## _wp07237

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---

### I. Introduction and market overview
- Sukuk market growth:
  - Less than $8 billion in 2003 → $50 billion by mid-2007.
- Role and issuance:
  - Provide sovereign governments and corporations access to the Islamic liquidity pool in addition to the conventional investor base.
  - Main issuance hubs: Malaysia and the Gulf region; issuance also from the United States, Europe, and Asia.
  - Sovereign and supranational issuers cited: State of Qatar, the Bahrain Monetary Agency, the Government of Pakistan, the Government of Malaysia, the State of Saxony-Germany, the Islamic Development Bank.
  - Corporate issuers cited: Nestle, several oil companies, companies in Dubai, the Standard Chartered Bank.
- Representative issue-size and coupon data (selected entries from Table 1 preserved exactly):
  - Malaysia Global Sukuk — Date: Jan-02 — Currency: USD — Issue Size (millions): 600 — Coupon: Libor 6m+0.95
  - Government of Bahrain — Date: May-03 — Currency: USD — Issue Size (millions): 250 — Coupon: Libor 6m+0.60
  - Islamic Development Bank — Date: Aug-03 — Currency: USD — Issue Size (millions): 400 — Coupon: Libor 6m+0.12
  - Government of Qatar — Date: Sep-03 — Currency: USD — Issue Size (millions): 700 — Coupon: Libor 6m+0.40
  - Dubai Global Sukuk — Date: Nov-04 — Currency: USD — Issue Size (millions): 1000 — Coupon: Libor 6m+0.45
  - Saxony-Anhalt State Properties — Date: Jan-04 — Currency: EUR — Issue Size (millions): 100 — Coupon: Libor 6m+1.00
  - Pakistan International Sukuk Co. — Date: Jan-05 — Currency: USD — Issue Size (millions): 600 — Coupon: Libor 6m+2.20
  - Standard Chartered Bank Malaysia — Date: Dec-04 — Currency: USD — Issue Size (millions): 100 — Coupon: ...
  - Durrat Al Bahrain Sukuk — Country: Bahrain — Date: Jan-05 — Currency: USD — Issue Size (millions): 152 — Coupon: Libor 3m+1.25
  - The Commercial Real State Sukuk Kuwait — Date: May-05 — Currency: USD — Issue Size (millions): 100 — Coupon: Libor 6m+1.25
  - Rantau Abang Capital Sukuk Malaysia — Date: Mar-06 — Currency: MYR — Issue Size (millions): 2029 — Coupon: 4.91 fixed
  - The Nakheel Group UAE — Date: Dec-06 — Currency: USD — Issue Size (millions): 3520 — Coupon: 6.345 fixed
  - Dubai Ports Authority UAE — Date: Jan-06 — Currency: USD — Issue Size (millions): 3500 — Coupon: 7.125 - 10.125
  - Daar International Sukuk Saudi Arabia — Date: Jul-07 — Currency: USD — Issue Size (millions): 1000 — Coupon: Libor 3m+1.94
  - Aldar Properties UAE — Date: Feb-07 — Currency: USD — Issue Size (millions): 2530 — Coupon: 5.767 fixed
- Structural and market behavior notes:
  - Sukuk are traded, rated, and cleared (mostly under Euroclear, listed in Luxemburg), similar to conventional Eurobonds.
  - Principal structural difference: bonds represent issuer’s debt; Sukuk represent ownership/participation rights in underlying assets (e.g., Ijarah lease creates a lessee/lessor relationship versus lender/borrower).
  - Investor protection mechanisms for Sukuk remain largely untested.
  - Taxation may be an issue where legal basis for taxation of Islamic securities is not legislated in the home country (Thuronyi, 2007).
  - Market behavior: holders tend to keep Sukuk to maturity with limited secondary market trading (El Qorchi 2005).
  - Specialized exchanges listing Sukuk: Dubai International Finance Exchange, Labuan Exchange (Malaysia), Third Market (Vienna).
  - London may emerge as a bridge between Islamic finance and conventional capital markets; tax law changes have given Sukuk equivalent tax treatment with conventional bonds.
  - Secondary market liquidity expected to develop gradually as issuance increases and investor familiarity grows.
- Research question and scope:
  - Do Sukuk provide diversification benefits to investors and issuers, and how significant are gains from diversification?
  - Alternatively, are secondary market behaviors of Eurobonds and Sukuk so similar that Sukuk add limited value?
  - Study models impact of Sukuk on hypothetical bond portfolios mixing Sukuk and Eurobonds vs portfolios of only Eurobonds.
  - Application limited to international issues of Sukuk and conventional bonds by governments of Malaysia, Pakistan, Qatar, and Bahrain due to data constraints.

