RISK & RISK MANAGEMENT
GLOSSARY
Black Monday 1987 Stock market crash that occurred on 19 October 1987. The crash began in the Hong Kong market before spreading around the world as other markets opened. It was the largest one-day percentage loss in US stock market history.
Black-Scholes-Merton option pricing formula Theoretical model for pricing stock options based on the current stock price, the option’s exercise price, expected stock price volatility, time to exercise and other factors. The model provides an initial theoretical foundation for option pricing, but traders typically use more sophisticated models based on more realistic assumptions about potential price movements.
dot-com bubble Period from the mid-1990s to the early 2000s of extreme speculation and investment in internet-based companies. Stock prices of technology companies soared, encouraging further investment and more companies to form, often without the normal checks. The bubble burst when investors cut funding, causing many companies to go out of business.
edge A gambler’s advantage in a bet; it is a factor in the Kelly criterion for sizing gambles.
hedge fund An investment fund formed by groups of individuals or institutions who pool their capital to invest in stocks, bonds, derivatives, currencies, and other assets. Managers typically receive a regular management fee and a share of profits.
insider trading The practice—usually illegal—of trading stocks and options based on material, non-public information about a company’s performance.
Ponzi scheme Fraudulent scheme that lures investors with promises of high returns for low risk. Earlier investors are paid using money from new investors, creating a pyramid structure. The deception can only continue if there is a regular stream of new investors. Named after conman Charles Ponzi.
portfolio theory Describes how investors can reduce the risk and increase the expected returns on their portfolios. Instead of focusing on individual investments, portfolio theory considers the risks and returns of an entire portfolio of multiple assets.
premium The charge paid to an insurer in exchange for covering a risk.
probability theory Mathematical analysis of the possible outcomes of an event.
quantitative investing Form of investment that uses mathematical computations and computer models to make trading decisions based on the analysis of complex data.
sovereign wealth fund A state-owned investment fund.
warrant The right to buy or sell a security at a fixed price before an expiration date. Warrants differ from stock options because they are issued by companies that receive any payments made in exercising a warrant.
HEDGING
the 30-second statement
Hedging is a form of insurance. A sovereign wealth fund of an oil-rich country hedges when it invests in stocks whose value tends to rise when oil prices fall. A baking company hedges its exposure to wheat prices by buying futures contracts that lock in the price at which it can buy wheat next year. A person hedges their exposure to major car repair bills when they buy automobile insurance. Hedges come in a variety of forms. One approach is to buy one asset whose value tends to move in the opposite direction of the second asset that the investor would like to hedge. Such strategies often work, but there is the risk that the two assets’ prices will not move together as expected, in which case the hedge provides imperfect insurance. Another type of hedge is when pension plans, which have long-term liabilities, purchase long-term bonds that are likely to provide the right amount of cash at the right time to meet the plans’ obligations. Other approaches to hedging include the purchase of conventional insurance, options and long-term contracts that smooth transactions prices. Financial markets made wider use of options, a primary form of hedging, after the development of the Black-Scholes-Merton option pricing formula in the 1970s.
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Entities hedge whenever they protect themselves from the effects of unexpected changes in economic circumstances.
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Hedges are only as good as the person or business on the other side. Counterparty risk is the risk that the other side of the hedging contract will refuse or be unable to pay off under the terms dictated by the contract. Regulation often limits counterparty risk in conventional insurance markets, such as those for life insurance, but the risk is often greater in unregulated markets. Several major financial institutions were surprised by counterparty risk during the 2008 financial crisis when the parties with whom they had hedged were unable to meet their contractual obligations.
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3-SECOND BIOGRAPHIES
EDMUND O’CONNOR
1925–2011
American trader who helped found the Chicago Board Options Exchange in 1973
ROBERT C. MERTON
1944–
American economist who advanced methods for pricing options and helped found Long-Term Capital Management in 1994
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William Carrington
Hedging protects investors from losing too much when a single asset falls in value.
DIVERSIFICATION
the 30-second statement
Should investors concentrate their investments or spread them over many assets? Probability theory provides a clear answer: spreading investments reduces risk. Suppose the average stock offers two equally likely outcomes: a 60 per cent gain over the next year or a 40 per cent loss. On average, you would earn 10 per cent by investing in a single stock. But it’s risky. Half the time you’d end up down 40 per cent. For many people, that’s a good reason not to invest. The story changes, however, if you can spread your investment over 100 different stocks with the same potential gains and losses. On average, about half will be winners and half losers. Your expected return is still 10 per cent. But you face much less risk. How much less depends on how correlated the stock returns are. If returns are completely uncorrelated, your risk evaporates. You would lose money only once every 35 years. If all 100 stocks rise or fall together, however, diversification does nothing. You face the same risk. Reality falls between these extremes. Stock returns depend on a mix of common and idiosyncratic factors. Diversification protects you from the idiosyncratic ones. That reduces the risk of big swings – whether down or up – in your wealth. But it cannot eliminate the common ones.
