An Application of Mahalanobis Distance in Estimating Value-At-Risk for Optimal Hedging Strategy of Bond and Sukuk Portfolios

by Bavani Chandra Kumar


The traditional models which are applied in the bond market in quantifying the VaR is not accurately assessing the Value at Risk. To overcome this problem, a new technique of mean-variance and covariance approach is applied as in the share market with Mahalanobis Distance (MD) in the bond and sukuk markets.

The Sukuk market is the fastest growing and promising segment of Islamic Finance and issuance of Sukuk is increasing at a great speed in Malaysia. In the first three quarters of 2018 the companies and others issued Sukuk RM123.9 billion globally. Islamic bond portfolios are growing as the investors like banks, fund managers and institutional investors are more interested in Sukuk.

Therefore, studying and researching the various properties of bond and Sukuk portfolio are pertinent. The properties include yield rate (not coupon rate), duration, modified duration and convexity and MD. These parameters are useful in estimating the VaR (Value at Risk) accurately which help in hedging and valuation of bond and Sukuk portfolios. The yield rate on a bond is a function of the length of time to maturity and also depends on the risk of the bond.

In practice, the yield curve is one of the key concerns of fixed income investors and also very important for valuation. Yield curve allows investors to predict the future income against the risk present in bond and Sukuk.
Duration and convexity quantify the VaR of a bond which is the risk to be hedged. Since risk is quantified in linear techniques in classical methods, Mahalanobis Distance is used to get accurate expected losses as a modern method. Mahalanobis Distance takes into consideration the covariances or interaction among the bonds in a portfolio.

The link between bond duration and price volatility is widely used for managing risk positions, portfolio value protection and how to hedge positions in fixed income securities due to the market volatility which can cause huge losses on large exposures.
In this study 14 bond and sukuk portfolios of fixed income securities are analysed. After analysing the real 14 bond and sukuk portfolios taken from Fundsupermart website, it was found that the traditional models underestimate the portfolio VaR.

This leads to underhedging and sub-optimal risk management. During the financial crisis, this underhedging caused heavy losses for the investment companies. To overcome this problem to achieve optimum hedging of bonds and sukuk portfolios’ VaR estimated via MD is found out to be more efficient.
Out of the 14 bond and sukuk portfolios the classical estimation of VaR is less than the MD estimation of VaR.

Though MD overestimates the VaR slightly on the higher side, it will protect the bond portfolios effectively during the time of crisis, which happen in cycles in bond and sukuk markets regularly. This study will assess the excess VaR when compared to traditional models and advice the management and fund managers to redesign their assessing VaR policies. This is also stressed by the BASEL Agreements all over the globe.

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