### II. Data and empirical methodology
- Data scope and sources:
  - Study scope limited to sovereign international issues of Sukuk and conventional bonds for which secondary market data are available: Malaysia, Pakistan, Qatar, Bahrain.
  - Clean price data (trade price less accrued interest) obtained from issue date or first available date until end-June 2007.
  - Data sources: DataStream (weekly and daily prices for Malaysian, Pakistani, and Qatari bonds from issue date through end-June 2007); Bloomberg (data for Bahrain available only from August 2006).
- Observed market patterns:
  - Sukuk often carry floating rate coupons indexed to Libor.
  - Sukuk are smaller in issue size and have shorter maturities compared to Eurobonds by the same issuer.
  - Sukuk are traded less frequently compared to conventional bonds by same issuer; pattern stronger for Malaysia and Qatar and less strong for Pakistan and Bahrain.
- Selected bond characteristics (from Table 2; entries preserved exactly):
  - Malaysia Global Sukuk — Issue Date: 25-Jun-02 — Maturity: 5 — Issue Size Millions USD: 600 — Coupon: 6m Libor+0.95 — S&P Rating: A- — Percent of Trade Days: 23%
  - Malaysia 2001 (Bond 1) — Issue Date: 30-Jun-01 — Maturity: 10 — Issue Size Millions USD: 1750 — Coupon: 7.5 Fixed — S&P Rating: A- — Percent of Trade Days: 90%
  - Malaysia 1999 (Bond 2) — Issue Date: 28-May-99 — Maturity: 10 — Issue Size Millions USD: 1500 — Coupon: 8.75 Fixed — S&P Rating: A- — Percent of Trade Days: 97%
  - Pakistan International Sukuk — Issue Date: 18-Jan-05 — Maturity: 5 — Issue Size Millions USD: 600 — Coupon: 6m Libor+2.20 — S&P Rating: B+ — Percent of Trade Days: 45%
  - Pakistan 2004 (Bond 1) — Issue Date: 12-Feb-04 — Maturity: 5 — Issue Size Millions USD: 500 — Coupon: 6.75 Fixed — S&P Rating: B+ — Percent of Trade Days: 54%
  - Pakistan 2006 (Bond 2) — Issue Date: 23-Mar-06 — Maturity: 10 — Issue Size Millions USD: 500 — Coupon: 7.125 Fixed — S&P Rating: B+ — Percent of Trade Days: 58%
  - Pakistan 2006 (Bond 3) — Issue Date: 23-Mar-06 — Maturity: 30 — Issue Size Millions USD: 300 — Coupon: 7.875 Fixed — S&P Rating: B+ — Percent of Trade Days: 56%
  - Qatar Global Sukuk — Issue Date: 30-Sep-03 — Maturity: 7 — Issue Size Millions USD: 700 — Coupon: 6m Libor+0.40 — S&P Rating: AA- — Percent of Trade Days: 12%
  - Qatar 1999 (Bond 1) — Issue Date: 13-May-99 — Maturity: 10 — Issue Size Millions USD: 1000 — Coupon: 9.50 Fixed — S&P Rating: AA- — Percent of Trade Days: 85%
  - Qatar 2001 (Bond 2) — Issue Date: 23-Jun-00 — Maturity: 30 — Issue Size Millions USD: 1400 — Coupon: 9.75 Fixed — S&P Rating: AA- — Percent of Trade Days: 95%
  - BMA International Sukuk (Bahrain) — Issue Date: 23-Jun-04 — Maturity: 5 — Issue Size Millions USD: 250 — Coupon: 6m Libor+ 0.60 — S&P Rating: A — Percent of Trade Days: 90%
  - Bahrain 2003 (Bond 1) — Issue Date: 21-Jan-03 — Maturity: 5 — Issue Size Millions USD: 500 — Coupon: 4 Fixed — S&P Rating: A — Percent of Trade Days: 98%
- VaR framework and methods:
  - Chosen methodology: Value-at-Risk (VaR).
  - Delta-normal (variance-covariance) approach:
    - σp = sqrt(w' Σ w) (notation preserved from source: 'ww p Σ=σ).
    - Portfolio VaR formula as presented: VaRp = -(μp − ασp W)
      - α = standard normal deviate (e.g., 2.33 for the 99 percent confidence level)
      - μp = average return of the portfolio
      - W = initial portfolio value
    - Assumes returns are jointly normally distributed.
  - Monte Carlo simulation approach:
    - Chosen stochastic process: geometric Brownian motion for price evolution.
    - Number of Monte Carlo iterations n = 10000.
    - Accuracy of estimated parameters proportional to 1/√n.
    - Monte Carlo relies on pseudo-random numbers; estimation error decreases as n increases.
  - Comparison notes:
    - Monte Carlo requires fewer strong assumptions but is more computationally demanding.
    - Delta-normal method has closed-form formulas for standard errors of estimation; those numbers are provided in the analysis (where applicable).
  - Limitations:
    - Normality assumption may understate tail risk because asset returns often exhibit fat tails and negative skewness.

