Sukuk spreads determinants and pricing model methodology

Afro-Asian J. Finance and Accounting, Vol. 3, No. 3, 2013

Sukuk spreads determinants and pricing model methodology Nader Naifar* and Slim Mseddi Department of Finance and Investment, College of Economics and Administrative Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 5701, Riyadh, Saudi Arabia E-mail: [email protected] E-mail: [email protected] *Corresponding author Abstract: The investment concept of sukuk was created as an alternative to conventional bonds since interest-bearing instruments are prohibited under Islamic law. Sukuk (commonly referred to Islamic bonds) represent a proportional ownership of tangible assets or a pool of assets. However, the key to understanding these instruments as a financial innovation is to focus on their pricing and risk characteristics. The challenge for sukuk issuing entities becomes to provide an efficient pricing model, which is compliant with Islamic law principles. The aims of this paper are two-fold. Firstly, we explore empirically the determinants of sukuk yield spreads and we describe within a coherent empirical framework the economic implications of the links between sukuk yield spreads, stock market conditions and macroeconomic variables; Secondly, we provide a methodology for estimating the fair price of sukuk in the presence of default risk. This paper presents the first empirical study for the determinants of sukuk spreads using available data and it has several practical implications that are of value for investors, risk managers and the development of Islamic financial markets. Keywords: Islamic finance; sukuk structure; sukuk yield spreads; stock market; macroeconomic variables; pricing methodology; default risk; real estate. Reference to this paper should be made as follows: Naifar, N. and Mseddi, S. (2013) ‘Sukuk spreads determinants and pricing model methodology’, Afro-Asian J. Finance and Accounting, Vol. 3, No. 3, pp.241–257. Biographical notes: Nader Naifar is a doctor of Finance and an Assistant Professor at the College of Economics and Administrative Sciences, Al-Imam Muhammad Ibn Saud Islamic University-Riyadh, Saudi Arabia. He has experience in teaching many courses in finance. His papers have been published in ISI indexed journals with impact factors (e.g., Economic Modeling, Journal of Computational and Applied Mathematics) and many reputable journals (e.g., Journal of Business and Economics, International Journal of Theoretical and Applied Finance, Journal of Risk Finance, Journal of Emerging Market Finance...). His research is closely linked to market finance, financial economics and Islamic finance. Slim Mseddi is a doctor of Finance and an Assistant Professor at the College of Economics and Administrative Sciences, Al-Imam Muhammad Ibn Saud Islamic University-Riyadh, Saudi Arabia. He has an experience in teaching many courses in finance. His research is closely linked to market finance, corporate finance and Islamic finance.

Copyright © 2013 Inderscience Enterprises Ltd.

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Introduction

Islamic finance is a fast-growing field of the global banking sector and Islamic corporate governance, and is based essentially on the prohibition of interest (riba). The association between risk-return and the notion of profit and loss sharing and partnership inherent in Islamic contracts are central to Islamic finance. One area of Islamic finance that attracted and continues to attract a lot of academic researchers and investors is the development of Islamic asset-based debt securities. Islamic securities have become more and more popular over the last decade, both as a means of raising government finance through sovereign issues, and as a way of firms obtaining funding through the offer of corporate issues. In the Islamic financial markets, sukuks1 are the most important Islamic financial securities. Sukuks are structured in such a way that they are compliant with Islamic law. The characteristics of sukuk have made it an attractive source of capital for issuers outside of the Muslim world seeking to tap into the liquidity currently offered by Islamic investors. Sukuks instruments are distinctively different from a bond (where the bond must be repaid with interest) and instead constitute a partial ownership in an asset (sukuk al ijara) or business (sukuk al musharaka). While a conventional bond is a promise to repay a loan and generally fixed interest, sukuk provides medium to long-term fixed or variable rates of return. Sukuk offers investors added portfolio diversification and investment opportunities in the form of new asset classes while issuers can benefit from increased liquidity by tapping into the growing demand among an increasing number of high net worth individuals and institutional investors for sharia compliant investment products. Global sukuk issuance has been concentrated in two regions, South East Asia (essentially Malaysia) and the Middle East (essentially the GCC countries). The Malaysian sukuk market is considered as the most important market in the world. It has been supported by the regular issuance by the Malaysian government and its central bank. According to Rabindranath and Gubta (2010), Global sukuk issuance totalled a cumulative 747 issues with a total value of 106.6 billion dollars from December 1996 to September 2009. Malaysia accounted for 46% of issues by value, becoming the single largest issuer by country while the GCC accounted for 49% of issues by value. The remaining 5% issues originated from the rest of the world. Sukuk have become one of the fastest growing financial instruments in the world. The sukuk market has seen an important growth in the last years because sukuk are asset-based that generates cash and that makes it a good investment mainly after the subprime crisis. However, sukuk issuance fell in 2010 in the aftermath of Dubai’s debt restructuring and high-profile sukuk defaults.2 Most of the research on sukuk is theoretical studies and focuses mainly on explaining and developing sukuk structures with an emphasis on legal considerations (Al-Amine and Al-Bashir, 2001; Abdel-Khaleq and Richardson, 2007; Tariq and Dar, 2007; Vishwanath and Azmi, 2009). In the recent years, some empirical studies are devoted either to research on structured sukuk instruments with case studies (Solé, 2008; Haneef, 2009) or on the relation between stock market and sukuk instruments (Ashhari et al., 2009; Godlewski et al., 2010). The difference this paper purports to make in the literature is to provide pricing methodology for ijarah sukuk. To construct a financial model to price it, we explore empirically the determinants of sukuk yield premium by using equity market variables and macroeconomic variables. In our knowledge, this paper is the first study that examines empirically the determinants of sukuk spreads and

