Imperial College MSc Finance Summer Term

This post is about the final term of the Imperial College Business School 2012-2013 MSc Finance programme. For the earlier posts, please go to the Imperial College category of this blog.

The summer term ended about two weeks ago with the final exams of the programme. The final term consists exclusively of electives and a research project, which is due for submission in August. MSc Finance students could choose from the following elective courses for the summer term: Cases in Finance and Investments, Credit Risk, Corporate Finance in Regulated Industries, Fixed-Income Securities, Mergers and Acquisitions, Private Equity and Venture Capital, Structured Credit and Equity Products, Behavioural Investment Management and Advanced Options Theory. Students doing the so-called "Applied Financial Research" (AFR) report had to choose up to three electives, depending on the number of courses taken in the spring term, and students doing the bigger traditional "Research Project" (RP) could choose a maximum of two electives. The business school also offered an optional course on programming in VBA, after already having offered a C++ class in the previous term. Since I have been one of the students doing the RP, I had two courses in the final term, namely Fixed-Income Securities and Advanced Options Theory, which are therefore the only ones I can review in this post.

Both of these courses relied heavily on the books by Paul Wilmott, especially Paul Wilmott Introduces Quantitative Finance and The Mathematics of Financial Derivatives. For your information, "PW Introduces..." is almost identical to the more expensive three-volume set Paul Wilmott on Quantitative Finance, the only difference being that the latter contains additional chapters on more specialized cases, so the aforementioned book is absolutely sufficient for studies and probably for practical use, too. I like Wilmott's books very much, because they were not written for hardcore mathematicians or physicists like some other quant finance books but for working finance professionals. They contain the required amount of math and asset pricing theory in continuous time, but all of this is presented in a very intuitive way.

As the name suggests, Advanced Options Theory (AOT) was about the evaluation of options. The course focused on the pricing of equity derivatives in a continuous-time framework. Naturally, we had the pleasure of dealing with all kinds of differential equations in each lecture. First, we derived the pricing PDE for derivative securities using the general no-arbitrage method and then went on to different ways of solving such partial differential equations. The solution methods we discussed included Laplace transformation, restating the problem in terms of the heat or diffusion equation, and similarity methods for reducing the dimensionality of the problem. We then went on to numerical solution methods, including finite difference methods, which we discussed in great detail and learned how to implement in the C++ programming language. In the following lectures, exotic options were introduced and priced in the PDE framework. During the remainder of the course, further assumptions of the Black-Scholes model were relaxed. For example, we later assumed interest rates and volatility to be stochastic instead of constant and allowed for the underlying asset price path to be discontinuous by incorporating a jump component.

Fixed-Income Securities (FIS) often relied on a set of tools similar to those used in AOT, but I personally think FIS was more challenging. The math itself was not difficult, but many models and techniques just are more abstract for interest rate derivatives than equity products, especially when it comes to models of the yield curve. The first lecture of the FIS course covered mostly basics, including definitions of simple interest rate instruments, such as LIBOR, forward rate agreements and interest rate swaps, but we also looked at interest rate derivatives (swaptions, caplets/floorlets) and Black's 1976 model. The second lecture was about one-factor term structure models, including Vasicek and Cox-Ingersoll-Roll (CIR), and, much like in AOT, we learned how to derive the pricing PDE and how to solve it (if possible). Lecture three, expectedly, continued with multi-factor models. We concentrated on the so-called exponential-affine class of models, such as the Gaussian Central Tendency (GCT) model, the Fong-Vasicek stochastic volatility model and the multi-factor CIR. From then on, the level of difficulty increased significantly as we proceeded to arbitrage-free models of the yield curve. Within this class of models there are basically two ways of perfectly fitting the initial yield curve. The first is to introduce time-dependent parameters, i.e. a time-varying drift or volatility, which then requires the calibration of the model parameters. The second possibility would be to use the 1992 Heath, Jarrow and Morton (HJM) framework, where the initial forward curve and volatility structure are given exogenously. Instead of calibrating the model parameters, you use a no-arbitrage argument to derive future movements of the forward curve. The lecture closed with the Markovian HJM model, an extension of the aforementioned HJM framework that gets rid of path-dependencies in the Brownian motion term by imposing a restriction on the volatility term. After this rather abstract topic, we went on to fixed income derivatives and the forward-risk adjusted measure. The remaining lectures covered market models (LIBOR and swap market models), different models for the pricing of defaultable bonds and convertible bonds.