### Application: portfolio setup and VaR choices
- Portfolio construction:
  - Two hypothetical bond portfolios with equal dollar values ($100 million) are constructed:
    - Portfolio 1: Sukuk and conventional bonds.
    - Portfolio 2: only conventional bonds.
  - Weight of each security in the portfolio is proportional to its issue size. (Results for equally weighted securities reported in Appendix III.)
- VaR parameters:
  - Confidence interval: 99%.
  - Holding period: a week, or 5 business days.
  - Rationale for weekly holding period: limited liquidity of Sukuk; weekly price better represents market price across differing business days in Gulf exchanges and other exchanges.

### Empirical VaR results (portfolio value $100 million)
- Delta-normal and Monte-Carlo comparisons (values are VaR in $ millions; delta-normal estimation error in parentheses where provided):
  - Pakistan
    - Delta-Normal Method: 1.11 (0.04) versus 1.53 (0.06) → Change: 27%
    - Monte-Carlo Simulation: 1.11 versus 1.31 → Change: 15%
  - Malaysia
    - Delta-Normal Method: 0.77 (0.020) versus 0.86 (0.025) → Change: 11%
    - Monte-Carlo Simulation: 0.74 versus 0.84 → Change: 11%
  - Qatar
    - Delta-Normal Method: 1.01 (0.05) versus 1.23 (0.06) → Change: 17%
    - Monte-Carlo Simulation: 0.99 versus 1.21 → Change: 18%
  - Bahrain
    - Delta-Normal Method: 0.04 (0.005) versus 0.06 (0.006) → Change: 40%
    - Monte-Carlo Method: 0.04 versus 0.05 → Change: 32%
- Equally weighted bonds VaR estimates (Appendix III):
  - Pakistan
    - Delta-Normal Method: 1.37 (0.05) versus 1.81 (0.07) → Change: 24%
    - Monte-Carlo Simulation: 1.36 versus 1.78 → Change: 22%
  - Malaysia
    - Delta-Normal Method: 0.98 (0.01) versus 1.52 (0.02) → Change: 55%
    - Monte-Carlo Simulation: 0.96 versus 1.57 → Change: 38%
  - Qatar
    - Delta-Normal Method: 0.91 (0.04) versus 1.59 (0.02) → Change: 42%
    - Monte-Carlo Simulation: 0.90 versus 1.56 → Change: 56%
  - Bahrain
    - Delta-Normal Method: 0.03 (0.002) versus 0.06 (0.001) → Change: 50%
    - Monte-Carlo Method: 0.03 versus 0.06 → Change: 50%
- Robustness and interpretation:
  - Monte-Carlo Simulation estimates are very similar to delta-normal results, indicating robustness to method.
  - Differences between methods reflect deviations from normality of portfolio returns.
  - For each issuer, inclusion of Sukuk improves portfolio VaR:
    - Monte-Carlo reductions: Malaysia 11%, Pakistan 15%, Qatar 18%, Bahrain 32%.
  - For all issuers, VaR of portfolio of only conventional bonds is statistically different from VaR of portfolio of conventional bonds and Sukuk together (estimation errors indicate statistical difference).

### Conclusions, policy-relevant findings, and caveats
- Main conclusions:
  - Evidence indicates Sukuk are different instruments than conventional bonds as shown by different price behavior.
  - Diversification by including Sukuk in an issuer’s bond portfolio can significantly reduce portfolio VaR compared to investing only in conventional bonds of that issuer.
  - Correlations of Sukuk returns with returns on conventional bonds are much smaller than correlations among conventional bonds themselves.
  - Reduced VaR arises partly from diversification by adding instruments with different duration and from distinct secondary market price behavior of Sukuk.
  - Example: Bahrain — Sukuk and conventional bonds have similar durations, yet correlation of returns is close to zero.
- Policy-relevant implications:
  - Sukuk issuance can provide diversification benefits to sovereign and corporate issuers and to investors, potentially lowering downside risk (VaR) of issuer-specific bond portfolios.
  - Jurisdictions should consider legal and tax frameworks for Islamic securities; taxation may be an issue where legal basis for taxation of Islamic securities is not legislated.
  - Development of secondary market liquidity is important for realizing diversification benefits; regulators and market infrastructure providers may support listing and clearing arrangements (e.g., Euroclear, Luxemburg listing).
- Limitations and cautions:
  - Possible gains from diversification must be weighed against lower return of Sukuk (most of the time Sukuk offer lower returns compared to conventional bonds).
  - Liquidity risk: Sukuk are illiquid compared to conventional bonds (lack of secondary market activity).
  - Illiquidity can impose more risk during volatility; the study mitigates this by using weekly data, but a more rigorous treatment of illiquidity effects on Sukuk prices and premiums is desirable.
  - Volatility measured reflects volatility on trade days, not necessarily true underlying price volatility.
  - Given data limitations, results are not conclusive but contribute to the debate on issuance of Sukuk as alternative investment/financing instruments.

