THE SCIENCE BEHIND
ANNOX investment policy is based on two fundamental pillars:
- The financial markets are not completely efficient, i.e. there exist market abnormalities which can be used to generate excess returns.
- Financial returns experience heavy tail risk, i.e. investment portfolios should be constructed to limit exposure to the extreme events.
LARGE ARRAY OF STRATEGIES
ANNOX invests using an umbrella approach by deploying a large array of investment strategies designed to target specific market abnormalities within different asset classes. The overall capital is allocated between equity, fixed-income, commodities and currency. ANNOX ensures exposure to the different asset classes by solely investing in index products such as Futures Contracts and Exchange Traded Funds. The portfolio includes both long and short positions – making it possible to generate positive returns in all financial environments.
CREATING EXCESS RETURN
ANNOX applies tactical asset allocation to benefit from the momentary investment opportunities by exploiting both known market abnormalities as well as discovered by the in-house researchers. These market abnormalities relate to momentum investing, value investing, return predictability, or factor investing.
Multi Strategy Optimization
Every single position has a purpose and is supporting the others to provide the most stable returns. We do not seek to find low correlated assets, we design our own using strategies.
Optimizing Optimal Strategies
Asymmetric return distribution due to momentum and minimization of tail risk. We optimize allocation of strategies with respect to:
- Expected return
- Tail Risk
- Marginal distributions
- Liquidity
- Investment policy.
Diversification is King
Actual in-sample correlation matrix for the 04.01.2016
Optimization
Actual in-sample correlation matrix for the 04.01.2016
Technology and Infrastructure
Broker
Interactive Brokers LLC
Electronic Trading
Automated executing of trades using API
Execution
AWS Amazon server continuously running all models and updating databases.
Correlation to Market
Correlation to Market
Correlation
Moving correlation calculated over 60 days between MSCI World, the BofA Merrill Lynch 10+ Year index and ANNOX Alpha.
June 2016: Brexit
August 2016: U.S. disappointing jobs report
September 2016: Oil price shock, U.S. election campaign, Worst day for DJ since 2007
April 2017: Surge in European markets following French Presidential election.
Model Overview
Enhancing Predictive Power
We combine non-perfectly correlated predictive models to form one strong predictor and diversify idiosyncratic model risk.
Predictive Models | |
Supervised Learning | Econometric models |
Boosted Random Forest | Structural vector autoregression models |
Multivariate Adaptive Regression Splines | Exponential smoothing state space models |
Neural Network | Seasonal ARIMA models |
Support Vector Machines | Theta method |
Principle Component regression | Dynamic regression models |
Unsupervised Learning | |
Dimensionality Reduction | Robustness |
Principal Component Analysis | Cross validation |
Optimal Universe Reduction | Bootstrapping confidence intervals |
Optimal Sub-set selection | |
Support Vector Machine | |
Neural Network |
Strategy Overview
Diversification is King
Every single position has a purpose and is supporting each other to provide the most stable returns. We don’t seek to find low correlated assets, we design our own using strategies.
Equity | Type | Bonds | Type | Commodity | Type | FX | Type |
US industries | L/S | US/EU Treasury | L/S | Metals | L/S | Major Pairs | L/S |
EU industries | L/S | High Yield | L | Agriculture | L/S | Minor Pairs (Carry) | L/S |
Developed Countries | L/S | Corporate | L | Livestock | L/S | Scandinavian pairs | L/S |
Asian Countries | L | Emerging Market | L | Energy | L/S | ||
Factor Weighting | L | Convertible | L |
Single Strategy Optimization
Single Strategy Optimization – Each strategy seeks to maximize risk-adjusted returns.
Targeting patterns
Each strategy is built upon an robust pattern present in data, which can be explained by an financial reasoning.
Finding an optimal portfolio
We apply stochastic programming to maximize expected return, while minimizing our corresponding multivariate error/residual distribution connected to our forecasts.
Diversify idiosyncratic model risk
We apply an array of predictive models from econometrics and machine learning, and combine them to make an even stronger predictor.
Momentum is a highly studied market abnormality among academics and practitioners.
The momentum effect describes that the behavior that an assets which have had strong increase in value in the past, has a high probability of continuing its trend in the near future, e.g. Stocks which outperform peers on a 3-12 month period tend to perform well also in the future. Countless studies show that this effect works for the U.S. stock market, stock markets in other developed countries, including emerging markets. The momentum effect is also present in small cap and large cap stocks, and it is one of the mostly academically investigated effects. Additionally, the momentum effect do not only hold true for equity, but it is also documented in the bond, commodity, and currency markets.
Fundamental Reason
Momentum is most often explained by investors’ irrationality – their underreaction to new information by failing to incorporate news in their transaction prices. Another explanation is that momentum investors are exploiting behavioral shortcomings in other investors, such as investor herding, investor over- and under-reaction and confirmation bias.