There isn't much more to say about the final term of the MSc Finance programme. I am currently working on my research thesis, which I will hopefully be able to submit in a few weeks. Most of the other finance students are also putting the finishing touches on their projects. The term officially ends in August, but many students have already started to work for various banks and companies in the city either as an intern or analyst. I will refrain from writing a thorough review of the MSc Finance programme at this point, as I hope my posts about the individual terms provide enough information for aspiring students interested in Imperial's finance degree. Instead, I am going to occasionally publish complementing shorter posts that will answer specific questions I have received from undergraduate students and applicants via email over the past months.

For now, however, I'd like to conclude by thanking all readers for their interest and by wishing best of luck to those who are about to begin their studies in September 2013 and to those who are thinking about applying to Imperial College Business School for a future start date!

Imperial College MSc Finance Spring Term

I know, it took way too long for me to publish this post, but good things come to those who wait! I've been super-busy over the past months, so please forgive the long wait. If you just arrived here for the first time via a search engine or a link and you haven't read my earlier posts about the Imperial College MSc Finance programme yet, please browse the IC section of my blog for the posts on the previous terms.

The spring term lasted from January through March and it was the first term where we were allowed to choose electives in addition to the term's two compulsory core courses, Asset Pricing and Derivatives and Advanced Financial Econometrics. Personally, I chose to do International Finance and Hedge Funds, but then dropped the Hedge Funds elective a few weeks later because it was different from what I had expected. Other electives, which students could choose from, included Banking, Advanced Investments and Advanced Corporate Finance. In addition, the business school offered an optional course in the C++ programming language. In this post, I will only comment on the courses I took. Let's start with the two core courses:

The course Asset Pricing and Derivatives (APD) was supposed to give students a more in-depth introduction into the pricing of assets in discrete time and by way of binomial trees than Mathematics for Finance had done in the first term. The course was also important, because it paved the way for the more advanced courses on options and fixed income securities that were to follow in the subsequent and final term. Unfortunately, I quickly got the impression that the lecturer had stepped in for someone else at the very last minute, because he was badly prepared. Apparently, there must have been a misunderstanding with the business school, considering that the lecturer initially assumed the course to be exclusively about models of the yield curve and the pricing of fixed income securities. He therefore had to change the syllabus while the course was already under way and I think the quality of the lectures suffered from this initial lack of structure. While the lectures on the fixed income world were actually quite good albeit highly theoretical, the lectures on equity derivatives often seemed improvised. Following negative feedback from the students, the business school promised that this would not happen again in the future and I can report that they organized an additional series of asset pricing lectures for us in the summer term, which were really excellent. This has been very professional, in my opinion, because it shows that while mistakes can happen, the business school is prepared to correct them quickly. But now on to the topics we covered: APD was not based on any book but on elaborate notes prepared by the lecturer. Of course, Options... by John Hull is usually a handy book when it comes to this subject matter. The courses started with a lecture on foundational issues in interest rate modelling and the use of binomial trees and then went on to no-arbitrage models, such as the Ho and Lee (1986) model, which takes the current yield curve as given and aims at matching model prices to observed market prices. In this part of the Asset Pricing course, we also learned about the calibration through Arrow-Debreu securities, which we applied to the Ho and Lee model and the Black, Derman and Toy (1990) model. In the second half of the course, the lecturer covered forwards and futures and possible explanations for backwardation and contango, the Black-Scholes model as well as the practice of hedging and volatility models (i.e. assuming volatility to be stochastic).

Advanced Financial Econometrics (AFE) was quite demanding, but it was very useful and one of the best lectures we have had. The lecturer was very well-prepared and I liked particularly that all theoretical concepts were followed up by a practical application in a statistical software package, such as OxMetrics or Matlab. The course started with non-parametric estimation and non-parametric regressions, followed by techniques to make inferences more robust. After that, we covered multivariate time-series models, including  vector auto-regressive (VAR) models, autoregressive distributed-lag (ADL) models and the concept of co-integration and the error-correction mechanism. I found this lecture particularly interesting and applicable to the analysis of financial time series. The course further covered time-series models of the variance, such as different versions of auto-regressive conditional heteroskedasticity (ARCH) models, and we looked at parametric models for qualitative variables, Monte Carlo methods and finally model specification issues. As said, the course was demanding. For those afraid of mathematics, it might seem a bit overwhelming at first, but the lectures and tutorials were really good and useful in preparing for the exam. The lecturer did not require students to purchase a textbook, because the lecture notes were already quite self-contained. Personally, I found The Econometrics of Financial Markets by Campbell, Lo and MacKinlay to be useful for some of the topics. Econometric Methods with Applications in Business and Economics by Heji et al. was also recommended to us, but it is more "wordy" than the book by Campbell et al.