### Appendix highlights: Monte Carlo algorithm and variance-covariance structure
- Monte Carlo single-asset simulation (equation preserved):
  - P_{t+Δt} = P_t + μ P_t Δt + σ P_t Δt Z_t  (equation (3) in source)
  - μ and σ are mean and standard deviation of returns over a holding period.
  - Z_t is a standard normal shock.
  - Holding period divided into T intervals of size Δt (usually Δt = 1/100 in practice).
  - Repeat n = 10000 simulations; VaR is the 1% or 5% lowest simulated price (or return).
- Multiple-asset simulation:
  - Each asset i evolves by its own Brownian motion (equation (4) in source).
  - Correlated shocks constructed via Cholesky factorization: R = H H'.
  - Starting from iid vector η with unit variance, Z = H η yields correlated Z with covariance matrix R.
  - Use correlated Z_t to simulate asset price paths, obtain portfolio price as weighted sum, repeat 10,000 times, compute VaR as 1% or 5% lowest portfolio price (or return).
- Selected entries from variance-covariance matrix of weekly returns (Appendix II; scientific notation preserved):
  - Malaysia:
    - Sukuk variance: 6.12E-06
    - Sukuk with Bond 1 covariance: 2.45E-06
    - Bond 1 variance: 1.56E-05
    - Bond 2 covariance entries: 2.03E-06, 9.50E-06, 1.01E-05 (as positioned in the matrix)
  - Qatar:
    - Sukuk variance: 2.41E-06
    - Bond 1 variance: 5.65E-05
    - Bond 2 variance: 3.71E-06
    - Covariance entries include -4.00E-07 and -1.30E-07 in positions shown
  - Pakistan:
    - Sukuk variance: 2.71E-05
    - Bond 1 variance: 7.80E-06
    - Bond 2 variance: 9.50E-06
    - Bond 3 variance: 1.18E-04
    - Selected covariances: 1.12E-08, 1.30E-07, 7.10E-06, -1.24E-05, 7.30E-06, 9.39E-5, 1.70E-04 (as positioned in matrix)
  - Bahrain:
    - Sukuk variance: 4.66E-08
    - Bond 1 variance/covariance entries include 3.60E-06 and other positions shown

*Source: _wp07237 — IMF working paper content unit (excerpted content provided).*

### References..............................................................................................................

