Shariah Compliant Profit Rate Swap

Similar in spirit to the Shariah-Compliant Swap using wa'ad (see Shariah Compliant Swap: Shariah "conversion" or subversion?, we present here some detailed papers on the Profit Rate Swap (PRS). The essential ingredients are parallel Murabahas.

In fact this first paper from Allen & Overy goes into some detail on the individual legs of the swap (the individual Murabahas/rolling murabahas).

The idea is simple enough:

• For the floating leg, we are allowed Murabahas with markups linked to LIBOR. We can enter into consecutive Murabahas on a rolling basis, with Wa'd to enter into Murabaha at the market price + market determined LIBOR to make for rolling Murabahas.
• For the exotic leg, some scholars would allow the linkage of the Profit Rate of the Murabaha to be almost anything so long as it is determined as of the time of entering into the Murabaha. So range accruals (i.e., the profit rate is LIBOR + X accruing times the number of days LIBOR is in between LowerBound and UpperBound) and almost any exotic payoff can be used as a markup so long as it is set at the time the Murabaha is entered into.

Allen & Overy's paper on Profit Rate Swaps


NOTES:

1. This not a typical exotic swap and in this case the exotic leg has a delayed payment. The typical structure for a range accrual is to pay periodically (say every 3M) LIBOR(t)+X% times the number of days LIBOR(t) is between LowerBound and UpperBound, for t between 0 and 3M, with payment made at t=3M. In the PRS version, t=3M is the first date that the coupon (oops, profit markup) is known with complete certainty and is then the date at which the Murabaha is entered into with payment of this markup at t=6M. This delay is nonstandard in the exotic world but is really only a small matter for traders/structurers/clients.
2. Sh Yusuf DeLorenzo's bjections to DB's "Shariah Conversion Technology" (link here) apply equally well to this structure. Can we asset swap Pork Bellies for LIBOR using Murabahas and make it all seem Shariah Compliant?
   

Further References

• Nathalie Schoon, Islamic Banking & Finance, (section on Murabaha + Wa'ad PRS)
• Allen & Overy on Cross Currency Swaps
• Azmi Law on Islamic Swaps in Malaysia
• Derivatives Week, article on Islamic CDS (short on details)
  

Shariah Compliant Profit Rate Swap

Case Study: Bank Runs in Turkey

This paper is presented in Topics in Middle Eastern and North African Economies (electronic journal, Volume 7, Middle East Economic Association and Loyola University Chicago, September, 2005). While the focus is on the behavioral aspects of bank runs (consumer over-reaction, information asymmetries, self-fulfilling elements, etc.) the authors also make a very interesting comparative analysis of the balance sheets of conventional banks versus Special Finance Houses (i.e. Islamic Financial Institutions in Turkey). The concluding remarks are focused on the benefits of deposit insurance, but the overall piece brings a refreshing view - one that is in stark contrast to claims of Islamic bank's "immunity." It would seem the most important behavior of consumers is their short-term memory!

Bank Runs in Emerging-Market Countries:

The Experience of Turkey’s Islamic Banks in the 2001 Crisis
Martha Starr, American University
Rasim Yilmaz, Dumlupinar University

Abstract: "This paper examines a set of runs on Turkey’s Special Finance Houses, an uninsured sub-sector of Islamic banks, during the 2001 financial crisis. We argue that, although fundamental factors were influential in initiating the runs, the magnitude of withdrawals from the SFHs was out of proportion with the risk, suggesting overreaction."

Case Study: Bank Runs in Turkey

Opalesque Islamic Finance Intelligence

Opalesque launches Islamic Finance Intelligence as industry faces great debates in a number of fronts

Setting a new standard: 19 pages of intelligence.

Welcome to the first issue of Opalesque Islamic Finance Intelligence (OIFI), designed with a practitioner approach – focused on precise and relevant content for investors, product manufacturers, and fund managers of this truly global community. This free, monthly publication complements Opalesque Islamic Finance Briefing (our daily industry news briefing) and leverages on the success of the Opalesque family of specialized publications (Alternative Market Briefing, A Square, Roundtable Series, etc).