In addition to the two core courses, students could choose up to two electives in the spring term. I took International Finance, because I am very interested in foreign exchange. I also wanted to do Hedge Funds at first, but the course seemed more like an introduction, which gave only a quick overview of the different strategies employed by hedge funds, so I dropped it after having been to a few of the lectures.

International Finance (IF) was another excellent course of the MSc Finance programme. I liked most about the course that we covered not just purely theoretical content but also looked at empirical evidence. In the first lecture, the professor talked mostly about foreign exchange market conventions. Having worked in FX before, I already knew about certain conventions, but it was a good refresher and certainly useful for students who have not yet had any contact with FX trading or research. Besides quoting conventions and specific terms used by currency traders, we were also introduced to certain types of arbitrage, such as spatial and triangular arbitrage. The lecture closed with some key statistics from the 2010 triennual central bank survey on the foreign exchange market. The second lecture covered foreign exchange market efficiency, including covered and uncovered interest rate parity and the carry trade. In the following weeks, we were taught about real exchange rates, purchasing power parity, the balance of payments and exchange rate determination and forecasts, which I found particularly interesting. The final two lectures covered current currency investment strategies and volatility strategies in FX. In the last two weeks, we also had talks by guest speakers from Goldman Sachs and Credit Suisse, both of which were very insightful. The recommended textbook for the International Finance course was International Financial Management by Bekaert and Hodrick, but the both the lectures and the final exam relied more heavily on the lecture notes and academic papers than on the textbook. All in all, International Finance has easily been one of my favourite courses so far.

Imperial College MSc Finance Autumn Term

Time is running fast! We are already halfway through the spring term of the MSc Finance programme at Imperial College Business School (ICBS) and I haven't even reported on last term's lectures yet. But as promised in October, here are my thoughts on the autumn term's four core courses.

For me personally, Corporate Finance was the least interesting course, so let's get it out of the way first. Basically, the lectures were closely based on the Corporate Finance textbook by Jonathan Berk and Peter DeMarzo. This had the advantage that the lectures were clearly structured and it was easy to find reading material going beyond the lecture slides. Unfortunately, in the first few lectures there was a bit of an overlap with the Business Valuation course we had had in September. But to be fair, this was the first time the Corporate Finance lecturer taught the course at Imperial and he later told us that he was going to compress some of the introductory stuff for next year's class in order to be able to spend more time on the more interesting topics. Roughly speaking, the course was divided into the aforementioned introductory part about the fundamentals of valuation for all-equity firms, and a part about valuation methods taking a firm's capital structure into account. This second part, stretched out over five lectures, started off with an idealized Modigliani and Miller setting. Each subsequent lecture new complications, such as debt, taxes, leverage and financial distress, were then added to make the valuation models more realistic. The course was concluded by a lecture on mergers and takeovers. Even though I said that I did not find it very interesting myself, I don't want to sound negative, because the course was all right overall. It could have used some examples containing actual company data or a more elaborate case study instead of exclusively relying on exercises from the book, in my opinion. But the course has been an especially useful introduction for those students going to work in mergers and acquisitions, equity research or related fields, and many of them have since chosen to continue with the Applied Corporate Finance and Advanced Corporate Finance electives, which are offered in the spring and in the summer.