### _wp07237 - References

### I. INTRODUCTION
- The market for Sukuk has grown from less than $8 billion in 2003 to $50 billion by mid-2007.
- Sukuk provide sovereign governments and corporations access to the Islamic liquidity pool in addition to the conventional investor base.
- Main issuance hubs: Malaysia and the Gulf region; issuance also from the United States, Europe, and Asia.
- Sovereign and supranational issuers cited: State of Qatar, the Bahrain Monetary Agency, the Government of Pakistan, the Government of Malaysia, the State of Saxony-Germany, the Islamic Development Bank.
- Corporate issuers cited: Nestle, several oil companies, companies in Dubai, the Standard Chartered Bank.
- Table 1 (Selected Issues of Sukuk) highlights specific issues with exact figures (excerpted fields preserved):
  - Malaysia Global Sukuk — Date: Jan-02 — Currency: USD — Issue Size (millions): 600 — Coupon: Libor 6m+0.95
  - Government of Bahrain — Date: May-03 — Currency: USD — Issue Size (millions): 250 — Coupon: Libor 6m+0.60
  - Islamic Development Bank — Date: Aug-03 — Currency: USD — Issue Size (millions): 400 — Coupon: Libor 6m+0.12
  - Government of Qatar — Date: Sep-03 — Currency: USD — Issue Size (millions): 700 — Coupon: Libor 6m+0.40
  - Dubai Global Sukuk — Date: Nov-04 — Currency: USD — Issue Size (millions): 1000 — Coupon: Libor 6m+0.45
  - Saxony-Anhalt State Properties — Date: Jan-04 — Currency: EUR — Issue Size (millions): 100 — Coupon: Libor 6m+1.00
  - Pakistan International Sukuk Co. — Date: Jan-05 — Currency: USD — Issue Size (millions): 600 — Coupon: Libor 6m+2.20
  - Standard Chartered Bank Malaysia — Date: Dec-04 — Currency: USD — Issue Size (millions): 100 — Coupon: ...
  - Durrat Al Bahrain Sukuk — Country: Bahrain — Date: Jan-05 — Currency: USD — Issue Size (millions): 152 — Coupon: Libor 3m+1.25
  - The Commercial Real State Sukuk Kuwait — Date: May-05 — Currency: USD — Issue Size (millions): 100 — Coupon: Libor 6m+1.25
  - Rantau Abang Capital Sukuk Malaysia — Date: Mar-06 — Currency: MYR — Issue Size (millions): 2029 — Coupon: 4.91 fixed
  - The Nakheel Group UAE — Date: Dec-06 — Currency: USD — Issue Size (millions): 3520 — Coupon: 6.345 fixed
  - Dubai Ports Authority UAE — Date: Jan-06 — Currency: USD — Issue Size (millions): 3500 — Coupon: 7.125 - 10.125
  - Daar International Sukuk Saudi Arabia — Date: Jul-07 — Currency: USD — Issue Size (millions): 1000 — Coupon: Libor 3m+1.94
  - Aldar Properties UAE — Date: Feb-07 — Currency: USD — Issue Size (millions): 2530 — Coupon: 5.767 fixed
- Key structural characteristics and market behavior:
  - Sukuk are similar to conventional Eurobonds in being traded, rated, and cleared (mostly under Euroclear, listed in Luxemburg).
  - Principal structural difference: a bond represents issuer’s debt; Sukuk represent ownership/participation rights in underlying assets (e.g., Ijarah lease creates a lessee/lessor relationship versus lender/borrower).
  - Investor protection mechanisms for Sukuk remain largely untested.
  - Taxation may be an issue where legal basis for taxation of Islamic securities is not legislated in the home country (Thuronyi, 2007).
  - Market behavior: holders tend to keep Sukuk to maturity with limited secondary market trading (El Qorchi 2005).
  - Specialized exchanges listing Sukuk: Dubai International Finance Exchange, Labuan Exchange (Malaysia), Third Market (Vienna).
  - London may emerge as a bridge between Islamic finance and conventional capital markets; tax law changes have given Sukuk equivalent tax treatment with conventional bonds.
  - Secondary market liquidity expected to develop gradually as issuance increases and investor familiarity grows.
- Research question and scope:
  - Do Sukuk provide diversification benefits to investors and issuers, and how significant are gains from diversification?
  - Alternatively, are secondary market behaviors of Eurobonds and Sukuk so similar that Sukuk add limited value?
  - Study models impact of Sukuk on hypothetical bond portfolios mixing Sukuk and Eurobonds vs portfolios of only Eurobonds.
  - Application limited to international issues of Sukuk and conventional bonds by governments of Malaysia, Pakistan, Qatar, and Bahrain due to data constraints.
- Risk measurement approach:
  - Chosen methodology: Value-at-Risk (VaR).
  - Use data up to July 2007 to derive covariance matrix of shocks.
  - Use structured Monte Carlo simulations (10,000 replications) and delta-normal approach.

