Methodology
This article models the result from subtracting costs of illiquidity from returns from shares to procure liquidity adjusted returns. The liquidity adjusted returns simultaneously approaches liquidity and market risk. Consider a riskless asset and a risky asset having M shares. At period t, the risky asset has stock price Ps, and illiquidity cost, Cs per share. Ps and Cs are random variables (Bekaert, Harvey, & Lundland, 2007: 1797). Brokers in the market may purchase risky assets at Ps and trade at Ps -Cs. the gross return from the riskless asset is R (f). Uncertainties concerning the share price create the market risk. Liquidity risk arises from uncertainties associated with the costs of illiquidity. Assume the illiquidity cost is an autoregressive process of order one.
Cs= C + βc(Cs-1- C) + αs ………………(a)
Net return for the risky asset, Rs, is [Ps/Ps-1-1] and the relative cost of illiquidity is Cs/Ps-1
Where C>0, 0≤βc≥1, and αs is independent identically distributed with mean of zero and variance ∑(C).
Hypothesis A: increase in illiquidity results in low returns
Covs(cs+1, rs+1) < 0
Evidence exists in the United Arab Emirates and other GCC stocks that support this position that there is a negative relationship between illiquidity and returns.
Hypothesis B: increase in conditional variance of illiquidity causes increase in conditional variance of variance.
∂Vars(rs+1)/ ∂Vars(Cs+1) > 0
Typical VaR models consider market risk while ignoring liquidity risk. This may result in underestimating the underlying risks and incorrect application of capital buffer for the sanity and security of financial institutions. The GCC markets are relatively illiquid. The disregard of liquidity risk in these markets results in significant understatement of the Value at Risk under harsh market states. Risk analysis occurs under normal, crisis, and illiquid states of the market. These permit the allotment of desired horizon of liquidity and assess economic capital with regard to the actual market conditions (Dowd, Blake, & Cairns, 2004: 53).
The Delta Normal VaR requires calculation of share volatility from observations across a specified historical period and estimation uses a GARCH –M model. The impact of each risk on the overall value is determined. These impacts are totaled across the whole portfolio of shares by correlations between the risk factors during the observation period.
VaRj= │[µj-h*σj] (Mark to Market share price * fz(j)) │
Where µj is the expected return from the share, h is the level of confidence, and σj represents the conditional volatility of the share price.
Total risk is the combined effect of both the magnitudes and correlations of individual risks. Risk factors influence portfolio effects for both individual tools and huge diversified portfolios. For a portfolio of shares, value at risk is influenced by both the correlation factor (ρj,k) between proceeds from stocks and risk on the single company shares.
VaRport= {(VaR)t ρ * [VaR]}0.5 ………….(q)
Where [VaR] can be written as a matrix.
[VaR]t= [ VaR1 …………. VaRm] and [ρ] is an n×n matrix
The solution of (q) represents the exposure to market risk.
It is critical to include the liquidity traits, the number of days needed to unwind a position. Illiquidity trading position can add significant losses to existing ones and convey negative stimuli to brokers since they have high returns.
L-VaR = VaR {[ (2s+1)*(s+1)]/6s}0.5 where L-VaR is VaR in illiquid market states.
S is the total position size of stockj/ day by day trading volume of the stockj. this the monthly average.
The total portfolio liquidation adjusted value at risk for t stocks takes the form of the solution to this matrix equation
L-VaRport= {[L-VaR]t[ρ][L-VaR]}1/2
Where [L-VaR]t is a matrix while [L-VaR] and [ρ] are vectors.
L-VaR= h*σj* (Mark to Market share price * fz(j))
Economic Capital (EC)= (hec/h) H1/2 ρ1/2 *{[L-VaR]t[ρ][L-VaR]}1/2
Where h is the day to day quantile, hec is the economic quantile, 3.43, H represents the total trading days in the year and ρ is the correlation factor.
EC= hec/h) H1/2 ρ1/2 * L-VaR
Economic Capital Portfolios’ Price Risk.
Economic capital props trade under normal, liquid, and illiquid market conditions. The indicators are from DFM General Index, BA All share Index, ADSM Index, KSE General Index, DSM20 Index, MSM30 Index, SE All Share Index, Shuaa Arab Index, and Shuaa GCC index for the period of October 2004 to November 2009. The Thomson’s Datastream dataset are the source of the dataset for the daily indices. The index returns,
Rj,s= LN(Pj,s) - LN(Pj,s-1) where Pj is the present index level, LN is the natural logarithm. The confidence interval is 0.95. Commence by computing the day to day returns of the nine GCC stock markets. The computed returns are used to calculate expected returns, conditional volatilities, correlation matrices, kurtosis, skewness, and sensitivity factors (Campbell, Huisman, & Koedijk, 2001: 1793). A conditional volatility technique reveals the relation between volatility and expected returns and determines the risk variables vital to the L-VaR and calculation of the economic capital needs and the daily asset market exposure to liquidity risk. A GARCH-M (1,1) model estimates the expected return and conditional volatility for the time series parameters outlined below:
Rjs= as + bsσjs + έjs
σ2j,s= cj + gj1 σ2j1-1 + gj2 έ2js-1 where Rjs is compounding return of the time series j, σjs is the measure of volatility, and έjs is the time series error. as, bs, cj, gj1, and gj2 are parameters whose values are to be estimated and are positive. Severe market conditional volatilities are computed by carrying out an experiential distribution of returns for each stock market indices’ time series. The maximum losses observed in the expected returns time series serve this purpose. This helps surmount a number of shortcomings of the supposition of normality and better analyses of L-VaR coupled with a competent evaluation of the economic capital allotment under illiquid and severe market conditions (Castellacci, & Siclari, 2003: 211).
