Peter Nystrup
Peter Nystrup
Responsible for regime based multi asset allocation, ph.d. and data scientist.

The purpose of dynamic asset allocation (DAA) is to take advantage of favorable regimes and reduce potential drawdowns during adverse regimes. Large drawdowns challenge investors’ financial and psychologicaltolerance and lead to fund redemption and firing of portfolio managers. By engaging in DAA it is possible to generate protection against drawdowns. Infact, portfolio insurance can be regarded as the most general form of DAA, as argued by Goltz et al. (2008).

Regime shifts, some of which can be recurring (recessions versus expansions)
and some of which can be permanent (structural breaks), are prevalent across a wide range of financial markets and in the behavior of many macro variables (Ang and Timmermann 2012). Observed regimes in financial markets are related to the phases of the business cycle (Campbell 1999, Cochrane 2005). The link is complex and difficult to exploit for investment purposes, due to the low frequency and large lag in the availability of data related to the business cycle.


A number of various published articles on regime changes can be found here at the DTU orbit database:

Belown are shown our initial live testing of the algorithms developed to utilitze regime changing properties of financial returns in various asset classes across time. 

ANNOX Regime

Live allocation

ANNOX Regime

Daily Returns (Live)

ANNOX Regime

(Monthly, since 2019 may)


SMART BETA2019-02-01T10:47:22+00:00

Smart Beta

Sitting between active and index strategies, smart beta represents an evolution in index investing and an opportunity for investors.

Rather than simply weighting stocks by market cap, funds are constructed to identify and exploit specific factors. Investors can capture these exposures by utilising ANNOX which offers exposure to the momentum, size, and quality and vol factors.

  • Smart Beta can help investors achieve targeted outcomes through factor-based investing
  • Factor investing seeks to systematically identify and exploit specific drivers of risk and return, aiming to deliver a premium above the traditional market-cap benchmarks
  • ANNOX can be used to get a diversified, transparent and cost-efficient access to smart beta.

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.

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 LEARNING2019-02-01T10:51:16+00:00

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.


Mathematical Optimization

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.

The decision space, where each dot represents a possible investment portfolio.

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.


Exhibit 2: The volatility reduction when combining assets with different levels of correlation.

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 which depicts sample correlations between the American, German and Japanese stock index over the period 2013-2016.

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

From the table,  it can be observed that correlations 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 lower 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.