### II. DATA AND METHODOLOGY
A. Data
- Study scope limited to sovereign international issues of Sukuk and conventional bonds for which secondary market data are available: Malaysia, Pakistan, Qatar, Bahrain.
- Clean price data (trade price less accrued interest) obtained from issue date or first available date until end-June 2007.
- Data sources:
  - DataStream: weekly and daily prices for Malaysian, Pakistani, and Qatari bonds from issue date through end-June 2007.
  - Bloomberg: data for Bahrain available only from August 2006 rather than original issue date.
- Observed market patterns:
  - Sukuk often carry floating rate coupons indexed to Libor.
  - Sukuk are smaller in issue size and have shorter maturities compared to Eurobonds by the same issuer.
  - Sukuk are traded less frequently compared to conventional bonds by same issuer; pattern stronger for Malaysia and Qatar and less strong for Pakistan and Bahrain.
- Table 2 (Characteristics of Sukuk and Conventional Bonds in the Study) — selected exact entries preserved:
  - Malaysia Global Sukuk — Issue Date: 25-Jun-02 — Maturity: 5 — Issue Size Millions USD: 600 — Coupon: 6m Libor+0.95 — S&P Rating: A- — Percent of Trade Days: 23%
  - Malaysia 2001 (Bond 1) — Issue Date: 30-Jun-01 — Maturity: 10 — Issue Size Millions USD: 1750 — Coupon: 7.5 Fixed — S&P Rating: A- — Percent of Trade Days: 90%
  - Malaysia 1999 (Bond 2) — Issue Date: 28-May-99 — Maturity: 10 — Issue Size Millions USD: 1500 — Coupon: 8.75 Fixed — S&P Rating: A- — Percent of Trade Days: 97%
  - Pakistan International Sukuk — Issue Date: 18-Jan-05 — Maturity: 5 — Issue Size Millions USD: 600 — Coupon: 6m Libor+2.20 — S&P Rating: B+ — Percent of Trade Days: 45%
  - Pakistan 2004 (Bond 1) — Issue Date: 12-Feb-04 — Maturity: 5 — Issue Size Millions USD: 500 — Coupon: 6.75 Fixed — S&P Rating: B+ — Percent of Trade Days: 54%
  - Pakistan 2006 (Bond 2) — Issue Date: 23-Mar-06 — Maturity: 10 — Issue Size Millions USD: 500 — Coupon: 7.125 Fixed — S&P Rating: B+ — Percent of Trade Days: 58%
  - Pakistan 2006 (Bond 3) — Issue Date: 23-Mar-06 — Maturity: 30 — Issue Size Millions USD: 300 — Coupon: 7.875 Fixed — S&P Rating: B+ — Percent of Trade Days: 56%
  - Qatar Global Sukuk — Issue Date: 30-Sep-03 — Maturity: 7 — Issue Size Millions USD: 700 — Coupon: 6m Libor+0.40 — S&P Rating: AA- — Percent of Trade Days: 12%
  - Qatar 1999 (Bond 1) — Issue Date: 13-May-99 — Maturity: 10 — Issue Size Millions USD: 1000 — Coupon: 9.50 Fixed — S&P Rating: AA- — Percent of Trade Days: 85%
  - Qatar 2001 (Bond 2) — Issue Date: 23-Jun-00 — Maturity: 30 — Issue Size Millions USD: 1400 — Coupon: 9.75 Fixed — S&P Rating: AA- — Percent of Trade Days: 95%
  - BMA International Sukuk (Bahrain) — Issue Date: 23-Jun-04 — Maturity: 5 — Issue Size Millions USD: 250 — Coupon: 6m Libor+ 0.60 — S&P Rating: A — Percent of Trade Days: 90%
  - Bahrain 2003 (Bond 1) — Issue Date: 21-Jan-03 — Maturity: 5 — Issue Size Millions USD: 500 — Coupon: 4 Fixed — S&P Rating: A — Percent of Trade Days: 98%

B. Methodology
- Value-at-Risk (VaR) framework:
  - VaR measures the worst expected loss of a portfolio over a holding period at a given confidence level under normal market conditions (Jorion 2006).
  - VaR example: with one percent probability or 99 percent confidence level, a certain dollar amount will be lost in a given period.
  - VaR depends on portfolio variance computed from weights and variance-covariance matrix:
    - σp = sqrt(w' Σ w) (notation preserved from source: 'ww p Σ=σ)
  - Delta-normal (variance-covariance) approach:
    - Assumes returns are jointly normally distributed.
    - Portfolio VaR formula (as presented): VaRp = -(μp − ασp W)
      - α = standard normal deviate (e.g., 2.33 for the 99 percent confidence level)
      - μp = average return of the portfolio
      - W = initial portfolio value
  - Interpretation: lower volatility implies smaller VaR; diversification gains arise when constituent asset returns have small or negative correlations.
  - Limitations of normality assumption:
    - Asset returns often exhibit fat tails and negative skewness; extraordinary losses may occur more frequently than normal distribution predicts.
- Monte Carlo simulation approach:
  - Requires specification of a stochastic data generating process and parameter estimation from data.
  - Simulate price paths using computer-generated random numbers to form distribution of returns and measure VaR.
  - Chosen stochastic process: geometric Brownian motion for price evolution.
  - Simulation specifics in this analysis:
    - Number of Monte Carlo iterations n = 10000.
    - Accuracy of estimated parameters proportional to 1/√n.
    - Monte Carlo relies on pseudo-random numbers; estimation error decreases as n increases.
  - Comparison notes:
    - Monte Carlo requires fewer strong assumptions but is more computationally demanding.
    - Delta-normal method has closed-form formulas for standard errors of estimation; those numbers are provided in the analysis (where applicable).
- Application to bonds:
  - VaR application requires decomposition of securities and estimation of variances and covariances of returns.
  - Variances and correlations are estimated from historical return data (up to July 2007).
  - Monte Carlo generates several possible paths for portfolio values (10,000 replications) and uses the delta-normal approach for comparison.