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provides pricing methodology. This study is intended to contribute to the enhancement of knowledge about Islamic finance in general and sukuk in particular. The remainder of the paper is organised as follows. In Section 2, we present an overview of sukuk structure development. Section 3 presents the difference between ‘asset-based’ and ‘asset-backed’ sukuk. Section 4 provides the determinants of sukuk yield spreads changes. Section 5 describes data and preliminary statistics. Section 6 presents the model and provides estimation results. Section 7 presents sukuk pricing methodology. The article ends with a conclusion.

2

Sukuk structure development: an overview

Modern Islamic financing techniques were developed in Muslim parts of the world including the Middle East, North Africa and Southeast Asia.3 The key principles of Islamic financing techniques are based on the prohibition of riba, the prohibition of uncertainty of payout (gharar) or gambling4 (but not risk because it is shared among all parties) and transaction must be backed by a tangible and identifiable asset. The most popular Islamic financing and investment techniques are based on sukuk structures. The investment concept of sukuk was created in the last few years and has gained universal acceptance as an alternative to conventional financial products. There are some similarities between sukuk and conventional bonds. It has fixed term maturity and is tradable in the normal yield price. However, there are significant differences between sukuk and conventional bonds, including the fact that conventional bonds that yield interest or coupon (riba)5 are prohibited under sharia law. According to Goud (2012), even if one excludes the legal costs for structuring a sukuk, it will still be more costly for investors because each sukuk is different and the prospective purchasers will have to spend more time reviewing the structure, rather than focusing on whether the issuer is risky or not. In addition, those who buy and sell conventional bonds are rarely interested in what is actually being financed through the bond issue, which could include activities and industries that are prohibited under sharia law such as the production or sale of alcohol. Sukuk structure essentially required the corporate to sell certain physical assets to a special purpose vehicle (SPV) or company and the physical assets were then leased-back by the special purpose to the corporate for a certain number of years. There are many types of sukuk depending upon the type of Islamic modes of financing and trade used in its structure. The types of sukuk have to be reviewed and approved by ‘sharia advisers’6 to ensure agreement with sharia law. Below, we present the most important sukuk structures that are based on ijara and musharaka mode of finance.7

2.1 Sukuk al ijarah8 The most popular sukuk structures in the market are sukuk al ijarah which are backed by leases. Sukuk al ijara are certificates representing the ownership of well defined existing and well known properties, that are tied up to a lease contract. This means that sukuk al ijara can be traded in the secondary market at a price determined by both the supply and demand. The main difference between sukuk al ijarah and conventional bonds is that sukuk al ijarah does not involve the payment of a fixed interest rate (riba) because the

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structure is based on the leasing of properties. The main steps involved in the structure of sukuk al ijarah are as follows: Step1

SPV purchases assets (e.g., buildings) from obligator (e.g., corporate).

Step2

The assets purchased by the SPV are funded by the issuance of sukuk to investors.

Step 3

The sukuk holders feed the SPV with their investment.

Step 4

Originator received cash proceeds.

Step 5

SPV rents property to the originator for specified period.

Step 6

SPV collects the rental payments.

Step 7

SPV passed the rental payments to investors (sukuk holders).

Step 8

The originator repurchase the assets from the SPV and pays cash on maturity date.

Step 9

SPV simultaneously pay investors cash for sukuk redemption.

