Modern Portfolio Theory

A theory for maximising portfolio returns according to a given amount of risk specified by an investor, or minimise risk for a given amount of returns.

The theory was introduced by Harry Markowitz and emphasises that risk is an inherent part of returns when making an investment.

Efficient Frontier

The efficient frontier is a curve which represents all the points where for a given level of risk (as measured by standard deviation) of a portfolio you are achieving the optimal rate of return. It is a theoretical curve and forms part of Modern Portfolio Theory as introduced by Harry Markowitz in 1952.

Ordinary linear dependence

In investments, ordinary linear dependence between asset classes describes 2 asset classes where the performance of one can be derived from the other using a linear relationship.

For example: if Asset A has an ordinary linear dependent relationship to Asset B with a value of 0.8. Then if Asset A moves from 100 to 110 then Asset B would move from 100 to 108.

Martingales

Martingale is a technical term in probability theory used for a scenario in which knowledge of past events cannot be used to predict the future. It means that at a particular point in a sequence the expectation of the next value is not known and therefore is equal to the currently observed value.

The term Martingale originally came about as a strategy for winning a game of chance. A gambler would win his stake if a coin toss came up heads and he would lose it if it came up tails. The strategy he would implement would be to double his stake on each bet after he lost so that the first time he won he would win back all of his original bets plus the original stake. The concept of martingale in probability theory was introduced by Paul Lévy in 1934.

Monte Carlo simulation

Monte Carlo simulation is a computerised mathematical technique used to understand the impact of risk and uncertainty in financial models (as well as various other areas). There are many different Monte Carlo methods in existence but in essence they rely on repeated random sampling to obtain numerical results. In investing they can be employed to make forecasts and through repeated sampling can assign a level of certainty to future outcomes.

Normal Distribution

The normal distribution is a symmetric probability distribution. It represents the distribution of a random variable in the form of a bell curve, with the exact shape defined by the expected value and the standard deviation. The normal distribution is often referred to as the Gaussian distribution or Gaussian bell curve after the mathematician Carl Friedrich Gauss. It is frequently used in natural and economic sciences to describe the deviations of measurements of many processes from the mean.

The graph below shows the probability distribution of the normal distribution, the area indicates the cumulative probability for certain value ranges. According to the standard normal distribution about 68.3 % of outcomes are within ± one single standard deviation (σ) from the expected value (μ), 95.4% in the interval μ ± 2σ and 99.7% in the interval μ ± 3σ.

Tracking Error

The term tracking error is defined as the deviation of the performance of an index fund or exchange-traded fund (ETF) from the performance of the index it tracks. Index funds / ETFs always try to replicate the performance of the index or basket of securities as exactly as possible, due to the complexity of certain indices (eg. The MSCI World over contains over 1,600 individual securities) or a lack of liquidity of the underlying individual stocks, this is not always 100 percent possible.

Synthetically Replicating ETFs

A synthetically replicating ETF (Exchange Traded Fund) refers to an index fund that track an index without buying the underlying assets of the index (eg. Shares).

The Custodian of a synthetically replicating mutual fund creates a (secured or underwritten) swap rather than a basket of securities. Synthetically replicating ETFs hold margin (also called “Collateral”) instead of the individual values of the index. The swap (i.e. an exchange transaction) is entered into with a counterparty and the collateral is held against the performance of the underlying index.

With synthetically replicating funds a company can replicate an index precisely, thus with no or significantly less tracking error than in most physical ETFs. Moreover, some indices, eg. commodities or certain emerging markets such as India, can only be replicated with synthetic ETFs as the underlying assets can not be bought or stored economically. e.g. oil and natural gas.

In addition to synthetically replicated ETFs, there are also physically replicating ETFs.

Physically Replicating ETFs

A physically replicating ETF (Exchange Traded Fund) refers to an index fund that track an index by buying, according to their weighting in the index, all or large parts of the securities included in the index (eg. Shares).

A 100 percent reproduction by a physically replicating ETF is called full replication and any proportionally physical replication is known as partial replication. When selecting which stocks to include in the index, those with the highest correlation to the index that is being replicated will be selected.

In addition to physically replicating ETFs, there are also synthetically replicating ETFs.

Interbank Rate

The interbank rate is the interest rate at which banks will lend money to each other in the short term. Banks have to lend and borrow money from each other in order to manage their liquidity and also to comply with capital requirements from the regulators.

Reference Index

The reference index of an Exchange Traded Fund (ETF) is the index which the ETF is aiming to replicate. For example in the Vanguard S&P 500 ETF the reference index is the S&P 500. One of the criteria of our selection process is the tracking error of the ETFs. This refers to the difference between the performance of the ETF and its reference index.

Counterparty Risk

Counterparty risk is the risk that an investor takes on when they enter into an agreement with another entity. The risk being that the other entity (counterparty) cannot fulfil their obligations in the agreement. One example where counterparty risk is relevant is in Synthetic ETFs since the ETF provider enters into a swap agreement with a counterparty (usually an investment bank) such that the investment bank agrees to pay the performance of an index against a basket of investments which the ETF provider holds. There is counterparty risk (all be it a very small risk) for the ETF provider that the investment bank might default on their side of the swap.

Net Asset Value

Net Asset Value is the value per share of an Exchange Traded Fund (ETF) or a Mutual Fund. The per share value of the Fund is calculated by taking the total value of the fund and dividing it by the total number of outstanding shares.

ETFs trade on exchange at a market value which can be above or below the NAV.

Black Swan Event

In finance a Black Swan event is an extreme event with a large market impact which in normal circumstances seems incomprehensible. Statistically these events should occur far less frequently than they do but recent history has made them a common topic of discussion in financial markets, with events such as the collapse of Lehman Brothers during the financial crisis being a prime example.

The term came about from the Roman satirist Juvenal who used “rare birds”, such as “white ravens” and “black swans”, as a synonym for “unimaginable” events. Then later in history the philosopher Karl Popper used the black swan as an example of the falsifiability of universal hypotheses, because until the discovery of Australia and of black mourning swans living there, the hypothesis that “all swans are white” was irrefutable. The mainstream application to finance came about in 2007 when Naseem Taleb, In his book The Black Swan: The Impact of the Highly Improbable, used Black Swans as a metaphor for the low probability of destructive events with extreme negative returns occurring in financial markets.

Econometrics

Econometrics uses Empirical data from mathematics, statistical studies and computer science to quantify economic data. In finance econometrics can be used to analyse large sets of data and draw relationships between economic theory and observed data.

Scalable Capital uses Econometrics in the core of our investment approach. Our team of financial engineers led by Professor Steffan Mittnick, use quantitative finance to drive the investment decisions of our model based on current market data and empirical evidence. See more on our investment approach.