Financial Econometrics is a course I found extremely relevant, considering the importance of econometric methods for empirical research. Especially in finance, however, econometrics is not merely used in academia but also in practice. Many quantitative trading strategies or risk management tools, for instance, are based on results obtained from empirical studies. Unfortunately, the course covered a myriad of topics. On one hand, you could argue that this gives you a complete overview of the basic econometric techniques and I can see why this might be important to the majority of students, most of whom are going to join investment banks upon graduation. On the other hand, however, one must acknowledge that we did not go into a lot of detail in most of the lectures, which I found slightly disappointing. I would have preferred if we had covered only a selection of the topics and looked at them more thoroughly instead. Still, I stand by my point that the course has been useful. It made me aware of many pitfalls to avoid in hypothesis testing and introduced important time series properties that you should test for before drawing any statistical inferences. Also, this was only the first of our econometrics courses: In the spring term, we currently have Advanced Financial Econometrics, which, as the name suggests, is more technical and builds on our knowledge from the previous term's lectures. Taken together, the two courses introduce a lot of material and they train students rather well in the use of econometrics. In addition to academic papers, the autumn lectures were mostly based on the textbook Introductory Econometrics for Finance by Chris Brooks. It is not very technical, which makes it easy enough to read. I found the book handy as a quick reference during my revisions for the final exam, but overall the lecture slides and the notes from the tutorial classes were already quite self-contained.

Another quantitative subject we covered during the autumn term was that of Mathematical Finance. The course presented an introduction into the pricing of assets in complete and incomplete markets. Almost everything that was covered in Mathematical Finance was new to me, so I got a lot out of the course. The course textbook was Mathematical Techniques in Finance by Ales Cerny. Following the outline from this truly excellent book, which I am certain to flip open again for future reference, the lecturer first introduced a one-period finite state model for the pricing of derivatives as well as the concept of Arrow-Debreu securities. He went on to lecture about state prices, the ubiquitous no-arbitrage pricing theorem and the utilization of risk-neutral probabilities in asset pricing. We eventually stepped from pricing securities in discrete time into the nebulous world of continuous time and stochastic processes, learning about Martingales, Brownian Motion and the Itô formula, to name the most important concepts. Although some of this was difficult to understand during the lectures, the book helped a lot and the course topics have proven useful in our follow-up lectures in the spring term. For instance, we regularly use the concepts from Mathematical Finance in our Asset Pricing and Derivatives course.

At least as insightful was the fourth course, Investments and Portfolio Management. The first lecture began with optimal portfolio selection in the mean-variance space and the capital asset pricing model (CAPM). While I knew this from my previous studies already, a lot of this was new to many students who had previously studied something unrelated, such as engineering or mathematics. We moved on to the APT, multi-factor models and the CCAPM, then discussed the efficiency of markets and behavioural biases and ultimately looked at the predictability of asset returns, which I found to be the most interesting part of the course. The lecturer, one of my favourites at Imperial so far, mostly explained things in detail, provided both practical examples and cited results from the academic literature. But he also moved fast, making IPM a very demanding course. The recommended textbook for the course was Investments by Bodie, Kane and Marcus, but as mentioned already, the lectures relied a lot on academic papers. The textbook was a good complement for the lecture notes, though. In addition, Asset Pricing by Cochrane proved to be an invaluable reference for what we covered on return predictability (some chapters were required readings).

All in all, we studied what feels like a thousand things during the autumn term. Time was always a scarce resource, especially since we were required to regularly submit either individual or group coursework, sometimes up to three assessed pieces of work in a week. The amount of time the coursework takes away from your study schedule is not to be underestimated. What made the autumn term even more demanding for many students is that September-December is the time of the year when the big firms in the finance industry are accepting applications for internships and graduate schemes. The majority of MSc Finance students applied for jobs during those months and thus had multiple job interviews and assessment centres throughout the term.

As I write this, the spring term is already well under way. I will most likely report back on the spring term's lectures in April. Before then, I'll have exams to prepare for -- they're not as far away as one might wish. (Four weeks can go by in an instant!)

Imperial College Application Questions

At least once a week I go through the traffic stats of this blog and my other websites. One statistic included in the reports is how people arrive at my sites. Expectedly, a big portion of the traffic is referred to me by search engines. So, naturally, I open the next report telling me what search terms were used by people who found my blog. Over the past month the number of visitors who searched for tips on how to apply to Imperial College increased significantly. For example, popular search terms over the last 30 days include:

Imperial College Career Planning Question Help
Imperial College MSc Finance Application
Imperial College Personal Statement
Career Planning for MSc Finance Imperial

The list goes on. Having studied a bit of economics, I duly noted this change in demand by my readers and I hereby react to it by supplying this short blog post.