Figure 1 illustrates the main steps involved in the structure of sukuk al ijarah. Figure 1

Sukuk al ijarah structure 1 Sales of assets 4 Cash payment

Originator/ seller

5 Lease of assets

2

Special purpose vehicle (SPV)

3 Investment

Investors/ sukuk holders

7 Rental payment

6 Rental payment

Repurshase of assets on maturity date 8

Issue of sukuk al ijarah

9

Redemption of sukuk on maturity date

2.2 Sukuk al musharakah9 Sukuk al musharakah are used for mobilising the funds for establishing a new project or developing an existing one or financing an activity based on partnership contracts. The holders of sukuk become the owners of the project as per their respective contributions. There are two major forms of musharakah: permanent (since the period of the contract is not specified) and diminishing (the pro rate of partnership is progressively reduced). Sukuk al musharakah can be traded in the secondary market. The main steps involved in the structure of sukuk al musharakah are presented as follows:

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Step 1

The originator (or corporate) contributes physical assets to the partnership.

Step 2

The SPV issue sukuk al musharakah.

Step 3

The sukuk holders feed the SPV with their investment.

Step 4

SPV contributes cash to the partnership by the proceeds received from the investors to the sukuk al musharakah.

Step 5

The partnership enters into its business and generates profits or losses that are distributed to the originator and the SPV.

Step 6

The part of the SPV in profit and loss is distributed to the to investors (sukuk holders).

Step 7

At maturity, the capital gets redistributed to the originator and investors. The SPV would no longer have any shares in the musharakah.

Figure 2 illustrates the main steps involved in the structure of sukuk al musharakah. Figure 2

Sukuk al musharakah structure (see online version for colours) Issue of sukuk

2 al musharakah

Special purpose vehicle (SPV)

Originator/ corporate

3 Investment

6

5 Profit/loss

Profit distribution

Investors/ sukuk holders

7 Capital

re-distributed

1

Phisical asset contribution

4 Cash contribution Partnership (musharakah)

3

‘Asset-based vs asset-backed’ sukuk

In this section, we explain the difference between ‘asset-based’ and ‘asset-backed’ sukuk. The issue has great implications on sukuk not only in term of pricing, but also credit, default, legal, sharia compliance and litigation. The key difference between asset-based sukuk and asset-backed sukuk is the concept of true sale. If the there is ‘true sale’ and the sukuk assets are owned the sukukholders, the performance and return of sukuk will be determined by the performance of the assets. However, if there is no ‘true sale’ then the performance and return is determined by the credit of the originator. Based on that, the sukuk could be considered secured or unsecured. ‘Asset-based’ sukuk represent an ownership interest in a specific asset so as to identify the proportional profit generated from that asset and represent a secured claim on some specific underlying equipment. The majority of sukuk was ‘asset-based’ rather than ‘asset-backed’ with the

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pre-determined coupon and guaranteed the repurchase at the face value on maturity and in the absence of a transfer in asset ownership to investors. In asset-based sukuk, the originator typically transfers only the beneficial ownership to the SPV issuer. According to the sharia principles there must be a transfer of assets to sukuk holders, however, since investors have no recourse to the assets, the transaction does not focus on asset risk, but rather on the creditworthiness of the sponsors of the sukuk. In asset-backed sukuk, there is a true sale, the originator sells the assets to SPV that holds them and issues the sukuk and the buyers (sukuk holders) do not have recourse to the originator if there is a shortfall in payments. A true sale denotes the assets of the issuer will not be consolidated with the assets of the originator in the event of the liquidation. Assets are owned by the SPV, returns are derived from assets, and asset prices may vary over time. In terms of credit risk profile, asset-backed sukuk are closer to an equity position because sukuk holders own the underlying asset and have no recourse to the originator in the event of a payment shortfall. Asset-based sukuk are closer to debt because sukuk holders have recourse to the originator if there is a shortfall in payments.

4

The determinants of sukuk yield spreads

In this section, we discuss and set the different theoretical variables (dependent and explanatory variables) that can be used in explaining the determinants of corporate sukuk yield spreads.

4.1 Dependent variable We use corporate sukuk yield to maturity as proxy for corporate sukuk yield spreads. Yield to maturity is defined as the implied return that sukuk holder will benefit from if all of the sukuk cash flows are invested until the maturity date. It is considered as the internal rate of return earned by an investor who buys the sukuk today at the market price, assuming that the sukuk will be held until maturity, and that all cash flows payments will be made on schedule.