The industry faces great debates in a number of fronts – from market gaps, distribution networks, standardisation initiatives, risk & compliance concerns, to structural question marks. These issues are faced by both current industry players as well as new entrants. A case in point is the recent debate over Tawarruq, with Nikan scrutinizing the matter in our Featured Structure section.

The range of topics is vast - Islamic finance products now extend to all asset classes (from exchange traded funds to private equity vehicles), the industry is ever-evolving in its core markets (the GCC and Southeast Asia) and product cross-pollination with conventional fund houses is an emerging trend. Our maiden edition further provides an overview of Islamic contract law - detailed by Khalil in our Editorial Column. We also debate over the outputs of the transaction: practitioners share their thoughts in our Discussion Forum on the use of conventional benchmarks (i.e. LIBOR) by Islamic banks, whilst Toby Birch of Birch Assets Ltd scrutinizes the industry pitfalls in our Allocator Interview.

Market awareness has skyrocketed in recent years - experts once touted the existence of 60 Islamic equity funds whereas the industry now boasts a universe of well over 700 Shariah compliant investment products. Growth projections usually land between 15 to 20 percent per annum, yet some of the largest Muslim countries (i.e. Indonesia, Egypt and India) remain untapped. A comprehensive product range is unheard of (in stark contrast to the conventional world), yet this bestows the industry with endless prospects. Bernardo sheds light on these by analyzing Islamic fund of funds in our Industry Tables section.

Opalesque Islamic Finance Intelligence is a free subscription- new readers can register here and make your choice from our menue of eleven specialized publications. (Note that while most of our publications are free, we also offer three premium/paid publications).

Download the first Opalesque Islamic Finance Intelligence issue here!


(Sorry for the Marketing Spiel, but we wrote it and its free).

Comments, as always, are welcome! JAK!

Opalesque Islamic Finance Intelligence

Scholars call for Shariah board under Central Bank

Lets all discuss the following points: Dr. Abozaid pointed out that there is currently a lack of a centralised control on Islamic banking products. Some products that are cleared as "Islamic" are sometimes controversial.

Until such time a central board is created, measures must be undertaken to ensure that the salaries of Shariah board members do not come from their individual retaining banks, but from a central pool. This would ensure neutrality, transparency and above-board decision-making, experts pointed out.

Scholars call for Shariah board under Central Bank
Emirates Business 24/7
By Eman Al Baik

Scholars call for Shariah board under Central Bank

Shariah Compliant Swap III: Shariah "conversion" or subversion?

Following our previous postings on DB's Shariah Compliant Swap, (here and here), we follow up with the last of our postings on the marked and unusual (note we do not say unwarranted) criticism of this structure.
The Criticism

"I believe that due consideration must be given to not only the literal structure of products and processes, but also to their consequences for the future of Islamic Finance. In other words, while up until now the Shariah supervisory boards of modern Islamic financial institutions have focused almost exclusively on the rules for transacting in compliance with the Shariah, it is now time for them to focus as well on the higher purposes of Islamic law or the maqasid al-Shari`ah."

Yusuf Talal DeLorenzo, The Total Returns Swap and the "Shariah Conversion Technology" Stratagem


Rather than evoke Sadd-al-Dharra'i (prohibition of legitimate means to illigitimate ends), Sh.Yusuf goes into some detail on tracing the cashflows. Unlike LIBOR based products where the LIBOR-linked return is merely the market-cost of capital or fair returns for investments, he shows this product actually enables cashflows for investment in haram activities. Were it not for the Islamic investor's cash, the haram activities would not be invested in. This is very astute, since it is clear that cash and profits flow from the Islamic investor to pork bellies, alcohol, any sort of wierd hedge fund or derivative, etc.

