Preface

This book discusses many key topics in investment and risk management, global economic situation and global investment strategies. The material in this book was largely written over the period of 2007–12, one of the most tumultuous times in global financial markets which called into question not only tenets of economic forecasting and also asset allocation and return strategies. We attempt to draw some conclusions on how the structural shifts currently underway in the global economy as well as cyclical trends will affect these industries, the globe and key sectors.

The various topics and case studies are relevant for hedge fund, insurance, pension fund, mutual fund managers and other investment professionals and investors. The book presents tools and case studies of real applications for analyzing a wide variety of investment returns and better assessing the risks which many investors have preferred to ignore in the search of returns. Many security market regularities or anomalies are discussed as is the process of building scenarios and using strategies to optimize returns. All the data in the book is current for the topics and dates discussed with updates to our publication date of September 30, 2012.

We are guided by the use of careful analysis to generate future scenarios. That is, what are the chances that various future events will occur over time? How should these events and their chances influence investment decisions? Assessing all possible outcomes is fundamental to risk management, financial engineering and investment strategies. Careful consideration of future scenarios in the macro outlook and micro level leads to better investment decisions and avoids financial disasters. We remain in a period where global growth is likely to be weak, and upside risks delivered by coordinated, concentrated policy responses - This adds to the complexity of anomalies and pricing in the markets.

Learning From Disasters

A key contribution of this book is both positive and negative case studies of great successes and blowouts to better assess explicit and implicit risks and mismatches in maturities and investment horizon. We discuss strategies used by the greatest investors to obtain their high returns. To do so, we analyze hedge fund concepts and performance including major fund disasters. Chapter 26 begins with a discussion of various ways traders lose money trading derivatives. These pitfalls remind one of what not to do to try to have successful trading. Some major disasters discussed are the Long Term Capital failure in 1998, an imported fear driven crash in 1997 that sunk the Niederhoffer fund, the 2006 Amaranth natural gas disaster and Société Générale. These failures all involve over betting and not being diversified in all scenarios.

These disasters have basic common characteristics, which we call the recipe for disaster. This negative outcome materializes when one overbets, that is, has too many positions relative to one's capital (including capital that can reliably be called upon in times of need) and one is not diversified. By diversified we do not mean that we are mean-variance diversified in average times. Rather diversification in all the possible scenarios is crucial. This means that low probability scenarios cannot, as in typically done, be assigned probability zero, that is disregarded. Also, and very crucially, scenario dependent correlation matrices are needed, so that one knows how assets correlate in a scenario that actually occurs. Simulations of past average correlations, which are typically done even with stress testing, are insufficient for full protection. Given the increasing role of political actors, including central banks, and greater financial linkages across countries - correlations have risen across a variety of global asset classes, meaning that investors have a greater need to differentiate the current investment regime, and making sure they are really diversified, rather than exposing themselves to a series of related risks in seemingly uncorrelated assets classes.

For example, equity correlations rise and equity/bond correlations fall with a decline in equity prices. However, when one is in a crash mode, then equity prices are falling but bond prices are generally rising so that the bond/stock correlation is negative. The bond/stock correlation is frequently negative even though most of the time this correlation is positive. Chapter 14 provides an example of these scenario dependent correlation matrices used in a model that has been used across Austria since 2000 for the Siemen's Austria and other pension plans and by regulators. Pension plans are less levered or not levered at all as compared to hedge funds.

If one overbets, and is not diversified in all plausible scenarios then two things can happen. One can be lucky and avoid a bad scenario, racking up excess profits and receiving large fees. Indeed many hedge funds and traders typically do this as there are huge rewards for making such profits and an adverse outcome is statistically less likely. In fact, even if traders know about the dangers, it may be optimal for them to just up the bets to make more fees assuming that a bad scenario will not occur or if it occurs, it is so far in the distant future that previous profits and fees will exceed the disastrous negative results. However, if one is over bet and not diversified and a bad scenario hits, then one can lose a large percent of one's wealth.