4.2 Explanatory variables After we have described the empirical proxy for corporate sukuk yield spreads, we now describe the measures we use in our analysis to proxy the main explanatory variables. We divide the theoretical determinants of sukuk yield premium into two categories: stock market conditions and macroeconomic variables. We retain the following variables: •

Stock market index return (SIR): According to Ferruz et al. (2007), stock market indices are complex, short-term numbers, normally weighted, generated for the purpose of reflecting the evolution of listed share prices over time. The stock market is neutral to announcements of conventional bond issues, but reacts negatively to announcements of sukuk issues (Godlewski et al., 2010). They attribute this finding to the excess demand for Islamic investment certificates.

Hypothesis 1

Sukuk yield spreads react positively to stock index returns.

Sukuk spreads determinants and pricing model methodology •

Stock return volatility (SRV): When significant changes in SRV occur, investors tend to panic. Yaziz et al. (2011) and Ravichandran and Bose (2012) stated that GARCH models can accommodate volatility clustering very easily. In this study, we estimate stock index return volatility using GARCH (1,1) model.

Hypothesis 2 •

An increase in the rate of inflation is likely to lead to economic tightening policies, which in turn increases the sukuk yield spread.

Slope of the yield curve (SYC): SYC is considered as a reliable predictor of future real economic activity. While short-term interest rates are administered by central banks, long-term interest rates are affected by market forces. Furthermore, SYC is believed to track embedded term risk premiums, which are investors’ rewards to bearing interest rate risk. Following Abid and Naifar (2006), the SYC was measured as the difference between the ten-year and three-month treasury rates.

Hypothesis 4

5

Sukuk yield spreads react negatively to stock price returns.

Consumer price index (CPI): CPI provides a measure of the average changes in the prices of consumer goods and services purchased by households in a specific country. According to Koohi (2006), CPI index has many applications as scale of prices generality level change measurement in economical, especially in reduction of economic variable to real numbers. CPI is commonly used as the proxy for unobserved inflation. Indeed, inflation tends to increase interest rates so fixed interest rate instruments decline in value. When the inflation rate rises, the price of a fixed interest rate instrument tends to drop, because the fixed interest rate may not be paying enough interest to stay ahead of inflation. Concerning sukuk, we anticipate that an increase in inflation rate leads to a decrease in sukuk price and therefore, an increase to the yield to maturity because an investor buying the sukuk has to pay less for the same return.

Hypothesis 3 •

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A positive SYC is associated with an increase of the sukuk yield spread.

Data description and preliminary statistics

We use data for liquid sukuk because they are completely negotiable and can be traded in the secondary markets. The first dataset consists of monthly yield to maturity data of sukuk from Bloomberg from October 2009 to July 201110 and we construct an equally-weighted index composed of 11 sukuk. Table 1 lists the issue size, issue date, maturity, and rating of each name in the constructed sukuk. The second dataset consists of SIR for the corresponding market. We notice all sukuk included in our constructed sukuk index are from the United Arab Emirates, then we use Abu Dhabi Securities Market General Index (ADSMI index) as proxy for stock market conditions . The daily stock index returns (Rt) are calculated as follows: ⎛ P ⎞ Rt = Ln ⎜ t ⎟ × 100 ⎝ Pt −1 ⎠

(1)

where Pt is the stock index at date t. The monthly stock index return is computed as the average of daily return.

