Chapter 1

Quantitative Finance Unveiled

IN THIS CHAPTER

Using probability and statistics in finance

Finding alternatives for cash

Looking at efficient (and not-so-efficient) markets

Tackling options, futures and derivatives

Managing risk

Doing the maths (and the machines that can help)

Quantitative finance is the application of probability and statistics to finance. You can use it to work out the price of financial contracts. You can use it to manage the risk of trading and investing in these contracts. It helps you develop the skill to protect yourself against the turbulence of financial markets. Quantitative finance is important for all these reasons.

If you've ever looked at charts of exchange rates, stock prices or interest rates, you know that they can look a bit like the zigzag motion of a spider crossing the page. However, major decisions have to be made based on the information in these charts. If your bank account is in dollars but your business costs are in euros, you want to make sure that, despite fluctuations in the exchange rate, you can still pay your bills. If you're managing a portfolio of stocks for investors and you want to achieve the best return for them at minimum risk, then you need to learn how to balance risk with reward. Quantitative finance is for banks, businesses and investors who want better control over their finances despite the random movement of the assets they trade or manage. It involves understanding the statistics of asset price movements and working out what the consequences of these fluctuations are.

However, finance, even quantitative finance, isn't just about maths and statistics. Finance is about the behaviour of the participants and the financial instruments they use. You need to know what they're up to and the techniques they use. This is heady stuff, but this book guides you through.

Defining Quantitative Finance

My guess is that if you've picked up a book with a title like this one, you want to know what you're going to get for your money. Definitions can be a bit dry and rob a subject of its richness but I'm going to give it a go.

Quantitative finance is the application of mathematics - especially probability theory - to financial markets. It's used most effectively to focus on the most frequently traded contracts. What this definition means is that quantitative finance is much more about stocks and bonds (both heavily traded) than real estate or life insurance policies. The basis of quantitative finance is an empirical observation of prices, exchange rates and interest rates rather than economic theory.

Quantitative finance gets straight to the point by answering key questions such as, 'How much is a contract worth?' It gets to the point by using many ideas from probability theory, which are laid out in Chapters 2 and 3. In addition, sometimes quantitative finance uses a lot of mathematics. Maths is really unavoidable because the subject is about answering questions about price and quantity. You need numbers for that. However, if you use too much mathematics, you can lose sight of the context of borrowing and lending money, the motivation of traders and making secure investments. Chapter 13 covers subjects such as attitudes to risk and prospect theory while Chapter 18 looks in more detail at the way markets function and dysfunction.

Just to avoid confusion, quantitative finance isn't about quantitative easing. Quantitative easing is a process carried out by central banks in which they effectively print money and use it to buy assets such as government bonds or other more risky bonds. It was used following the credit crisis of 2008 to stimulate the economies of countries affected by the crisis.

Summarising the mathematics

I'm not going to pretend that quantitative finance is an easy subject. You may have to brush up on some maths. In fact, exploring quantitative finance inevitably involves some mathematics. Most of what you need is included in Chapter 2 on probability and statistics. In a few parts of the book, I assume that you remember some calculus - both integration and differentiation. If calculus is too much for you, just skip the section or check out Calculus For Dummies by Mark Ryan (Wiley). I've tried to keep the algebra to a minimum but in a few places you'll find lots of it so that you know exactly where some really important results come from. If you don't need to know this detail, just skip to the final equation.

Time and again in this book, I talk about the Gaussian (normal) distribution. Chapter 2 has a definition and explanation and a picture of the famous bell curve.

Please don't get alarmed by the maths. I tried to follow the advice of the physicist Albert Einstein that 'Everything should be made as simple as possible, but not simpler.'

Pricing, managing and trading

Quantitative finance is used by many professionals working in the financial industry. Investment banks use it to price and trade options and swaps. Their customers, such as the officers of retail banks and insurance companies, use it to manage their portfolios of these instruments. Brokers using electronic-trading algorithms use quantitative finance to develop their algorithms. Investment managers use ideas from modern portfolio theory to try to boost the returns of their portfolios and reduce the risks. Hedge fund managers use quantitative finance to develop new trading strategies but also to structure new products for their clients.

Meeting the market participants

Who needs quantitative finance? The answer includes banks, hedge funds, insurance companies, property investors and investment managers. Any organisation that uses financial derivatives, such as options, or manages portfolios of equities or bonds uses quantitative finance. Analysts employed specifically to use quantitative finance are often called quants, which is a friendly term for quantitative analysts, the maths geeks employed by banks.

Perhaps the most reviled participants in the world of finance are speculators. (Bankers should thank me for writing that.) A speculator makes transactions in financial assets purely to buy or sell them at a future time for profit. In that way, speculators are intermediaries between other participants in the market. Their activity is often organised as a hedge fund, which is an investment fund based on speculative trading.

Speculators can make a profit due to

• Superior information
• Good management of the risk in a portfolio
• Understanding the products they trade
• Fast or efficient trading mechanisms

Speculators are sometimes criticised for destabilising markets, but more likely they do the opposite. To be consistently profitable, a speculator has to buy when prices are low and sell when prices are high. This practice tends to increase prices when they're low and reduce them when they're high. So speculation should stabilise prices (not everyone agrees with this reasoning, though).

Speculators also provide liquidity to markets. Liquidity is the extent to which a financial asset can be bought or sold without the price being affected significantly. (Chapter 18 has more on liquidity.) Because speculators are prepared to buy (or sell) when others are selling (or buying), they increase market liquidity. That's beneficial to other market participants such as hedgers (see the next paragraph) and is another reason not to be too hard on speculators.

In contrast to speculators, hedgers like to play safe. They use financial instruments such as options and futures (which I cover in Chapter 4) to protect a financial or physical investment against an adverse movement in price. A hedger protects against price rises if she intends to buy a commodity in the future and protects against price falls if she intends to sell in the future. A natural hedger is, for example, a utility company that knows it will want to purchase natural gas throughout the winter so as to generate electricity. Utility companies typically have a high level of debt (power stations are expensive!) and fixed output prices because of regulation, so they often manage their risk using option and futures contracts which I discuss in Chapters 5 and 6, respectively.

Walking like a drunkard

The random walk, a path made up from a sequence of random steps, is an idea that comes up time and again in quantitative finance. In fact, the random walk is probably the most important idea in quantitative finance. Chapter 3 is devoted to it and elaborates how random walks are used.

Figure 1-1 shows the imagined path of a bug walking over a piece of paper and choosing a direction completely at random at each step. (It may look like your path home from the pub after you've had a few too many.) The bug doesn't get far even after taking 20 steps.

© John Wiley & Sons, Ltd.

FIGURE 1-1: A random walk.

In finance, you're interested in the steps taken by the stock market or any other financial market. You can simulate the track taken by the stock market just like the simulated track taken by a bug. Doing so is a fun metaphor but a serious one, too. Even if this activity doesn't tell you...