It is worth briefly summarizing the experiences of several big blowouts which will be addressed in more detail in the book below. All have at their heart several similar traits, even if the exact circumstances are different. For LTCM the bad scenario was subtle, namely investor confidence. They were greatly overbet but reasonably well diversified except in this confidence failure when all the correlations rose so that they lost in all of their investments. Option volatilities rose, bond yields rose and this led to their 95%, $4 billion loss in August and September 1998. LTCM was loaded with talent but their risk control based on value at risk plus simulations around one average correlation matrix was insufficient to protect them. At the end of 1997, they returned $2.8 billion to investors hoping to boost their returns. The lack of liquidity, after returning money to their investors, was crucial it left them exposed after the market move following Russia's currency devaluation in August 1998.

The October 1997 imported crash caused a 7% fall on the 27th and -3% on the morning of the 28th in the S&P futures which caused the Niederhoffer fund to fail. There the positions were just too many and not diversified, namely, short out of the money S&P500 futures puts. Regrettably, the market returned to its initial value by the end of the week and the puts went to zero a few weeks later. So the 10% fall on Monday and Tuesday was recovered by Friday. This underscores the importance of having ample liquidity and capital sufficient to weather big moves in the markets. Amaranth, in 2006 had typical disaster common elements: a trader way overbet in one market, natural gas, and lost $6 billion when the gas prices fell from $7 to $5. Of course, natural gas prices fluctuated wildly in the past few years ranging from $2 to $11, due to structural changes so such a drop is not surprising. Chapter 32 has a recent update on the natural gas market and the decoupling of U.S. markets from global markets - a trend which has started to emerge also in the oil markets. That the largest most liquid resource market (U.S.), with the most timely demand and supply data is increasingly decoupled from global markets because of infrastructure bottlenecks and a different demand response, poses risks of mispricing and uncertainty in global markets. Uncertainties of demand in China and other EM in particular, as well as hard to forecast geopolitical risks, risk keeping the oil price is a wide but high band that could dent global growth and appetite.

This book is organized into seven sections plus a data appendix. Part I has key basic concepts. This includes arbitrage, risk arbitrage and the favorite longshot bias. By arbitrage, we mean buy something and sell it at the same time for more to generate riskless profits. Besides being basic for understanding, searching for arbitrage opportunities is profitable. In risk arbitrage there are also generally two sides - the buy and the sell - and the goal is to create an arbitrage. Since the matchup might not be possible risk is involved. Mean reversion of asset prices are crucial in some risk-arb applications such as NFL football betting as shown in Chapter 38 for the 2012 playoffs and the Super Bowl. Another type of risk-arb is mispriced option prices for various reasons and Chapter 12 describes a very successful trade on Nikkei put warrants that one of us was involved with in 1990. There expensive warrants were sold and cheaper ones were bought and the trade was closed when the prices converged. The Japanese stock market in 1989 was overvalued but held up with low interest rates. Nikkei put warrants (three year puts) appeared in Canadian and later in US markets. The Canadian puts traded for prices substantially above fair value based on historical volatility. Hence, a risk arbitrage trade was to short the Canadian overpriced warrants while simultaneously hedging by buying fairly priced US puts. Both sides do not constitute an arbitrage as the two sides were not the exact same product but one that was close. Then one waits until the two sides converge within a transaction band. A second successful trade with both puts on the same (the American stock exchange) was based simply on the size of the contract. This trade, similar to the small firm advantage effect, was to buy cheap puts worth half a Nikkei and to short 2.5 times as many expensive puts worth 0.2 of a Nikkei. then in about a month, the prices converged. These types of trades are very good for hedge funds but are not without various risks.

An important concept is the perception of probabilities. Low probability events tend to be overestimated and high probability events underestimated. This favoritelongshot bias, discussed in Chapter 1, is useful in many applications.