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Table 1

Composition of the constructed sukuk index Issue date

Issuer

Maturity

Amount issued

Rating Country Currency

Structure

Abu Dhabi Islami

12/12/06 12/12/2011 800000000

A

UAE

USD

Sukuk al ijara

DIB Sukuk Co Ltd

03/22/07 3/22/2012 750000000

Baa1

UAE

USD

Sukuk al musharakah

EIB Sukuk Ltd

06/12/07 6/12/2012 350000000

A3

UAE

USD

Sukuk al ijara

SIB Sukuk Co Ltd

10/12/06 10/12/2011 225000000 BBB+

UAE

USD

Sukuk al ijara

TDIC Sukuk

10/21/09 10/21/2014 1000000000

AA

UAE

USD

Sukuk al Ijara

Dana Gas

10/31/07 10/31/2012 1000000000

NA

UAE

USD

Sukuk al mudarabah

Aldar Sukuk

06/17/08 6/17/2013 3750000000

B3

UAE

AED

Sukuk al ijara

Dubai Sukuk

06/13/07 6/13/2012 1250000000

B3

UAE

USD

Sukuk al mudarabah

Jafz Sukuk

11/27/07 11/27/2012 7500000000

B2

UAE

AED

Sukuk al musharakah

Dewa Funding

06/16/08 6/16/2013 3200000000

Ba1

UAE

AED

Sukuk al ijara

Wings FZCO

06/16/05 6/15/2012 750000000

NA

UAE

USD

Sukuk al musharakah

The third dataset consists of monthly stock index return volatility. We estimate monthly stock index return volatility using GARCH (1,1) model11. The most popular approach for modelling conditional volatility is the GARCH family of models as introduced by Engle (1982) and generalised by Bolerslev (1986) and Nelson (1991). GARCH models are appealing because of their simplicity, ease of estimation and empirical success in modeling time-varying volatility in a variety of contexts. The preferred model is a GARCH (1,1): ht = α 0 + α1ε t2−1 + β1ht −1

(2)

where εt is the innovation in the levels model, ht is the conditional variance. The GARCH model is to be preferred for short term horizons because it is mean reverted. Estimates of equation (2) and Ljung–Box statistics for the series are presented in Table 2. From Table 2, we reports that all the coefficients in the GARCH (1,1) model are significant and positive, indicating that stock volatilities are characterised by a heteroscedastic process. In addition, it is important to verify the adequacy of a fitted GARCH (1,1) model. The Ljung–Box statistics of the series for standardised errors and squared errors, respectively, up to the 10th lag (two weeks) are reported in the last two rows of Table 2. The Ljung-Box statistics for autocorrelation up to 10 lags and its corresponding p-value are presented. Under the null hypothesis of no serial correlation, the p-values corresponding to the Ljung–Box statistics are not significant, suggesting that

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we fail to reject the null of no serial correlation at the percent level. Then, the fitted GARCH(1,1) model is adequate in having captured all of the volatility dynamics. Table 2

Parameter estimates for the GARCH (1, 1) model

Coefficient

Estimation 7.25E-06*** (6.203246) 0.367883*** (4.560142) 0.619821*** (10.31912)

LB(10)

7.3283 (0.8119)

LB(10)

2

4.3181 (0.7326)

Note: ***Indicates statistical significance at least at the 1% level. LB(10) and LB(10)2 indicate the Ljung-Box statistics of the series for standardised errors and squared errors, respectively, up to the 10th lag (two weeks).

For macroeconomic variables, we use monthly data for the important economic indicators: CPI and SYC. The first variable is commonly used as the proxy for unobserved inflation. The second variable is used as the proxy of economic growth. The data are obtained from Bloomberg database, National Bureau of Statistics and the Central Bank of the UAE. Table 3 summarises the preliminary statistics of the data. Table 3

Preliminary statistics

Name of the company

Mean

SD

Max

Min

Constructed sukuk index yield spreads

6.77

0.82

8.47

5.18

0.01

2.63

0.12 (0.322)

115.21

0.92

116.75

114.01

0.12

1.66

1.69 (0.117)

2.63

0.39

3.37

1.89

0.20

2.38

0.5 (0.241)

Consumer price index Slope of the yield curve

Skewness Kurtosis Jarque-Bera

Stock index return

–0.0003 0.002

0.003 –0.0062

–0.36

3.34

0.6 (0.094)

Stock index volatility

0.0001 0.0001 0.0008 0.00002

3.75

16.25

212.71 (0.000 )

Note: The values in parentheses indicate the probability (p-value) that Jarque-Bera statistic exceeds the observed value under the null hypothesis of a normal distribution.

Table 3 shows the summary statistics for the data. This table shows the mean, standard deviation (SD), maximum, minimum, skewness, kurtosis, and Jarque-Bera statistic with its associated probability value (p-value). The mean is the average value of the series; the SD is a measure of dispersion in the series; Max is the maximum, or largest, value of the variables; Min is the minimum value of the variable; Skewness is a measure of asymmetry of the distribution around its mean; Kurtosis is a measure of peakedness or flatness of the distribution of the series and the Jarque-Bera test is used to detect

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normality. From Table 3, we notice that the skewness values are around zero for all series, (except for stock index return series), which mean that distributions tend to be symmetric like the normal distribution. The kurtosis statistic is more than three only for stock market series, showing that these series have fat tails compared to the normal distribution. The Jarque-Bera test is used to detect whether the series are normally distributed. The test statistic measures the difference of the skewness and kurtosis of the series with those from the normal distribution. Under the null hypothesis of a normal distribution, the statistic has a Chi2 distribution with 2 degrees of freedom, (one for skewness one for kurtosis). The data support the assumption that the residuals have normal distribution based on non significant p-value of the Jarque-Bera statistics (except for stock index volatility that is not support normality, based on a significant pvalue = 0.000).