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Spreading investments over many assets reduces risk, especially when their returns have little correlation.
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To fully benefit from diversification, think broadly. Investing in stock mutual funds, rather than individual stocks, is a good start. Investing in bonds, real estate and other assets reduces risk further. So does investing abroad. In addition, consider diversifying your personal financial risks. Think twice about owning stock in your employer. A sudden downturn could hit your job and your portfolio. And take care if you and your spouse work at the same employer or even in the same industry.
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MUTUAL FUNDS & EXCHANGE TRADED FUNDS
RISK, REWARD & THE KELLY CRITERION
3-SECOND BIOGRAPHIES
SAMUEL ORCHART BEETON
1830–77
English publisher of Beeton’s Guide to Investing Money with Safety and Profit, one of several sources endorsing diversification long before modern portfolio theory
HARRY MARKOWITZ
1927–
American economist and Nobel Laureate who began modern portfolio theory, the mathematical analysis of risk, return, correlation and diversification
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Donald Marron
To minimize risk, don’t place all your eggs in one basket.
RISK, REWARD & THE KELLY CRITERION
the 30-second statement
Losing investments are painful. If your portfolio falls 50 per cent, you need a 100 per cent gain just to get back to even. But you have to take some risks to earn investment rewards. So how much should you invest in promising opportunities? In 1956, John Kelly provided a rigorous answer. He started with the obvious. Invest more when the potential gains are large or the chance of success is high. Invest less when potential losses are large or the chance of failure is high. From those building blocks, Kelly determined how much to invest if your goal is maximizing your portfolio’s long-term growth. Kelly’s formula is simple for casino-style bets where you either win some amount or lose your bet entirely. In that case, each bet should be a fraction of your stake equal to your edge divided by the odds. The edge reflects the average return on the bet, and the odds reflect how risky it is. Casinos typically don’t let you get an edge, so Kelly’s criterion suggests you avoid them. But the same concept applies to investing more broadly. Scale investments to the size of your portfolio, invest more when expected returns are higher and invest less when potential outcomes vary a lot.
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Building wealth requires a balance of risk and reward. The Kelly criterion shows how to strike that balance when sizing bets and investments.
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The Kelly approach maximizes the long-term expected growth rate of wealth. That’s a great starting point for planning investments or placing a long series of bets. But there is more to consider. Some investors dislike the volatility – up and down swings in wealth – the Kelly approach allows. Some have specific goals for which they are investing. And some have limited time frames. Investors should consider all those factors, as well as Kelly’s insights, when deciding how much to invest.
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3-SECOND BIOGRAPHIES
DANIEL BERNOULLI
1700–82
Swiss physicist and mathematician famous for work on fluid dynamics, probability and decision-making under uncertainty
JOHN L. KELLY JR.
1923–65
American physicist and Bell Labs researcher who developed a betting and investing formula that maximizes the long run growth rate of wealth
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Donald Marron
Savvy investors choose how much to invest according to how favourable the odds are.
BLACK SWANS & FAT TAILS
the 30-second statement
Financial markets are often assumed to follow a regular pattern with frequent small changes and rare large changes. That assumption gives rise to a bell curve for fluctuations that has a fat middle and skinny tails. That assumption is explicitly embedded in option pricing formulas and is implicitly built into the actions of many investors. Yet large changes are more common and severe than people often expect. Like Europeans discovering black swans in Australia, investors are occasionally stunned by large market moves. In statistical jargon, the distribution of possible market changes is fat-tailed, meaning that extreme moves are a serious risk. Oft-cited examples of black swan events in financial markets are the Black Monday stock market crash of 1987 and the ‘dot-com bubble’ of the late 1990s. Black swan events have several implications for financial markets. First, standard formulas that assume a smooth distribution may seriously misprice certain assets. Second, it is difficult to learn about an unknown fat-tailed distribution from only a few events or observations – a black swan could be lurking in the near future even if we haven’t seen one yet. The biggest historical black swan events have been negative – it is even more rare for asset prices to increase quickly and dramatically.