The second key concept chapter introduces the bond-stock earnings yield model which has been very useful in predicting stock market crashes. It is known that stock prices tend to fall when the PE ratios are too high but when? The BSEYD model provides an answer, namely that when bond interest rates are much above stock earnings yield by enough the stock market enters a phase that leads almost always to a 10%+ decline from the initial signal time value. This was discovered by the second author in Japan in 1988-89 by considering the 1987 US stock market crash, and tested backwards on Japanese data from 1948-88 (12/12 successes for the model out of 20 actual 10% crashes) and forward in Japan, the US and other countries since then. The usual situation is the model moves into the danger zone, then it rallies more, then it crashes more than 10% below the start. Chapter 21 discusses the use of the model during the 2006–9 period and it called the crashes in China, Iceland and the US. In Chapter 2, the BSEYD model is used for long term investing by suggesting when to be in the market and when to be in cash. From 1985-2005 and 1980-2005 the final wealth of the suggested strategy is about double buy and hold for the five countries (US, Japan, UK, Canada and Germany) with lower risk. The behavior of various investors is explained by separating investors into five distinct camps as discussed in Chapter 3.

Part II discusses hedge funds, sovereign wealth funds and other investment ag-glomerations. We begin in Chapter 4 with the study of average hedge funds and the impact of the managers stake in the fund and the incentive structures. We find in a continuous time theoretical model using realistic data and a prospect theory type utility function (losses are more bad then gains are good) that:

(1)risk decreases as the manager has more of the fund's money as his investment;

(2)at 30%+ for the manager's stake, the risk is close to that of a 100% stake in the fund;

(3)risk increases as the incentive fees increase; and

(4)the value of the option on other people's money varies from about 18% to close to zero as the manager's stake increases from zero to 30%+.

Chapter 5 presents an empirical study of a large number of actual live and dead hedge funds. The results indicate that it is hard to make back the average 2% management and 20% incentive fees and that funds of funds have higher returns the more risk they take.

In Chapter 6 we propose a modification of the standard Sharpe ratio to evaluate great investors. The Sharpe ratio, which is based on normal distributions, penalizes large gains as well as losses, as well as its large gains. To avoid this we propose a measure that is based solely on losses. Investors with high mean returns and few monthly losses score well on this measure. Berkshire Hathaway improves with this measure to about 0.90 but the Ford Foundation, Harvard, the Quantum Fund (George Soros) and the Windsor fund do not. Still Ford and Harvard beat Berkfshire Hathaway slightly because Berkshire Hathaway had too many losses. By this measure, Thorp was at 13.8 for his Princeton-Newport hedge fund with only three monthly losses in 240 months from 1969–88. Renaissance Medallion the pioneer of high frequency trading at 26.4 is even higher. These funds and some others, with even higher DSSRs from the University of Massachusetts hedge fund data base, are studied.

Chapter 7 discusses the common practice that employees of companies hold more of their own company stock in their portfolios than the theory predicts and is advisable. These high holdings can only be justified by high expected value estimates of the own company stock and low risk aversion

Sovereign wealth funds and government owned assets are discussed in Chapter 8 with their relatives, government pension funds tackled in Chapter 10. While government investment funds are not new (some of the first SWF were launched early in the 20th century, their proliferation, the scale of assets under management and the diversity in asset allocation warrants deeper study. These funds invest largely for economic and financial reasons, despite the fears of their detractors, but over the longer horizon political pressures from domestic constituencies constrain their asset allocation and mean that several find it difficult to be as long-term investors as they would like. In fact, one take away from the global boom and bust cycle has been that investment horizons have tended to shorten, particularly in public markets which are increasingly buffeted by many short-term trading trends. We update our analysis on sovereign funds, which now manage around US$3 trillion in assets, largely in oil exporting countries amplifying the assets managed by global central banks, which is nearing US$10 trillion.

Chapter 11 discusses top US university endowments including Yale which had excellent returns, about 13% for the past twenty years. Harvard has a similar good record, up about 12% over the past twenty years. They do this with very careful analysis in their own internal trading plus good relationships with excellent outside private placement, real assets such as real estate and timber and hedge funds. The proportion of typical exchange traded equities and bonds has declined to be only a small part of the portfolio.