Moreover, Sh.Yusuf explains why Sadd-al-Dharra'i is inapplicable. Rather it can be applied in cases where illicit activities are a probable outcome of any set of halal actions. Then it can be invoked to rule out such action. In this case, the illicit activities occur with absolute certainty and since whatever is required to ensure the performance of a required act is itself required
(لا يتم الواجب إلا به فهو واجب ) and it is required to abstain from illicit acts and thus to abstain from combinations of legal acts that result in illicit activities.

Sh. Yusuf calls the fatwa that supports this the Doomsday Fatwa for Islamic Finance. Why? Because he rights states that doing this swap is easier than going through all the effort of true-sales and lease-backs and SPVs for all the sukuk out there, so why bother? It's just plain cheaper to operate in the conventional space, and then Shariah-wrap (swap) it. It makes all the effort of the past 30+ years for nothing.

This paper does raise the question of the legitimacy of rolling murabahas as a means of synthesizing structured products or the Shariah Compliant Profit Rate Swaps (PRS). LIBOR may be a cost of capital but the payoff of a commodity-linked range accrual requires hedging using commodity options, and again an Islamic Investor is setting off the action that links his cash to haram investments.

Does Islamic Finance run the risk of turning into pure legalistic formalism? In some ways this structure reminds me of the case of Observant Jews on the Sabbath who get a Gentile to light a fire for them and at least in that case there is the benefit of not freezing to death on a cold winter's night.

So what benefit can Islamically "wrapped" pork-bellies give? Do we actually believe in the prohibition on riba or are we just unduly burdened by it? How about the prohibition on Maysir? On other haram investments? What exactly do we believe in?

Stepping Back: Listing Some of the Merits
Is there merit in this structure? The answer should be yes. The criticism cannot be levied at the structure itself--rather the overreachingness of the fatwa.

Sh Yusuf's article does not indicate that he considers the structure itself to be distasteful. It is the use that can be questioned. If, on the other hand, the structure is applied to "compliant" activities, e.g.,

• Cross Currency Swaps
• Fixed for Floating (to reduce/increase duration of liabilities/assets)
  
• Other hedging where all underlyings are halal (e.g., an Islamic Fund Manager pays DJIM to reduce beta, and receives cash--LIBOR instead, etc).

then the criticism is null.

Shariah Compliant Swap III: Shariah "conversion" or subversion?

Islamic Microfinance Report - IDLO

A rather recent report (February 2009) authored by Allen & Overy giving an overview of Islamic microfinance for the International Development Law Organisation (IDLO), with an interesting review of microfinance initiatives across the Middle East and Southeast Asia (from Pakistan all the way to Indonesia). The report goes on to provide a review of basic Islamic law principles governing the provision of Islamic finance products and services (including a brief anlaysis of "Defaulting on Personal Debt in the United Arab Emirates and Saudi Arabia").

Islamic Microfinance Report - IDLO

Allen & Overy LLP

International Development Law Organisation (IDLO)

February 2009

Islamic Microfinance Report - IDLO

Shariah Compliant Swap II: Shariah "conversion" or subversion?

Following up on our first post on DB's Shariah Compliant Swap, we continue our discussion with details of the transaction, which apparently has been used by DIB to offer principal protected investments in some GSAM hedge fund (with GSAM it is a very lucky thing that the principal was protected!) (see article here). This has resulted in some sort of backlash (please see article here).

Although DB's is just one of the many platforms being developed for the rapid issuance of new structured product, the question is whether DB's method (and perhaps some of the others) may be a step too far?

The Structure
A total return swap (the performance of a Shariah compliant asset A swapped for the performance of a non-Shariah compliant asset B) can be split into two outperformance options.

• Party A (doing the investment in asset X - a shariah-compliant SICAV/Mutual fund) writes an outperformance option, giving the outperformance of asset X compared to asset Y to Party B - the primary DB entity

• Party B writes an outperformance option giving the outperformance of asset Y compared to asset X to Party A
  

then this combination is the same economic result as a total return swap.