6

Model specification and empirical results

We look at the relationship between sukuk yield spreads, stock market conditions and macroeconomic variables. For sukuk yield spreads, we construct equally-weighted index of the sukuk. For macroeconomic variables, we use monthly data for the important economic indicators (CPI and SYC). For stock market conditions, we use stock index return and stock market volatility for the corresponding market. We use a time series regression model and we estimate the equation as linear regression. SYPt = Constant + α1CPI t + α 2 SYCt + α 3 SIRt + α 4 SRVt + ε t

(3)

where SYPt is the sukuk yield spread for the month t, CPIt is the CPI, SYC is the slope of the yield curve, SIRt is n the stock index return and εt is the error term. Results of equation (3) and the t-test are presented in table 4. Table 4

Estimation results

Variables

Constant

CPI

SYC

SIR

SRV

Coefficients

20.68903

–1.496542

1.283730***

1.676344**

–901.3096

(1.128735)

(–0.965102)

(2.928708)

(2.822100)

(–1.132956)

Adjusted R2 :

0.473024

F-statistic:

5.712508

Prob ( F-statistic):

0.004208

Notes: (**) and (***) indicates that coefficients are significant or the relevant null is rejected at 5 and 1% level, respectively. CPIt is the CPI, SYCt is the SYC. SIRt is the stock index return and SRVt is the SRV.

Table 4 shows that the model is reasonably well specified with the significance level of 1% (F = 5.712508) and adjusted R2 on 47.30%. We find that the variables (CPI) and (SRV) are not statistically significant. However, we find that the variables (SYC) and (SIR) are statistically significant and we see that the signs of the coefficients are in line with our predictions. The SYC is an important indicator that explains sukuk yield spread. If we invest in sukuk al ijarah, we can use the SYC to help us in our investment decisions. For example, while a slow-down in economic activity might have negative effects on current real estate prices, a dramatic steepening of the yield curve (indicating

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an expectation of future inflation) might be interpreted to mean future price will increase. In addition, sukuk yield spread react positively to stock market implying that an increase in stock index return is accompanied with an increase in sukuk yield spreads.

7

Problem formulation for sukuk fair value

Sukuk pricing is the determination of the fair price of sukuk. For the purpose of this study, we limit our pricing methodology to sukuk al ijara because there is the most popular form of sukuk in the Islamic financial markets. A common question when considering the development of sukuk instruments is how they should correctly be priced. sukuk al Ijara depend on more than just one category of risk, which depend on credit risk of the issuing firm and the risk of real estate sector. A model that prices sukuk al ijara require, directly or implicitly, as parameter inputs default probability, recovery rates, cost of maintenance and damage to the real estate each period in order to compute the expected price. In this section, we propose a model for sukuk pricing in the presence of default risk12 and we present a methodology for parameters calibration.

7.1 Sukuk valuation in the presence of default risk The valuation of sukuk al ijarah in the presence of default risk is based on two cash flow legs: the variable leg and the default leg. The variable leg is obtained from the present value of all the rental payments made by the SPV to the investors (sukuk holders). VVariables =

∑

n i =1

Rent i P (t , T )Q ( ti ) C ( ti −1 , ti )

(4)

with: VVariables

the present value of the variable leg

Renti

the rental incomes of the assets which are assumed to be variables

P(t, T)

the discount functions for a rental income from valuation date to rental payment date

Q(ti)

the probability of no default (survival probability)

C(ti – 1, ti) the accrual function denoting the fraction of year between date i – 1 and i n

the specified period of time.

The default leg is given by expected amount received by the sukuk holders in the case of a credit event13. VDefault =

∫

T

0

(1 − R )P(t , T )(1 − Q(t ))dt

VDefault

the present value of default leg

R

the recovery rate

dt

the length of the time interval.

(5)

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The value of sukuk al ijarah is simply the difference between these two legs: Vsukuk =

∑

n t =1

P (t , T )Q ( ti ) C ( ti −1 , ti ) −

∫

T

0

(1 − R )P (t , T )(1 − Q(t ))dt

(6)

The values of the discount function and survival probability will be calculated using Monte Carlo or bootstrap methods to simulate possible realisations of the interest rate and the default intensity.