Chapter 13 focusses on the Kelly criterion which is used by many great investors to achieve high returns. The Kelly or capital growth criterion-fortune's formula is the maximization of long run asymptotic wealth and the minimization of the time to sufficiently large goals. This is equivalent to maximizing the expected logarithm of final wealth period by period. If you plan forever, the Kelly investor will not only get the most final wealth but get all the wealth. In the short run, with its almost zero Arrow-Pratt risk aversion, log is the most risky utility function one would ever want to use. If the data is uncertain, it is very easy to overbet. Also, even in the long but not infinite run, one can still lose a lot of money with the Kelly criterion. A simulation shows that over 700 independent bets, all with a 14% advantage, that most of the time the Kelly criterion will generate very high final wealth. But in a small percent of the time, a sequence of bad scenarios coupled with the large bets the Kelly criterion recommends, leads to enormous losses. Hence, one should use the criterion carefully and consider fractional Kelly strategies which blend the Kelly optimal portfolio with cash. These strategies provide more security but have less growth. Great investors such as Keynes in the 1920s–40s, Warren Buffett of Berkshire Hathaway, and George Soros of the Quantum Fund have acted as if they were Kelly bettors. Other, more mathematical types such as Ed Thorp and Jim Simons have used the Kelly criterion along with investment strategies with positive means to make hundreds of millions in hedge fund investment vehicles. Bill Benter and other syndicates have used the Kelly and fractional Kelly strategies successfully in race track betting.

Part III discusses seasonal effects such as investing in the January turn-of-the- year effect in the futures markets, the January barometer and sell-in-May and go away as well as powerful effects from the Fed and presidential party effects. Chapter 15 discusses a trading strategy that goes long a small cap index and short a large cap index to attempt to capture the January small firm effect. The effect has been successfully tradeble but has moved to December. Chapter 16 reviews January barometer signals which show that if January is positive then most of the time the rest of the year is positive but if January is negative the rest of the year is usually noise going up or down about 50% of the time.

Chapter 17 discusses the sell-in-May and go away anomaly. Historically, September and October have had low returns on average and the months of November to April have had high returns, on average. Data from 1993 to 2011 show that the strategy be in the stock market from the turn-of-the-month of November to the beginning of May and in cash, the rest of the year greatly outperforms a buy and hold strategy. The effect is strongest for small cap stocks as are most anomalies. Another effect occurs around the announcement of the Fed meetings. The data show that most of the gains in the stock market since 1993 to 2011 have occurred in the three day window around these meetings. Chapter 18 shows that there is a strong presidential party effect. The strategies go long small cap stocks with Democrats and long either large cap stocks or intermediate bonds with Republicans has greatly outperformed 60-40 bond stock policies as well as small and large cap stocks.

Part IV discusses volatility, correlation and liquidity.

Chapter 20 discusses changing correlations, rising VIX and violent market moves. This is in the context of the 2008 world economic and financial crisis. Subprime loans and the growth of world wide derivative exposure are discussed as well as impacts on commodities such as oil and gold and currencies.

Chapter 9 on a new age for liquidity discusses sovereign wealth funds and other government pools of capital. Their liquidity is less than commonly assumed and some had had substantial losses at a time when these governments need more liq- uidity.In particular, for resource rich countries, the correlations between investment returns and resource returns remains high, calling into question the ability to really diversify their economic and financial portfolios.

Part V deals with the predictability of stock market crashes, the accuracy of signals, how to lose money trading in derivatives and some important case studies of huge hedge fund blowups. Many crashes seem predictable by the bond-stock earnings yield model and other signals. This is discussed in Chapter 21 which focuses on the Iceland, China and US 2006–09 crashes which the model called. In Chapter 22 we discuss three mini (less than 10%) crashes that the models did not seem to predict. One of them was the September 11, 2001 attack of the World Trade Centre. An option based behavioral bias crash prediction model and its results are discussed. This was useful to call four major crashes from 1986 to 2003 that together lost over 40% of the value of the S&P500. This chapter also discusses Chinese investment markets. Chapters 23–25 assess what signals worked and what did not to predict crashes in equities and other assets due 1980–2009. The US subprime crisis and how it evolved is discussed. The Chinese and Japanese markets are updated. Chapter 26 discusses how to lose money in derivatives and examines a number of cases including LTCM, Niederhoffer and Amarath..

