Risk - a measure for measure

It is springtime and a favourite period of the year when a number of bonds are on offer to the discerning Maltese investors. As always bonds tend to be issued as unsecured instruments, offering better than average, high coupon rates which appear doubly attractive to the otherwise miserable rates offered by banks on savings and other term deposits.

Naturally with higher returns come higher risks, and it is incumbent on independent investor advisers to warn us that ‘the past is not a guarantee of the future’. Yes this innocuous term is so commonly used in the financial sector that promoters of financial products whisper it so quietly it is practically inaudible to the human ear or written in fine print that even the sharpest eyes tend to miss. Undoubtedly, this phrase brings with it a sense of uncertainty, a sword to the soul of the meticulous but nonetheless a veritable challenge to researchers and analysts who, in a quest to mitigate uncertainty, try to predict the future.

These prediction methods are sans the magical glass ball but instead are based on the use of concrete formulas and well-researched techniques within the scientific area of statistics.

In fact it is true that the evolution of statistical techniques is a growing family that, among others, embrace regression modeling whereby one of the main aims of such a procedure is in fact a scientific form of prediction. As a technique, it seeks to build a relationship between two types of variables; the independent ones and dependent ones while keeping in mind an element of error. 

This relationship is based on what are generally known as the regression coefficient estimates. Each value corresponds to an independent variable and they represent the unit change in the dependent variable given that the other variables are kept constant.  As a rather basic yet important regression technique one can find the Ordinary Least Squares, credited to be the invention of Gauss, a famous mathematician.  As a technique it tends to excel given that there exist no relationships between the independent variables and also when the data the analyst is working with is not a high-dimensional one. 

It goes without saying that tricksters tell us the road to hell is paved with good intentions and when these two conditions are violated, the model tends to have poor predictive ability.

Moving on to other developments we came across Ridge regression, which is another regression technique with an added twist. Such a method tackles the problem of any existent relationships between the variables by what is commonly known in the statistical camp as shrinkage. This technique considers the regression coefficient estimates assigned to every independent variable and if it detects any dependency between any variables, shrinkage is applied or in other words, the value of the regression coefficient estimate is reduced.

This dependency in fact might be a common occurrence in the financial world whereby financial instruments leading to the same dependent instrument might be indirectly related. A shortcoming of this technique is that if the analyst is dealing with voluminous data, ease of interpretability is lost.

In light of this, another technique was formed in the late 20th century namely the Least Absolute Shrinkage Selection Operator regression, also goes by the name of LASSO regression. Such technique embraces the shrinkage property discussed in the previous technique and furthermore it is capable of selecting variables that deem to contribute most to the dependent variable. 

Then, case in point, if this time an analyst is faced with a large econometric or financial data, interpretability is salvaged as the dimensions of the data are reduced.  It is no exaggeration to declare that LASSO can be considered to be a revolutionary technique with its subset selection ability.

The concept of prediction is more or less common between these three techniques. Once the regression coefficients are obtained, what is called the regression equation is obtained. Then it is up to the analyst to plug in potential values and through the equation, the dependent variable/s is obtained.

In a sea of uncertainty, particularly since the recession that hit the globe in 2008, it is no small consolation that investors find statistically sound techniques to be pennies from Heaven. Luck or chance are excluded as much as possible in the financial sector. In fact the quest to try and predict figures is overwhelming and therefore analysts are always working to improve such techniques. 

The techniques discussed here are only few of the many that exist in the arsenal of effective weapons against uncertainty. In conclusion, readers are advised that prior to selecting a prediction technique, the data under study is analyzed carefully and it is important to remark that validation of certain assumptions must not be overlooked so to ensure a higher level of reliability.

On another aspect, PKF Malta ensures that when any statistical analysis is done, the data upon which this is based is consistent and reliable. In the early stages, when the questionnaire is being designed, we keep in mind our target population. In a world where time is money, it helps to ensure that a questionnaire is straightforward and easy to comprehend. Such a guarantee is usually obtained through what is generally referred to as a pilot study whereby a predetermined amount of questionnaires are sent to the target audience and feedback is obtained from their end.

Perhaps one of the key factors that one must keep in mind is that a questionnaire must be used to analyze the current situation or for potential improvements, hence questions must be short, concise and if possible the respondents are given various choices they can select. It is wrong to assume that a questionnaire is a priority to the respondent and to further assume that he/she has all the time in the world at his/her disposal to answer such a questionnaire.

Such a mantra is one that PKF embraces and adopts. It is useless to create questionnaires that in concept will cover various areas however they are so long that they are practically a burden to the respondent. Thus, long questionnaires can lead to consequences such as a low response rate, untrue responses or questionnaires that were not filled properly.

Another important aspect in statistical analysis is data cleaning. This is a process that takes place after the data has been collected and prior to analysis. Its main aim is to ensure that the study is executed using data without any errors and it is as coherent as possible. An example of when data cleaning is useful is when the responses are manually inputted, thus data cleaning and checking is essential to minimize human errors as much as possible. 

Although the period of such task might be a lengthy one, together with other factors it is the key to a successful, uniform analysis and more importantly reliable. When the study reaches the analysis stage, it is extremely important to make use of statistical tools that are reliable and that adhere to the assumptions arising from the data. It is never suggested to have a ‘one size fits all’ mission, and the same applies in analysis - one test does not fit all.

In fact, various diagnostic tests exist to help in determining which statistical test should be used. When reaching the crucial yet important stage when we are ready to present our results, one cannot emphasise enough the importance of making a document that is easy to interpret and follow. To conclude, it is regretted that one of the blunders that might exist in the statistical world is to forget who the audience of the study are. After all, it is useless to speak perfect Greek to a Russian who fails to know the Greek language!

Lynsey Schembri is a senior statistician with PKF.

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