A wa’d (structured as a deed) seems natural in this structure. But, in order to be both compliant and binding but without a set price, cannot be bilateral or be offered for consideration. Therefore, we need a third Party.

We now name them DB I and DB II (the "pass-through" entity, related by control to DB I)--the two subtle little blue boxes in the diagram above, I with an arrow going into it, II with an arrow going out of it-- whereby

• Customer writes an outperformance option to DBI (read: gives a promise to DBI ).
  
• DBI writes an outperformance option to DBII
• DBII assigns or transfers this same option to Customer (so Inv Bank II is in effect just a "pass-through" vehicle for Customer and has no resulting position except for a credit risk on DB II).
  

Restating the above

The cash received by issuing certificates to a client will be:

• Shares selected from DJIM (primary investment structure) or shares that qualify applying the same screening as used by DJ to obtain their Islamic universe.

The Investor will also enter into the following agreements on an at arm’s length basis:

1. Wa’d 1 agreement whereby the Investor promises unilaterally to DBI to sell a basket of above mentioned Shariah shares at a predefined Settlement Price
2. Wa’d 2 agreement whereby DBII, promises unilaterally to the Investor to buy the Basket at the Settlement Price.
   
3. (Wa'd 3 agreement between DBI and DBII is their own business)

The Settlement Price is determined using familiar mechanics of asset swaps. Please see the original posting to the white paper in order to have all payoff formulas and little actual explanation.

The Economic Effect

The economic effect of the above structure is as follows:

• Scenario I: The value of the Basket goes up more than the Index:-
  

In this case, DBI can purchase the Shares from the Investors at a price lower than the market value for such Shares at that time. DBI would hold the Investor to its promise given under Wa’d I.

The Investor will not be interested in holding DBII to its promise given under Promise 2 as selling a Basket of Shares at a value which is lower than the market value at that time would incur a loss.

• Scenario II: The value of the Basket goes up less than the Index:-

In this case, DBI can purchase the Shares from the Investor at a price higher than the market value for such Shares at that time. However, as this would incur additional expense, DBI will not hold the Investor to its promise given under Promise 1.

The Investor, on the other hand, will be interested in holding DBII to its promise given under Promise 2, as it can then sell the Shares in the relevant Basket at a value higher than the then market value for such Shares at that time.

In both Scenario I and Scenario II noted above, the Investor will sell its Basket to either DBI or DBII in return for a price as determined on the basis of the performance of an Index.

Disadvantages

• need of use of third party
• synthetic long position via Investor on Shariah compliant assets that needs to be offset via shorting (by DB)
• perception of the market that a swap cannot be made Shariah compliant

Although there are such disadvantages, it is a more cost effective structure than most murabaha-based derivatives. In fact the running costs are on the order of 10-40bp per annum. It is perhaps this cost savings combined with the rather questionable nature of this structure, the ability to offer Shariah Compliant Pork Bellies (i.e., 'completing the market' in financial lingo), that lead Sh Yusuf Talal de Lorenzo to state that the fatwa backing this was more aptly called the "Doomsday Fatwa for Islamic Banking". Or paraphrasing Sh Yusuf, why would we ever go through the trouble of structuring a sukuk through true sale or figuring offset to devise call options, or actually use commodities in murabaha transactions if we could instead just do a conventional deal and Islamically-wrap it?

Stay tuned for more posts on DB's Shariah Conversion Technology.

Next post: Criticisms.

Shariah Compliant Swap II: Shariah "conversion" or subversion?

A Comparative Literature Survey of Islamic Finance and Banking

This article comes from the archives of the Microfinance Gateway, it is an introductory paper but one that covers a wide range of metrics and would prove useful as an introductory reading (and a good measure of how much the industry has changed over the past decade). A brief summary is provided as well:

How can Islamic financial markets be helped grow? With Muslims comprising about 27 percent of the world population, Islamic finance is a growing niche set to reach new levels of sophistication. However, Islamic finance with identifiable products and markets is in its infancy, and many problems and challenges related to Islamic financial instruments, markets, and regulations must be addressed and resolved. This paper provides a comprehensive review of the literature of the Islamic finance as well as introduces Islamic financial instruments in order to compare them with those existing in other parts of the world. It also discusses the legal problems that investors in Islamic financial instruments encounter.