It makes sense that search traffic for the above search terms spiked over the past weeks, considering that the first application deadline for the Imperial College MSc Finance programme was on 14 January. The next deadlines for the 2013 intake will be on 4 March, 30 April and 30 May, according to the ICBS website. I would advise to apply as early as possible.

Regarding tips for how to write the short essay and how to answer the career questions, I'm not going to say too much. First of all, what worked for me might not be good advice for you, because our academic background and work experience are likely to differ. Secondly, the Imperial College admissions office wants you to thoroughly think about these questions yourself and personalized answers will do far better than standard ones.

As part of the application for the MSc Finance programme, you are required to write a personal statement of roughly one page in length and you are asked to answer four career questions. (At least that is what I had to do. The application requirements might have changed in the meantime.)

The main purpose of the personal statement is for you to communicate why you want to pursue MSc studies, your reasons for choosing Imperial College and your motivation for applying to the particular programme. Keep your writing concise, as there is a strict page/word limit. I would recommend that you spend some time thinking about your motivations and your goals before you begin to actually write the text. This might just save you time because you won't have to edit the text so much later on. Personalize your statement by highlighting important stages in your academic or professional career and how they might have influenced your decision to study at ICBS. It is also important that you collect as much information on Imperial College and the MSc programme as you can. You might want to include one or two of these details in your statement to show that you understand what sets ICBS apart from other universities and why you think you are a good fit for the programme. Additionally, you might be asked to highlight a personal achievement that you are particularly proud of. I guess you could write about pretty much everything here. Just make sure that you present it in such a way that the person reading it can relate to it and that it comes across as genuine. Finally, format your statement in a professional way. That is, use paragraphs, do not use fancy font types or colours, and check your spelling and grammar. I know, this is obvious. Just make sure you don't forget it. Also, uploading the statement as a PDF might look nicer that simply uploading a Word document.

Regarding the career questions, I had to answer four of them:

1. Please describe your short-term (3 year) career goals. (200 words)

2. Please outline the challenges you think you will face in achieving these career goals and how you will overcome them. (200 words)

3. Please describe your long-term career goals or, if these are not clear, please outline the industry sectors that are of particular interest to you and why. (200 words)

4. What skills do you think are important in the career that interests you, how would you demonstrate that you have been developing these skills so far? (300 words)

Gather your thoughts and again do a bit of research before answering the questions. For example, when describing your career goals you might want to consider what type of company you are interested in working for as well as recent industry developments and how these might affect your professional career. You might already have some companies in mind that you want to apply to in the future. In that case it would be a good idea to look at job descriptions they have posted on their websites and what skills they are looking for. You will need many of these hard and soft skills in business school, too. Of course, you will have the chance to improve your skills during your MSc studies. As for the career goals, be as precise as you can. If you already know that you want to work in asset management, M&A or sales and trading, write that. Don't just say you want to work for a bank and stop there. On the other hand, you are not required to have a detailed career plan laid out already. The admissions office is well aware of the fact that your career prospects might change over time and that your studies might even push you in a slightly different direction. I don't think I need to go into more detail here, because Imperial has a useful page with tips for answering the career planning questions, too.

To sum up, my final advice is to be honest. Also remember that it is an actual human being who will be reading your statement, so make it easy to read and interesting. If what you write is not believable, if it is too general or even boring, this might reflect negatively on you. Collect your thoughts, transform them into the right words and then arrange those words in a presentable fashion. This is no magic. Good luck!

Imperial College MSc Student Blogs

As one might have been able to tell from the long-lasting silence on this blog, I have been very busy with my studies lately. The workload increased significantly compared to the introductory September courses. Usually we have between two and three assessed courseworks to complete in any given week, all the while trying to keep up with new material introduced in the lectures and revising past lectures for the exams coming up in two weeks. It may well be another three weeks until I will have the time to sit down and review the autumn trimester. I also received requests via email to write a bit about the application process at Imperial College Business School. I'm going to do this shortly.

In the meantime, I recommend prospective students take a look at Imperial's official MSc student blogs. The site features student bloggers from most programmes, including MSc Finance, Risk Management and Financial Engineering, Strategic Marketing, and International Health Management to name a few. If you're still undecided as to whether to apply for any of the business school's MSc programmes, don't hesitate to contact the current students with any questions you might have. I'm sure they will respond with useful advice.