Slow Macro Styles
Some of the strongest trends in financial markets coincide with phases of macroeconomic cycles. The businesscycle itself is characterized by momentum: individuals smooth their consumption expenditures, firms make long-term decisions to commit to investment projects, wages and employment are sticky and the government sector explicitly tries to smooth fluctuations. Likewise, emerging markets take time to emerge, and do so with predictable rises in consumption and demands on industrial commodities. Such macro trends manifest themselves in the prices of many financial instruments, and trending behavior can arise if the underlying economic factors are not fully discounted by the market.
Dissemination and Reaction to Information
Economic and other news disseminates unevenly. Different market participants react only when such news reaches them, each potentially having their own reaction rate. For example, traders focused on a specific industry typically react to events related the industry almost immediately, whereas large institutional investors may require a lengthy decision-making process and retail investors may take longer again. Periods of sustained buying or selling thus develop as news spreads and participants react in similar ways but over different timehorizons. This effect leads to persistent trends.
Behavioral Biases
Market participants exhibit some consistent but seemingly non-rational behaviors. Most studies of these behavioral phenomena in financial markets are based on observing trades and portfolios in equities, but much carries over to other asset classes. Some of the more well-known behavioral biases include:
– Anchoring, i.e. Holding losing trades too long in the hope they will come back
– Closing winning trades too soon.
– Underreaction, leading to sequences of incremental actions.
– Crowding/Herding, i.e. buying because everyone else is buying.
Behavioral biases which lead to individuals losing money or foregoing profits, such as the first two examples above, are effects where a systematic trader, uninfluenced by emotion, can profit either by taking the other side of the trade or holding onto a winning trade when others have closed out. The second two examples lead to explicit trends as partial reactions and herd behavior can induce sustained price momentum.
Explaining Predictability of Returns
Returns of many financial assets can be forecasted into the future with statistical significance evidence. The length of the possible forecast is unique to the individual considered asset and highly dependable of the sophistication of the applied forecast model.
Until the early 1980s, the standard assumption for estimating and forecasting expected returns for equity was to assume to be a constant rate. Then, empirical evidence was uncovered showing that returns were predictable by financial ratios, such as the price-dividend or price-earnings ratio. Later other variables, such as the spread between long-term and short-term bond yields, the consumption-wealth ratio, macroeconomic variables, and corporate decision variables were also shown to have predictive ability. Inspired by the findings in the equity markets, the academic literature has expanded its interest to returns on other asset classes, such as government bonds, currencies, real estate, and commodities and found similar results.
Information processing
The empirical patterns in returns are can either be consistent with the efficient market hypothesis or irrational mispricing. In general terms, market efficiency implies that all prices fully reflect all available information. Consequently, market efficiency has the underlying assumption that all investors are rational and can instantaneously process and act on all available information. Contrary, irrational mispricing relates to the natural limits of information that an investor can process. If investors are only partly rational and subject to an intention span, then some assets will be mispriced and information with only gradually be included in market prices. The latter leads to predictability of returns.
Tail Risk
Tail events are events with a low probability of realization but with tremendous consequences. In investment theory, future outcomes are often assumed to follow a normal distribution, but empiric market data shows that this assumption seldom holds true. Contrary, financial returns often experience distributions much “fatter” than normal curves meaning that tail events are much more frequent than many investors realize.
The “tail” in tail risk refers to the end sections of the bell‐shaped curve that illustrates the Normal probability distribution of events. In the context of investments, the extreme left‐hand side of the bell‐shaped distribution represents the lowest returns, whereas the right‐hand side represents the highest returns. The art of tail‐risk protection is to asymmetrically protect against left‐hand events (losses) while maintaining participation in those events on the right (profits).
The Normal Distribution
In order to understand the significance of tail risks, it is important to understand the notion of a normal distribution and its shortcomings. A normal distribution assumes that, given enough observations, all values in the sample will be distributed equally above and below the mean. About 99.7% of all variations falls within three standard deviations of the mean and therefore there is only a 0.3% chance of an extreme event occurring. This property is important because many financial models such as Modern Portfolio Theory, Efficient Markets and the Black-Scholes option pricing model all assume normality. However, the financial markets are less than perfect and largely influenced by unpredictable human behavior, which leaves us with fat tail risks. The Normal distribution together with two heavy-tailed distributions are displayed in exhibit 1.
[Inset tail risk graph] Exhibit 1: Financial returns usually experience negatively skewed distributions, which means that extreme events are more probably than judged by the Normal distribution. Hence, financial returns are subject to tail risk.
Fat Tails
By definition, a distribution with a fat tail is a collection of potential future outcomes, where the probability of the occurrence of an extreme event exceeds three standard deviations. The aftermath of the 2008 Financial Crisis highlighted the shortcomings of conventional financial theory, which has only been further emphasized by the continuation of smaller and larger economic shocks e.g. 2001 Dot-Com crisis, 2008 Financial Crisis, 2011 European Debt crisis, 2014 Russian Financial Crisis, 2015 Chinese Stock Market Crash. Hence, the assumption of the normal distribution in financial risk management can pose an inherent threat to invested capital as the consideration of tail risk has shown to be of paramount importance.
