Choosing your risk

By Marcus Williamson

Risk is not a simple entity, it comes in many flavours, and requires respect and consideration even when you least expect. If one was to try ‘totally avoid’ risk in their market endeavours they would most likely just be holding cash – where are the returns in that?

The truth is that in almost all circumstances one must take at least some form of risk to have the chance of potentially generating returns. Let’s face it, you’ve got to crack some eggs to make an omelette!

Those, including myself, who have experienced first hand what it is like to feel the full effects of taking on too much risk, will most likely find it a life changing experience. You will either withdraw your remaining investments and consider other ventures, or you will revisit your mistakes with single goal; of never ending up in a similar situation again. Read more

Intro to Hidden Markov Chains

By Bonolo Molopyane

In a situation where you wish to determine the returns on an investment, one may have all the expertise to do this but without certain information (missing pieces) it would not be possible to derive to a conclusive figure. In practical terms “assume you have the value of all returns of all assets in your portfolio; without the rate at which each asset produces the returns we will not have a true reflection of the portfolio returns at a specific point in time as such we may not provide accurate returns estimate.” A process termed the Hidden Markov model may be used to shed some light in this problem.

The process is split into two components: an observable component and an unobservable or ‘hidden’ component (van Handel, 2008). Nevertheless, from the observable process we can extract information about the “hidden” processes. As such our task is to determine the unobserved process from the observed one. Read more

Introduction to Value at Risk


By Bonolo Molopyane

Large institutions deal with immense amounts of currencies which enter and leave their accounts on a daily bases. Furthermore they have their own funds that it has to efficiently allocate so as to maximize their return on investment but also wish to hedge against adverse events. With a certain confidence the entities (particularly commercial institutions) should be conscious of their profits and also know how much they stand to lose.  With requirements stipulating certain amounts to be kept for times of need, introduction of capital buffers  which should build up in prosperous times (SARB, 2015) as well as other regulatory matters institutions have increased the need to know how much they posses and the risks they are exposed to.

In recent years the trading accounts at large commercial banks have grown substantially and become progressively more diverse and complex (Jorion, 2001). To manage market risks, major trading institutions have developed large scale risk measurement models. While approaches may differ, all such models measure and aggregate market risks in current positions at a highly detailed level. Read more

Introduction To Monte Carlo Analysis Part 3

By Bonolo Molopyane

Financial Applications

Within the Monte Carlo realm a vast number of applications exist. In this final part I bring together all the previous work as well as put into practice the theory we have gathered so far.

Applying the Metropolis-Hastings Algorithm

From the previous section we deduced a way in which we can generate a sample using arbitrary factors which combined produce a fairly accurate representation of reality

For absolute simplicity we will consider only one variable in which we wish to model, but this process is applicable to combinations of assets or derivatives of those assets with minimal adjustments. Here we make use of Dynamic asset pricing to estimate equilibrium as well as exploit arbitrage opportunities with the theory of mean reversion being the basis of our strategy. I will neglect the actual computation to give an intuitive understanding of the usage of the theory developed here: Read more

Introduction to Monte Carlo Analysis Part 2

By Bonolo Molopyane

Markov Chains, Central Limit Theorem and the Metropolis-Hastings

In the previous article I gave a generic overview of Monte Carlo as well as introduced importance sampling. We now dive deeper by giving strict definitions of some of the widely used and yet misunderstood or rather commonly neglected concepts due to its perceived importance. There after we explore the Metropolis-Hastings algorithm which form a foundation of numerous Markov Chain Monte Carlo methods. Read more

Fama-French five factor asset pricing model

By Rujeko Musarurwa

The relationship between risk and return has long been a topic for discussion and research. Investors and investment managers seek financial models that quantify risk and translate that risk into estimates of expected return on equity (Mullins, 1982). This post will look at and discuss the Fama-French five factor model and its applications. It will begin by discussing the theory and where the model originated from. A discussion of when and how the model is implemented and applied will then follow. Ultimately it will be seen that the five factor model is an improvement from previous models but that it still has some drawbacks and areas that can be improved on. Read more

Resistance to High Frequency Trading (HFT) Strategies

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“This is John Connor – if you are reading this, you are the Resistance. Listen carefully. We have been fighting a long time and we are outnumbered by machines. Humans – have a strength that cannot be measured.” (Terminator Salvation)

I see it now; this is tomorrow’s over dramatised headline. A strange world where we are trapped somewhere between the Matrix and Terminator franchises.

Recently, on 31 March 2014 there was an interview by CBS 60 Seconds in which famous author Michael Lewis states: “The insiders are able to move faster than you. They are able to see your order and place it against other orders in ways that you don’t understand. They are able to front run your order … .” The biggest surprise to me was his comment, “The United States Stock market is rigged!” Talk about a sensational notion. (Bloomberg TV, 2014). Read more