other risk factors must be involved. Hence I wouldn't be interested in doing a test (but which I did several years back). What is surprising is the paper by Fama & French (1992, 1993), that including book-to-market and size as factors can in fact explain asset return variation better. It is also quite robust to different time periods. So much so as this is taken as the industry benchmark in comparing investment portfolios. But how do we intepret BM and size as risk factors? And are there other missing factors?

Why?

Questions that have been frequently thrown all over the place: Why...
1) does a quant need a PhD?
2) isn't a Masters enough, since in the long run, knowledge and industry experience count more than a PhD under your belt?
3) do banks like mathematicians and physicists?
4) must I graduate from the top universities?

See here for a discussion.

Desk allocations

Just got a confirmation on my desk allocations. I'll be rotating across fixed-income, equity derivatives and structured credit. Don't really know what to expect as I'm a green horn but I'm looking forward to learning new stuff. It'll be both stressful and enjoyable at the same time. Let's just hope everything turns out well and they won't send me packing. Oh boy, it's gonna be a long summer.
Anyway, there are other things to worry about at the moment - exams.

I'm still seething from the wrong options I chose. Damn. As usual, I could've done much better had I put in more effort. Never satisfied with my output anyway.

EC411 Microeconomics

This is a core module for MSc F&E, and it covers standard micro theory - consumer, producer, welfare, perfect competition, monopoly, oligopoly, product differentiation, game theory applications, signalling, bargaining and auctions. The structure of the exam is very much applied in nature, and questions "look" rather easy. But they can be extremely tricky, e.g. you don't see nice functions like CES or Cobb-Douglas. More often than not, you will have to solve for corner solutions rather than interior ones.

Sat for the paper this afternoon. I thought it was relatively harder compared to past years, but many people thought otherwise. Most of my classmates have an Econ background, so I guess it's easier for them (I didn't major in Econ). Besides, this is also a core module for the MSc Econ programme in arguably the most prestigious economics school outside of US (I see Oxbridgers shaking their heads in denial), so we have some of the best Econ students around (Vinayak calls them creme de la creme, but as in any programme, you have duds as well). Anyway, I was a little disoriented in a room filled with weirdos, and I skipped the game theory questions which requires more brain energy. In other words, I'm an airhead. I'm not sure if I chose the right options in part B of the paper. Not confident of a distinction grade for this one.

Oh well, 1 down, 4 to go.

Coin tossing game

This is a question posted in the Wilmott forum some time ago and has attracted considerable attention. It looks like a simple problem (but I don't think it is).

In a fair coin tossing game, your payoff is the number of heads divided by the number of tosses (i.e., m heads of N tosses give you $m/N). You can quit anytime. What is the fair price of playing this game? (fair means that the house breaks even in the long run).

Answer to problem posted in previous blog (22/05/07):
In period 2, player B proposes. If A rejects, both get 0. So B proposes 1 for himself (hence 0 for A), since either way A gets 0 (A is indifferent between the two). Discounted to period 1, B's proposal is d.
In anticipation of B's proposal, in period 1, A proposes 1-d since he has no incentive to give B more than d.
Hence optimal solution is (A,B) = (1-d,d)

Game theory

A simple game-theoretic model can provide insights to a problem. It is another tool used in the analysis of the interaction of players. Everyday life poses game theory problems, e.g. firms deciding whether to enter a particular industry, how companies set prices in view of the actions of competitors, how one responds to a given incentive or disincentive, etc.

My microeconomics exam is on this Friday. I have never liked this subject, and having lecturers like mine didn't further help the cause. Anyway, in preparation for the paper, I was forced to read up and found to my liking, the simple applications of game theory (though Nash equilibrium is an easy concept, the solutions can sometimes be a little illogical at first glance).

A simple problem:
Suppose there are 2 players (A and B) bargaining over a cake of size 1 in 2 periods. There is a common discount factor, d (if you have 1 in period 2, that means it is worth d in period 1).
In period 1, player A proposes a share x for himself (and hence 1-x for player B). If B accepts, the game ends, otherwise we go to period 2.
In period 2, B proposes a share y for himself. The game ends after period 2.
What are the optimal responses for both players?

ps. You should watch "A Beautiful Mind" if you haven't already done so. It's one of my all-time favourite films.

The battle over ABN Amro

There is heightened uncertainty in the air as the drama continues to unfold. Who will win the takeover battle? Barclays? RBS?
Fortis, RBS and Santander have submitted a proposal to acquire LaSalle (a subsidiary of ABN) when the proposed sale to Bank of America was put on hold.
Hugh Scott-Barrett has announced that he will step down as CFO. There are reports that customers are fleeing. Employees are uncertain about their future. It is believed that the retrenchment number will be close to 4500, with the technology group more probable to be highly affected. (An insider source revealed to me that ABN will pay a compensation worth of 2 years' pay to new employees if they are retrenched. I wonder if this is good news).