7.2 Parameters’ calibration Once a model is specified, one has to feed it with values for the different parameters in order to obtain fair price for sukuk. There are four main groups of parameters which have to be estimated: term structure of rental property, discount function, default probability and recovery rate. •

Modelling term structure of rental property: Expectations about term structure of rental property is major fundamental underlying the pricing of sukuk al ijarah. The estimation of the future evolution of spot rental property would result in different rent levels for lease contracts with different lengths of tenure. McConnell and Schallheim (1983) evaluate a variety of options embedded in lease contracts by using option-pricing theory. In Grenadier (1995) the term structure is endogenously determined from investors’ rational expectations about the timing of new supply in a competitive equilibrium with free entry, given exogenous stochastic evolution of the demand for space as well as construction costs. Grenadier (2005) shows that leases are simply contingent claims on building values. The value of leasing an asset for T years is economically equivalent to a portfolio consisting of buying the building and simultaneously writing a European call option on the building with expiration date T and a zero exercise price. Then, in equilibrium, the value of the stream of lease payments must equal the value of this portfolio of assets. Stanton and Wallace (2008) propose a simple no-arbitrage based lease pricing model and present new measure (the option adjusted lease spread) to compare leases with different maturities.

For the purpose of this study, the term structure of the rental incomes of the assets which are assumed to be variables (Rentt) can be expressed as follows: Renti = CF0 × SLRt

(7)

where CF0 is the amount of rent at time 0, SLR is the spot lease rate from a new building. We suppose that SLRt follows a geometric Brownian motion process: dSLRt = μ x dt + σ x dZ t SLRt

where μx

the expected rate of increase of the spot lease rate

σx the volatility of the spot lease rate.

(8)

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The spot lease rate is different according to the nature of space. For office space the SLR might be driven by job growth. For industrial space, SLR might be driven by changes in industrial production. For hotel space, SLR might be driven by changes in disposable income. The estimation of unobservable parameters (such as the volatility of the spot lease rate) can be performed by considering multiple leases on the same property or in the same city. •

Modelling discount function: The development of sukuk pricing methodology in an Islamic financial system involves revisiting the foundational principles of pricing theory, so as to take account of the absence of interest and the emphasis on partnership and profit and loss sharing. Obaidullah (2006) proposes the use of expected rate of profits on sovereign sukuk as a proxy for risk-free rates. According to Siddiqi (2005), the cost of capital from of capital in Islamic finance is expressed as an expected rate of profit. When it is introduced as an element of cost it would remain a flexible item, whose magnitude can be decreased or increased in the short run.

Recently, Thomson Reuters launched the world's first Islamic finance benchmark rate, designed to provide an objective and dedicated indicator for the average expected return on shariah-compliant short-term interbank funding: the Islamic Interbank Benchmark Rate (IIBR)14 assume that IIBR process is described by a mean reversion forecast model: dIIBRt = a ( b − IIBRt ) dt + σ dZ t

(9)

where IIBRt is a instantaneous short-term interbank funding, a(b – IIBRt) is a mean reversion drift, σ is a volatility, dZt is a Wiener process and a, b and σ are constants. The short-term interbank funding is pulled to a level b at rate a and σdZt is normally distributed stochastic term. The expected value of the discount function in time t is: ⎡ T IIBRs ds ⎤ P (t , T ) = E ⎢e ∫t ⎥ ⎢⎣ ⎥⎦

(10)

The expected discount factor can be simulated using the Monte-Carlo method. •

Modelling default probability: Marginal default probability of sukuk issuer can be obtained in several ways: 1 Using structural models15 of default risk developed by Merton (1974). It is supposed that the firm defaults if its assets are not sufficient to pay off the due debt. Structural models relate default to the process for the firm’s asset backing and define the default event in terms of boundary conditions on this process. 2 Using reduced form model and data of the firms’ defaultable instruments (bonds, credit spreads). Reduced form models estimate the risk neutral probability of default over a given interval from actual credit spreads without necessity to know the cause of default. 3 Using information (transition matrix16) from rating agencies about default probabilities.

We assume that the credit event process is modelled directly by modeling the probability of the credit event itself using reduced form approach17. We assume that the default

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process follows a Poisson distribution with stochastic intensities or hazard rate λ(t). The probability of default occurring within the time interval [t,t + dt) conditional on surviving to time t, is proportional to the hazard rate. Furthermore, denote Q(ti) the probability of no default (survival probability) between time t and t + Δt as seen at time zero. Q(t ) = e

⎛ ⎜− ⎝

t

⎞

∫0 γ τ dτ ⎟⎠

(11)

where γτ is the instantaneous forward rate of default at time τ. In addition, we assume that the default intensity process follows the stochastic equation:

d ln ( ht ) = a ( b − ln ( λt ) dt + σ dZ )

