Refining risk assessment – The Lambda VaR Approach to Market Risk Measurement
Market evaluation and financial investment are, by definition, activities that are fraught with risk. Potential losses have to be predicted using the most accurate measurement models available and capital put aside depending on the level of risk identified.
This challenge applies as much to the more prudent, rational manager as the more audacious one. The key is to successfully balance the probability of losing money with the amount potentially at stake. It sounds simple, until you realise that the current measurement methods applied in the field don’t necessarily do the job….
Risk management is just one of the myriad of professions to have been impacted by the global economic crisis, as budgets have become tighter and the need to accurately forecast the risk of an investment has increased tenfold. However, the basic “art” of the profession has not changed so radically – the core skill remains that of assessing the probability of potential profit and loss and setting aside the necessary capital as a result. For many years risk managers have relied upon a tried-and-tested mathematical model known as the Value at Risk (VaR) measure that enables them do just that – assess the amount of risk for a pre-determined level of probability. However, research has underlined the need to vary the probability of the losses with the amount, something that the measure currently in use fails to do.
Sensitive markets require sensitive measures
The question facing risk managers is one of acceptability – what is a reasonable amount of money to stake and what are the chances of making an extreme loss? In the latter event, how much capital is required in reserve to offset a potentially negative outcome? The Value at Risk measure has been used for some time to try to answer these questions and has been endorsed on a worldwide scale since the Basel Committee on Banking Supervision gave it the thumbs-up in 1996.
However, a number of shortcomings in the measure have been identified. Academics point to its inability to account for the subadditivity property (where the Value at Risk of the overall portfolio might be higher than the sum of the risk of its parts). Practitioners have bemoaned its lack of sensitivity to the market fluctuations. The financial crisis has underlined its failure to capture what is known as “tail risk”, which refers to the risk of having higher probability of extreme losses. This limitation of the current measuring model creates the danger of under-forecasting of risk estimates before the crisis or even over-forecasting of them post-crisis. Above all, the measure fails to link the probability of loss with the amount in question.
Acceptable investment loss – how much and how likely?
The reason why the connection between the probability and the amount of a financial loss is so important to the theory and practice of assessing the risk of an investment can be seen from the behaviour of managers themselves. In more stable times, greater risks may be taken. However, the more prudent, rational manager (especially in today’s economic climate) can work with greater potential loss, on the condition that more capital is put aside in anticipation of the worst case scenario.
In light of this, the opinion of regulators and financial institutions has shifted towards the proposal and application of a new model, a move that was also welcomed in 2013 by the very same Basel Committee on Banking Supervision that approved the previous VaR model back in 1996. Recent research activity has unearthed the Lambda Value at Risk measure as a new, more sensitive and therefore market-relevant alternative.
Mathematics applied to finance, for the good of the markets
The new proposed mathematically-based model has been recently tested and back-tested, including via historical simulation cases and also applied to 12 different stocks from 6 countries affected by the financial crisis, over the period March 2005-June 2011, and using the S&P500, EURO STOXX 50 and FTSE 100 as equity benchmarks. The new alternative Lambda Value at Risk measure displays the sensitivity to the changes of economic cycle so required by investors and risk managers. It is also able to track the risk of investments with higher probability of severe losses, and from a practical perspective is easily computable since no radical change of bank codes would be required in order to implement it.
In addition to the practical arguments for the new measure, it also opens up new avenues for theoretical discussion and exploration, including analysis of the behaviour in case of equity portfolios, other types of risk factor, and risk aggregations. Most importantly, though, it offers an opportunity for investors and risk managers to assess more accurately financial risks, by rapidly reacting to the market fluctuations in full mind of the different asset responses.
This article draws inspiration from the paper Risk measures on P(R) and Value at Risk with Probability/Loss function, written by Marco Fritelli, Marco Maggis and Ilaria Peri and published in Mathematical Finance, Vol 24 n.2 (2014).
Ilaria Peri is an assistant professor of Finance and Accounting at ESC Rennes School of Business, France. Her research interests include Risk and Performance Measures, and Quantitative Finance.