Barclays and RBS stock prices have fluctuated widely over the last 2 months, with the risk index increasing by 1.5 to 2 folds.
I am keen to grab hold of analyst reports on the predictive impact of this takeover. Any sources?

Consolidation in the financial industry has been going on for some time, following the trend from the US. As the financial landscape reshapes and giant conglomerates form, one wonders if there are efficiency gains or economies of scale and scope.
What are the consequences and future implications?

The Quintessential Quant

I happened to chance upon this article published in Business Week. Thinking of working for Renaissance Tech or DE Shaw?

ps. James Simons is the 2006 IAFE Financial Engineer of the Year .

All-rounder

In this increasingly competitive society, a myriad set of skills is essential, in fact a pre-requisite for a quant. And this doesn't guarantee success. Success is a combination of motivation, desire, diligence, entrepreneurship, innate talent and an element of luck.

Just to get to the starting point of the race, one needs to have an advanced degree. A working knowledge of stochastic calculus, probability theory, measure theory, statistical theory, programming and simulation, ODE, PDE, numerical analysis, real analysis, complex analysis, functional analysis, metric spaces, optimization theory.

Is it all about math? Scientific curiousity, good business acumen, excellent presentation skills, ability to intepret results, client-oriented and being a team player - all come into the equation.

You have to understand the dynamics of financial markets, the behaviour of assets, how to replicate them and structure new products, transcation costs and liquidity constraints, impact of uncertainty as well as legal, accounting, tax and regulatory implications among other issues.

Seems daunting isn't it? But I wouldn't know until I have had a taste of it.

On a separate note, I'll be making a trip to Cambridge after my exams to visit an old friend who has just completed his PhD and will be working as a quant in a top-tier IB. He might be able to provide more insights from his past internship experiences. I'm looking forward to that. And I'm starting work next month too, I'm so excited.

Good times?

A recent article posted on eFinancialCareers stated that this year has been exceptionally good in terms of job opportunities in the financial industry. I'm not sure how Morgan McKinley came up with the results, but it certainly didn't seem that easy.
My batch has experienced difficulties getting offers, though by now about 50% of the class should have found something. Certainly not 2 to 8 offers. How absurd.

Another article claimed that bonuses will increase. I certainly hope so. I need cash to finance my Hugo Boss and Armani suits, and Burberry, Gucci and LV accessories. Ok that's so not true.

Wrong decision?

Well, the MSc programme I am currently in isn't that rigorous you might say, and I can't agree any better. I had initally planned on applying to Financial Math/Financial Engineering programs in US for entry in 2007, but it didn't work out. I wanted a change of scenery so badly that I was too hasty in making the decision to apply for 2006 entry, and in the process of doing so, I missed out on almost all the deadlines for US schools. I only managed to apply to Columbia MAFN, NYU and UK schools.

Even then, with the offers I had, I chose LSE over the likes of Columbia, Imperial and Oxford. Though I have now landed a quant internship with a bulge bracket firm after convincing them I was good enough, the decision still stings somewhow. Right, so in LSE neither did I learn C++ nor Matlab, and the courses are not mathematical enough. Why the heck did I choose LSE then? Sadly, I lost focus along the way, and opted for an easier programme - no math proofs, no programming, just plain theory and applications.

I'm contemplating doing a PhD to have a good shot on becoming a quant, but my math skills aren't quite up there. My programming skills aren't up to par either, though I'm comfortable coding in Excel VBA. Perhaps I should just be content with the internship and work my way through.

I'll think about what I want to do when my exams are over. Over the next few weeks, I'll be blogging on my exams, and perhaps will write an article on "Surviving the MSc Finance and Economics at LSE", much in the spirit of what Vinayak has done for MSc Econ. Hopefully it'll prove useful for prospective applicants.

Demand for quants

From the pioneering work on modern financial economics by Harry Markowitz, William Sharpe and Merton Miller to the revolutionary Black-Scholes formula by Robert Merton, Fischer Black and Myron Scholes, coupled with the advent of rapid technological progress over the past decades, the financial industry has undergone vast changes in terms of complexity and innovation. There is now an ever increasing need for highly quantitative and numerate people - mathematicians, physicists and engineers to work at the forefront of financial markets.

For starters, refer to the following resources for a better definition and introduction to the role of a quant.

wikipedia
Mark Joshi (pdf)

The Beaver