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Black swans are things you thought couldn’t happen but suddenly do, and their existence implies that our familiar bell curves should have fatter tails than we typically assume
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Black swan events occur outside of financial markets too. Earthquakes and wars, for example, have fat tails with low-probability, extremely costly events. Martin Weitzman has argued that carbon-induced climate change and collision with meteors are phenomena with fat-tailed cost distributions, as either event could generate catastrophic losses. He argues that governments should devote considerable resources to the mitigation of these low-probability risks, in part because the size and likelihood of those extreme events are so uncertain.
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3-SECOND BIOGRAPHIES
BENOIT MANDELBROT
1924—2010
Most famous for his work on fractal geometry, this French-American mathematician also explored how randomness and fat tails appear in financial markets
NASSIM NICHOLAS TALEB
1960—
Lebanese-American statistician, risk analyst and former option trader who wrote The Black Swan (2007) about the implications of fat-tailed distributions for financial markets
30-SECOND TEXT
William Carrington
Black swan events are rare – until you realize they aren’t.
INSURANCE
the 30-second statement
Insurance works by pooling and spreading risk among a large number of insured. Risk is spread from those who can’t bear the full financial cost of a negative event on their own, to an insurance company that takes in premiums from a large number in order to pay out claims to a few when harmful events occur. Individuals or firms purchase insurance to cover a wide range of harmful high-cost, low-probability events, paying a premium for a certain amount of coverage in case of financial loss. Car and home insurance provide protection for our property, while life and health insurance offer security for our livelihood in case illness prevents us working. Wherever the possibility of an adverse event, there is usually an insurance product available to mitigate that risk. Actors, artists and athletes can purchase insurance to cover the loss of income in case of damage to certain body parts. Individuals and businesses can purchase liability insurance to protect against lawsuits. Some insurance companies will also purchase insurance, called reinsurance, from other insurance companies to cover their financial risk, such as when large numbers of people file claims in a national disaster area after hurricane or wildfire damage.
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Insurance provides protection against risk of financial loss from high-cost, low-probability negative events.
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Insurance isn’t just a private market product. Social insurance is a public programme designed to protect the public from financial harm due to a loss of income from adverse events, such as redundancy, old age, disability or death of a primary worker.
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ALTERNATIVE FINANCIAL SERVICES
3-SECOND BIOGRAPHIES
EDWARD LLOYD
c. 1648–1713
Edward Lloyd’s coffee house sold maritime insurance and was the beginning of Lloyd’s of London Insurance Company
WARREN BUFFETT
1930–
The most famous American investor, Buffett built insurer Berkshire Hathaway into a leading global conglomerate
30-SECOND TEXT
Jason J. Fichtner
Insurance provides protection against loss of life, income or property.
ANNUITIES
the 30-second statement
An annuity is a financial contract that provides regular payments over time. Annuities arise in many contexts, including payments from lotteries and lawsuits, but they are especially important for retirement saving. Outliving your savings is a major retirement risk; annuities help manage that risk by converting savings into predictable payments. Governments structure public retirement programmes as annuities; beneficiaries receive payments as long as they live. Financial institutions, typically insurance companies, also offer private annuities. These allow you to invest some of your savings in return for future payments. Private annuities come in many varieties. Some offer a fixed number of payments, while others continue until death. Some annuities start paying out immediately, while others pay at a future time. Some provide benefits to one person, while others include survivor benefits, providing income after a person’s death to a surviving spouse or children. Fixed annuities provide a guaranteed fixed payment amount. Variable annuities link payments to the performance of financial markets. Variable annuities provide a less stable cash flow, but can be a good option for people who want some investment in financial markets. Good returns could allow a higher payout than a fixed annuity would offer.
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Annuities are financial products that protect your savings by converting an upfront lump sum into a stream of future payments.
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Though there are many benefits to annuities, many people fail to buy them. Economists call this the ‘annuity puzzle’. Perhaps people are scared off by the complexity of the product or the associated costs and fees. Maybe instead of viewing annuities as insurance, people instead view them as a gamble on how long they’ll live, in which a person has to live a certain number of years in order to break even purchasing an annuity.
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MUTUAL FUNDS & EXCHANGE TRADED FUNDS
3-SECOND BIOGRAPHIES
OTTO VON BISMARCK
1815–98
Under his leadership as Chancellor, Germany became the first nation in the world to adopt an old-age social insurance programme in 1889
FRANCO MODIGLIANI
1918–2003
Italian-American economist and 1985 Nobel Laureate in economics, known for his work in how people save, how they spend and the annuity puzzle
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Jason J. Fichtner
Annuities’ regular payments help to manage income risk.