Findings
The Saudi Arabian SE All Share index has the greatest volatility under normal market conditions. The Dubai based DFM General Index displays the greatest volatility in severe market settings. Suppose that a year has 260 trading days. Multiplying the daily conditional volatilities by 2601/2 gives the annualized volatilities. SE All share index has a sensitivity factor of 0.98, the top in the GCC. Manama based BA All Share Index has a better factor of 0.06, the least in the region. Shuaa Arab index has a beta factor of 1.0 that is closely aligned to the Shuaa GCC index having a sensitivity factor of 1.05.
Tests of asymmetry and non normality, and detailed statistical analyses were conducted on the indices under investigation. The Jarque-Bera test is used to test for non normality in sample equities (Alexander, & Baptista, 2008: 793). All the nine GCC indices give both positive and negative outcomes signaling their asymmetry. The Muscat based MSM30 Index exhibits a negative skewness of -0.57 and a kurtosis of 18.40. The DSM20 index indicates little abnormality of -0.57, and kurtosis of 5.59. GCC stocks have little correlation in the long run. These results significantly differ from normality. The JB statistic is computed using this formula:
JB= n/{S2 + [K-3]2/4} = χ2(2) where K is kurtosis, S is skewness, and χ2(2) is a chi-square density function with two degrees of freedom at 99% and 95% confidence level. The results from the GCC stock markets are greater that the χ2 (2) of 9.21 and 5.99. The low long term correlation encourages investors to diversify their portfolio within the Gulf region in the long run. The Shuaa Arab and Shuaa GCC indices have the strongest correlation. The SE All Share Index dominates the regional trade followed by the Abu Dhabi and Dubai based bourses. The GARCH model indicates the beta factors in relation to the benchmark index and computes volatilities under severe market conditions. These correspond to the optimum losses for the GCC market indices. This eases the incorporation of short selling positions to reduce exposure to risk (Onour, 2010:54).
Economic capital is the least possible loss within a specified confidence interval and a specified duration. The maximum negative return at confidence interval 97.5% confidence interval is 5.6 % of the total value of the portfolio and is likely to occur 0.025 of the time. The L-VaR for the portfolio is therefore 5.6% of its value. This is important information when evaluating economic capital vis-à-vis the general financial position of the business. The firm and potential lenders need information on the Value at Risk before electing to lend funds to the equity trading unit. The incapacity to soak up big negative returns imperils the ability to service interest and principal debt repayments. Risk management strategies, for example, options and futures contracts may be implemented to hedge against potential fluctuations in the share prices and cushion against abnormal shocks to the system. Risk mitigation strategies would further minimize the extreme losses in the stocks trade which occur 2.5% of the time (Yiu, 2004:1330).
This technique efficiently handles various correlation factors and liquidity horizons of the nine GCC stock markets. It can simulate and tackle different equity portfolios and fund management scenarios. This method may be utilized to develop an efficient economic capital frontier. It also permits the optimization of expected returns while avoiding big risks (Brooks, & Persand, 2003: 32).
Conclusion and Recommendation
Investors are increasingly targeting the GCC nations to invest their money. These emerging markets fashion equity assets that offer substantial expected returns, considerable managerial benefits as the equity assets have little correlations with one another and other assets. The lessening of constraints on foreign participation, liberalization of stocks, rapid development of market based systems, bonds and forex markets has informed this growth. This has propped the vital role of L-VaR and economic capital allocation in evaluating trading risk financial institutions are exposed to. This article attempts to estimate the value at risk of the GCC stock markets: Saudi, Abu-Dhabi, Muscat, Doha, Kuwait, Dubai, Manama and the Bahrain stock exchange.
Fund managers, who practice the Modern portfolio theory, allot assets through optimization of the expected risk premium for every unit of risk. The mean-variance technique compels fund managers to mull over the possibility of both positive and negative returns. This article factors in risks resulting from illiquidity of assets and no-normality in the portfolio by employing the L-VaR in its assessment. It discusses economic capital allocation optimization strategies which factor different correlation factors. It provides techniques of minimizing value at risk while operating within the budgetary restrictions the trading unit is under. This may mould the spread of positive and negative returns. The data from the GCC stocks daily returns between 2004 and 2009 provide a multivariate context for analysis of the markets using different scenarios of crisis and illiquidity.
The results of the study indicate that this method satisfactorily handles the large data across several investment regimes. L-VaR and the economic capital are dependent on the least expected return and the conditional volatility from a GARCH-M model, liquidity horizons for every security, the portfolio weights, the level of correlation under severe market settings, and the individual L-Var positions. The Jarque-Bera statistic rejects the normality assumption in the data. The L-VaR better analyses potential risks. Used in combination with the economic capital allocation, it permits fund managers to strategize on risk minimization.
References
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