### Key Findings and Analytical Notes (as presented)
- Sukuk market expansion:
  - Less than $8 billion in 2003 → $50 billion by mid-2007.
- Market liquidity and trading frequency:
  - Sukuk traded less frequently than conventional bonds by same issuer (percent of trade days reported per bond; examples preserved above).
  - Pattern of lower trading frequency stronger in Malaysia and Qatar; less pronounced in Pakistan and Bahrain.
- Structural and legal considerations:
  - Sukuk represent ownership/participation rights; common structures include Ijarah (lease).
  - Investor protection mechanisms and taxation frameworks for Sukuk are areas of concern or uncertainty.
- Methodological choice and limitations:
  - VaR (delta-normal and Monte Carlo) used to quantify downside risk and to test diversification benefits of adding Sukuk to bond portfolios.
  - Monte Carlo simulations run with n=10000 replications using geometric Brownian motion.
  - Normality assumption in delta-normal approach may understate tail risk due to fat tails and skewness in asset returns.

*Source: _wp07237 - References (excerpted content provided).*

### Appendix I, as well as generalizing to a portfolio of many assets, accounting for correlations

### Appendix I, as well as generalizing to a portfolio of many assets, accounting for correlations

### Application to Sukuk and Eurobonds — portfolio setup and VaR choices
- Two hypothetical bond portfolios with equal dollar values ($100 million) are constructed:
  - Portfolio 1: Sukuk and conventional bonds.
  - Portfolio 2: only conventional bonds.
- Weight of each security in the portfolio is proportional to its issue size. (Results for equally weighted securities reported in Appendix III.)
- Holding period and confidence interval chosen for VaR computation:
  - Confidence interval: 99%.
  - Holding period: a week, or 5 business days.
- Rationale for weekly holding period:
  - Limited liquidity of Sukuk; ratio of traded days reported.
  - Weekly price can better represent market price across differing business days in Gulf region exchanges and other exchanges.

### VaR calculation methods and interpretation
- Two VaR methods applied:
  - Delta-normal method.
  - Monte-Carlo Simulation method.
- VaR definition and interpretation example:
  - Delta-normal method implies a VaR of $1.11 million for the portfolio of all Pakistani bonds.
    - Interpretation: weekly loss on market value will not be larger than $1.11 million or 1.11% of its value (as of end-June 2007) 99% of the time; 1% chance loss could be larger than $1.11 million.
  - Estimation errors are provided to compare VaR values; statistical differences between portfolios account for estimation error.

### VaR results by issuer (portfolio value $100 million)
- Table 4 (Conventional bonds and Sukuk vs Conventional bonds; estimation error shown for delta-normal):
  - Pakistan
    - Delta-Normal Method: 1.11 (0.04) versus 1.53 (0.06) → Change: 27%
    - Monte-Carlo Simulation: 1.11 versus 1.31 → Change: 15%
  - Malaysia
    - Delta-Normal Method: 0.77 (0.020) versus 0.86 (0.025) → Change: 11%
    - Monte-Carlo Simulation: 0.74 versus 0.84 → Change: 11%
  - Qatar
    - Delta-Normal Method: 1.01 (0.05) versus 1.23 (0.06) → Change: 17%
    - Monte-Carlo Simulation: 0.99 versus 1.21 → Change: 18%
  - Bahrain
    - Delta-Normal Method: 0.04 (0.005) versus 0.06 (0.006) → Change: 40%
    - Monte-Carlo Method: 0.04 versus 0.05 → Change: 32%
- Appendix III — equally weighted bonds VaR estimates:
  - Pakistan
    - Delta-Normal Method: 1.37 (0.05) versus 1.81 (0.07) → Change: 24%
    - Monte-Carlo Simulation: 1.36 versus 1.78 → Change: 22%
  - Malaysia
    - Delta-Normal Method: 0.98 (0.01) versus 1.52 (0.02) → Change: 55%
    - Monte-Carlo Simulation: 0.96 versus 1.57 → Change: 38%
  - Qatar
    - Delta-Normal Method: 0.91 (0.04) versus 1.59 (0.02) → Change: 42%
    - Monte-Carlo Simulation: 0.90 versus 1.56 → Change: 56%
  - Bahrain
    - Delta-Normal Method: 0.03 (0.002) versus 0.06 (0.001) → Change: 50%
    - Monte-Carlo Method: 0.03 versus 0.06 → Change: 50%

### Robustness and interpretation of results
- Monte-Carlo Simulation estimates are very similar to delta-normal results, indicating robustness to method.
- Slight differences between methods attributed to deviations from normality of portfolio returns:
  - Delta-normal assumes normality.
  - Monte-Carlo drops normality assumption; differences reflect how returns deviate from normality.
- For each issuer, inclusion of Sukuk improves portfolio VaR:
  - Monte-Carlo reductions: Malaysia 11%, Pakistan 15%, Qatar 18%, Bahrain 32%.
- For all issuers, VaR of portfolio of only conventional bonds is statistically different from VaR of portfolio of conventional bonds and Sukuk together (estimation errors indicate statistical difference).