Part VI discusses bubbles and debt and related investment topics.

Chapter 27 attempts to understand the financial markets in the subprime era focusing on the 2007–09 world wide crisis. Various trading disasters are discussed including Sumitomo, Barings, Daiwa and the Allied Irish Banks.

Chapter 28 continues the 2009 story discussing the rise from the March 6 low of 676.53 in the S&P500. Cheap money and the Fed, low prices, supposedly over priced bonds, good earnings and portfolio catch ups were part of the recovery.

Chapters 29–31 highlight a series of resilience of key countries and the global economy to key economic political and resource stresses. These include the Chinese growth model on the verge of the financial crisis, the effects of the Arab Spring and Japanese tsunami in the global oil markets and the Turkish policy response to steer the economy towards a soft landing. Chapter 32 studies the dynamics of natural gas to see what might be necessary to bring new discoveries to market and to use their proceeds.

Chapter 33 discusses market events that undermined the fragile economic and fi-nancial trajectory in April 2011 including the Icelandic volcano, SEC charges against Goldman Sachs and the linked sovereign, financial, fiscal and economic crisis of the PIIGS especially Greece and the flash crash. The reliance of the global economy on stimulus in the face of rebalancing and rebuilding of balance sheets, as well as the increased correlation across asset classes, leaves the global economy and markets vulnerable to these shocks.

Chapter 34 discusses the current US political and economic situation, which is increasingly gridlocked with some suggestions for improvement. We see little prospect for improvement after the 2012 elections despite Obama being re-elected for a second term; but we are hopeful.

Chapter 35 presents country studies concerning Korea, India, Russia and Cyprus, countries that are facing a series of challenges in the fight to attract global capital and integrate into global supply chains. In all cases, some of the growth drivers that stabilized these economies in the recent past have weakened.

Part VII discusses investing and arbitrage in NFL football and horse racing.

Chapter 36 discusses a common decision problem in football. That is punt on fourth down or go for the first down with short yardage. The context was in a crucial game between top teams Indianapolis and New England near the end of the game. A correct analysis is to estimate the chance of winning the game with the two actions and pick the best one. We see that famed New England coach Bill Belichick made the right decision even though his team lost the game, while the TV commentators who do not do such analysis thought otherwise and criticized him.

Chapters 37 and 38 discuss the 2010, 2011 and 2012 Super bowls and the accuracy of the Elo ranking system. That approach ranks teams by the scores of games they played adjusting for the home bias. In betting on Betfair, for example, a valuable risk arbitrage strategy is to rely on mean reversion to lock in prices as the scores change. Chapter 38 especially shows some interesting examples. The team that was originally the best can lose but you the bettor can win by locking in these risk arbitrages

Chapters 39–42 discuss horse racing betting strategies and applications. In Chapter 39, a very hittable nearly $2 million Pick 6 at the Breeders' Cup is described. Then Chapters 40 and 41 focus on the great female horses Rachel Alexandra and Zenyatta as well as Goldikova, the only three time Breeders' Cup winner. Finally Chapter 42 discuses betting with the Dr Z system for place and show at the first Breeders' Cup in 1984.

Most of the chapters in this book have appeared in Wilmott magazine. We have edited all the chapters for consistency, duplication, updates and other necessary changes. Also some new chapters have been added to make the book more complete. The Wilmott columns begin where our previous book Ziemba and Ziemba (2007) left off in mid 2007. In some cases earlier columns are presented here where updates plus the original story is warranted. So between them, this book and the 2007 book have updated complete collections of our 2002–2012 columns plus some later ones in Wilmott magazine since its first issue in September 2002.

Rachel wrote her columns (Chapters 8, 9, 10, 29, 30, 31, 32) and the joint ones (Chapters 11, 22) independent of her current employment with Roubini Global Economics in New York and London, although these experiences clearly influence the work, as noted in the acknowledgments.

All mistakes and opinions are our own.

Rachel E S Ziemba

London

and

William T Ziemba

Vancouver

May 2013