(12)

where λ(t) is the default intensity, a(b – ln(λt)) is a mean reversion, σ is the variance or volatility in the hazard rate, dZ is a Wiener process, and a; b, σ are constants used to forecast the intensity of default with a log-normal distribution. The evolution of the hazard rate λ(t) can be simulated using the Monte-Carlo method. •

Modelling recovery rate: Recovery rates play an important role in the estimation of credit risk and pricing of sukuk. Jarrow (2001) presents a methodology for implicit estimation of a liquidity premium, the recovery rate, and the default probabilities using debt and equity prices. Recovery rates and default probability are correlated and depend on the state of the economy. Following Guo et al. (2008), empirical literature studying recovery rates can be divided into a variety of groups. The first group is industry papers that provide estimates of recovery rate (e.g., Moody’s Investor Service, 2007). The second group is academic papers that use these industry generated recovery to study the behaviour of the recovery rates at default (e.g., Altman et al., 2005). The third group use pre-default risky debt pricing models to infer the embedded recovery rate (e.g., Janosi et al., 2002). Recently Guo et al. (2008) provide direct estimates of recovery rates using distressed debt prices. For the purpose of this study, we can use the different recovery rates available from rating agencies to calibrate our model.

8

Conclusions

In this paper, we explore empirically the determinants of sukuk yield premium by using equity market variables and macroeconomic variables. Using regression technique, we find that the model is reasonably well specified with an explanatory power of more than 47%. Furthermore, we find that stock index return and the SYC are statistically significant. In addition, we present a methodology for pricing sukuk al ijara. A fundamental part of the pricing framework is the estimation of term structure of rental property, default probabilities, discount function and recovery rate. In our knowledge, this paper is the first study that examines empirically the determinants of sukuk spreads and provides pricing methodology with stochastic rental payment and default probability. Finally, we can address important topics for future research that might be addressed. For example, we can present empirical test of the model with real data. More research on this is needed to compare market prices against fair value prices.

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Acknowledgements We greatly appreciate the financial support by SABIC chair for Islamic Financial Markets Studies at Al Imam Mohammad Ibn Saud Islamic University (IMSIU). We thank Professor Mohammad Al-Suhaibani for his constant recommendation during the course of this work. We thank also the editor (Professor D.K. Malhotra) and an anonymous referee for helpful comments.

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Notes 1 2

3 4

5 6

Sukuk (plural) or saak (singular) is referred to Islamic bonds, Islamic debt security or Islamic trust certificates. On 25 November 2009, Dubai World requested a restructuring of $26 billion out of a total debt of $60 billion. The most urgent problem facing Dubai World is the delay in the repayment of $3.52 billion sukuk, issued by World’s developer Nakheel, and maturing on 14 December 2009. According to Chong and Liu (2009), Islamic banks operating in over 75 countries have total assets of about $300 billion and enjoy an annual growth rate exceeding 15%. According to Al-Suwailem (2000), gambling represents the pure form of gharar, it is natural to argue that gharar contracts in general have the same property. That is, a gharar transaction is simply a zero-sum game with uncertain payoffs. The Islamic word for interest is riba. Sharia advisers are professionals in Islamic finance that take the role in advising consistency with sharia law.

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8 9 10 11 12 13 14

15 16 17

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The Accounting and Auditing Organization for Islamic Financial Institutions (AAOIFI) has laid down 14 types of sukuk. In this study, we present only two types which are favoured in the market. Ijarah literally means rent. Musharakah literally means sharing. We use all liquid sukuk available on Bloomberg database covering the period from October 2010 to July 2011 that present regular daily data. Stock index return volatility estimated from daily data is more precise than GARCH volatility estimated from monthly data because of the higher frequency of daily data. The underlying assets of the Sukuk certificates are subject to a risk of loss, which is a significant risk in the case of equipment and large scale construction. The credit event that triggers a default is defined in the contract; it usually includes bankruptcy and failure to pay. The IIBR, announced at the 18th Annual World Islamic Banking Conference in Bahrain (on November 2011), uses the contributed rates of 16 Islamic banks and the Islamic sections of conventional banks to provide a reliable and much-needed alternative for pricing Islamic instruments to the conventional interest-based benchmarks used for mainstream finance. It is called the ‘structural model’ because it depends on the actual capital structure of the firm. The transition matrix represents moving probabilities from one rating level to all other rating levels within selected rating. Reduced form models generally have the flexibility to refit the prices of a variety of credit instruments of different maturities.