Machine Learning is an umbrella term
Machine Learning is an umbrella term for a range of applied practical algorithms that can identify repeatable patterns and relationships within observed data, and importantly can do so without having to be told explicitly what kind of patterns and relationships to look for. This distinguishes Machine Learning from more traditional data analysis techniques. Machine Learning is a hybrid discipline as applied algorithms commonly originated from fields such as computer science, information engineering, statistics and various mathematical disciplines. Just as there have been Machine Learning breakthroughs in many other areas of applied science and business, it is also have a positive impact on quantitative investment.
Generally, Machine Learning is built on three separate corner stones:
- Computing power
- Data generation, storage and retrieval
- Methodology and practical techniques
In quantitative finance, Machine Learning is used in various ways, which include prediction of future asset prices, optimizing parameters of trading strategy, managing risk and detection of signals among noisy datasets. Machine Learning applied within quantitative finance offers a coherent, versatile and practical way of combining numerous and varied weak information sources into investment systems that have greater signaling power than any individual source. Such systems capture insights that both human intelligence and less sophisticated systematic models may miss.
A major branch of applied mathematics
Mathematical Optimization is a major branch of applied mathematics focus on aiding decision-making when the problem at hand experience an extreme level of complexity and/or uncertainty. It includes advanced analytical techniques used to find the best solution given a set of parameters and instructions about restrictions and physical limits of the problem. Optimization problems are found in a broad range of fields and industries, such as structural optimization in civil engineering, data fitting in weather forecasting, and parameter estimation in chemistry.
Maximizing & minimizing
In general, an investment portfolio seeks to satisfy two overall goals simultaneously, i.e. maximizing the expected return of a portfolio, while minimizing the adherent risk. As it is impossible to foresee market movements with certainty, then it becomes crucial to plan for the unexpected and position trades in such a way that the invested capital is robust towards the future by evaluation thousands of possible scenarios. Mathematical optimization plays a crucial role in determining the optimal relationship between the two investment objectives, while considering the complex dynamics present in the financial markets.
Explaining Diversification
Most investors are familiar with diversification — reducing one’s risk profile (e.g, annual volatility) without affecting returns by adding different asset classes or investments to a portfolio. While this is true, the degree of potential risk reduction depends directly upon the correlation of the portfolio’s underlying assets. Correlation is the measure of how assets move relative to each other, usually in response to changing economies and market conditions. Highly correlated assets will more often move in unison i.e. increase or decrease together. Contrary, assets with low, zero or negative correlations will behave more independently or even oppositely. Hence, the less correlated assets are in an investment portfolio, the lower is the risk. This is illustrated in Exhibit 2.
The left axis shows the volatility of a portfolio as assets (with the same standard deviation) are incrementally added for different levels of correlation. If one had four investments with zero correlation, then the portfolio’s risk is reduced by 75% compared to having invested in only one asset. Contrary, one would need more than 100 assets with a 0.33 correlation to bring down risk by 34%. Hence, as correlation rises, even marginally, the benefits of diversification disappears. It is noteworthy to emphasize how quickly the level of diversification disappears for the 0.33 and 0.66 correlation lines. This is illustrated by the lines, which becomes almost horizontal after including a certain amount of assets. Putting things on edge, adding just one zero-correlated asset to a portfolio reduces risk by 50%, while adding a thousand 0.66% correlated assets reduces risk by only 33%. In short, the correlation and composition of an investment portfolio matters greatly when it comes to risk reduction.
Zero correlated assets
Zero correlated assets are notoriously difficult to find, which becomes evident from the following table.
S&P 500 | DAX | Nikkei 225 | |
S&P 500 | 1,00 | 0,75 | 0,67 |
DAX | 0,75 | 1,00 | 0,59 |
Nikkei 225 | 0,67 | 0,59 | 1,00 |
Table 1: correlation between the American, German and Japanese stock index over the period 2013-2016.
From table 1, it can be observe that correlation even among demographically distant markets can be high; hence, only little diversification benefit is available. Instead, fund managers can create risk reduction by diversifying between asset classes and investment strategies (e.g. momentum and value investing), which by construction experience low correlation.
Process of applying a trading strategy
Backtesting is the process of applying a trading strategy or analytical method to historical data to see how accurately the strategy or method would have predicted actual results.
Back testing is a key component in developing and effective testing an investment strategy. It is accomplished by reconstructing, with historical data, trades that would have occurred in the past using rules defined by a given strategy. Decisions made by the strategy are then compared to how the financial markets actually developed at the given time. Hereby, it becomes possible to test if the theoretical foundation of a strategy holds economic value by generating profit. Furthermore, it is possible to illuminate any pitfalls or threats that the strategy may be subject to, such as specific economic environments or market movements.
After back testing a strategy and confirming the robustness of it over a sufficient time period, then it is important to paper trade it. This is done by trading the strategy live but on paper. Practically, this means testing the strategy by writing down current suggested trades, and observe the performance over a time window to ensure that the strategy continues to show profitable results.