### Conclusions and policy-relevant findings
- Evidence indicates Sukuk are different instruments than conventional bonds as shown by different price behavior.
- Diversification by including Sukuk in an issuer’s bond portfolio can significantly reduce portfolio VaR compared to investing only in conventional bonds of that issuer.
- Correlations:
  - Correlations of Sukuk returns with returns on conventional bonds are much smaller than correlations among conventional bonds themselves.
  - If an instrument is not perfectly correlated with other assets, reduction in VaR is expected.
  - Example: Bahrain — Sukuk and conventional bonds have similar durations, yet correlation of returns is close to zero.
- Reduced VaR arises partly from:
  - Diversification by adding another instrument with different duration.
  - Distinct secondary market price behavior of Sukuk compared to conventional bonds.

### Limitations and cautions
- Possible gains from diversification must be weighed against:
  - Lower return of Sukuk (most of the time Sukuk offer lower returns compared to conventional bonds).
  - Liquidity risk: Sukuk are illiquid compared to conventional bonds (lack of secondary market activity).
- Illiquidity can impose more risk during volatility; the study mitigates this by using weekly data, but:
  - A more rigorous treatment of illiquidity effects on Sukuk prices and premiums is desirable.
  - Volatility measured reflects volatility on trade days, not necessarily true underlying price volatility.
- Given data limitations, results are not conclusive but contribute to debate on issuance of Sukuk as alternative investment/financing instruments.

### Appendix I — Monte Carlo simulation algorithm (single-asset and multi-asset)
- Single asset procedure:
  - Price evolution follows geometric Brownian motion:
    - P_{t+Δt} = P_t + μ P_t Δt + σ P_t Δt Z_t  (equation (3) in source)
    - μ and σ are mean and standard deviation of returns over a holding period.
    - Z_t is a standard normal shock.
    - Holding period divided into T intervals of size Δt (usually Δt = 1/100 in practice).
  - Starting from P_t, draw random Z_t and apply equation (3) to construct a path of prices  p_{t+1}, ..., p_{t+T}.
  - Repeat many times (e.g., 10,000) to obtain distribution of next period prices.
  - VaR is the 1% or 5% lowest simulated price (or return).
- Multiple asset procedure:
  - Each asset i evolves by its own Brownian motion (see equation (4) in source).
  - Random numbers Z_{1t}, Z_{2t}, ..., Z_{Nt} may be correlated; correlation pattern equals correlation matrix of asset returns.
  - Construct correlated random numbers via Cholesky factorization of the variance-covariance matrix of asset returns.
    - Cholesky factorization: R = H H', where R is symmetric real correlation matrix and H is lower triangular.
    - Starting from iid vector η with unit variance, construct Z = H η; covariance matrix of Z is R.
  - Use correlated Z_t to simulate price paths for all assets, obtain portfolio price as weighted sum, repeat 10,000 times, compute VaR as 1% or 5% lowest portfolio price (or return).

### Appendix II — variance-covariance matrix of weekly returns (selected entries as presented)
- Malaysia (variance-covariance entries shown in scientific notation):
  - Sukuk variance: 6.12E-06
  - Sukuk with Bond 1 covariance: 2.45E-06
  - Bond 1 variance: 1.56E-05
  - Bond 2 covariance entries: 2.03E-06, 9.50E-06, 1.01E-05 (as positioned in the matrix)
- Qatar:
  - Sukuk variance: 2.41E-06
  - Bond 1 variance: 5.65E-05
  - Bond 2 variance: 3.71E-06
  - Covariance entries include -4.00E-07 and -1.30E-07 in positions shown
- Pakistan:
  - Sukuk variance: 2.71E-05
  - Bond 1 variance: 7.80E-06
  - Bond 2 variance: 9.50E-06
  - Bond 3 variance: 1.18E-04
  - Selected covariances: 1.12E-08, 1.30E-07, 7.10E-06, -1.24E-05, 7.30E-06, 9.39E-5, 1.70E-04 (as positioned in matrix)
- Bahrain:
  - Sukuk variance: 4.66E-08
  - Bond 1 variance/covariance entries include 3.60E-06 and other positions shown
- (Full variance-covariance matrix presented in Appendix II of the source.)

*Source: Appendix I and associated sections of the IMF working paper content unit provided.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp07237.pdf_