As the paper assesses the performance of the Islamic banking and financial sector and highlights the regulations, current challenges, and bottlenecks, it concludes that:

• The lack of developed markets in which Islamic financial instruments can be traded is one of the problems caused by the lack of cooperation among Muslim financial institutions;
• The further growth and development of the Islamic financial system will depend largely on the nature of innovations introduced in the market;
• The Islamic financial system can offer alternatives at the microfinance level;
• A well-developed Islamic financial system can play a vital role in the economic development of Islamic and non-Islamic countries by mobilizing dormant savings and facilitating the development of capital markets.

A Comparative Literature Survey of Islamic Finance and Banking
Tarek S. Zaher & M. Kabir Hassan
Indiana State University, Terre Haute, Indiana, University of New Orleans, Louisiana

A Comparative Literature Survey of Islamic Finance and Banking

CSR Disclosure in Malaysian Companies

We had earlier touched on the crossroads of ethical and Islamic finance in our earlier discussions and on the paper by Zubai Hasan relating to Sustainable Development from an Islamic Perspective. Another paper - also from the International Islamic University of Malasyia - delves into CSR Disclosure in Malaysian Companies, as it scrutinizes the type of information that comes under the banner of ethical or responsible behaviour. The paper does not especifically address Islamic finance or the Shariah compliance of the corporates which are under scrutiny; Nevertheless, it is very poignant in exploring the pitfalls of SRI/CSR (plenty of acronyms to choose from). It is especially critical as it relates to how profound and/or superficial these labels really are in the context of the modern politically-correct corporate culture:

"Findings from the study suggest that the disclosures have a public-relations bias, with a very general, ‘good news’ type of disclosures being the norm. Consistent with prior studies in other developing countries, quantitative or monetary disclosures, as well as ‘bad news’ disclosures are minimal."

CSR Disclosure in Malaysian Companies

Derivatives in Islamic Finance

Derivatives in Islamic Finance
Dr. Sherin Kunhibava, Researcher, ISRA
ISRA Research Paper (No. 7/2010)

"The main objective of this paper is to review the use and status of derivatives in Islamic finance. This is done by first explaining the basic derivative contracts of forwards, futures, options and swaps. Thereafter, the discussion turns to the use of derivatives with sukuk. The paper then explores the debate between scholars on the admissibility or otherwise of forwards, futures and options in Islamic finance. It then examines contracts in Islamic finance that have derivative-like features and which can be used for the same purposes of hedging as forwards, futures, options and swaps. It concludes by highlighting areas for future research."

Derivatives in Islamic Finance

Shariah Compliant Swap I: Shariah "conversion" or subversion?

We will stretch this topic over a few posts since there are numerous components to discuss, initially we detail the justification of Deutsche Bank for their Islamic swap product (a major developer and promoter of this instrument), later going over the structure in much more detail, and finally the criticisms that this solution has received from other industry participants.

The Shariah Justification
The structure is discussed (to a limited extent) in DB's now famous White Paper. In fact the white paper, whether you agree with the product or not is a toure de force. It is probably the best single article on the rationale for Wa'd to be legally binding.

The paper has two main arguments

1. Wa'd must be legally binding. The arguments involve maqasid, principles of commutative justice (derived from the thesis of Dr Hussein Hassan--sorry copyright prevents posting pdf), and is probably the best single source for this sort of argument.
2. Pricing of Islamic Contracts can be determined at the time of execution (see, e.g., Bay' bi Sirr al Suqq/Istijrar Revisited) and when indexed, markups need not be related to halal activities, e.g., LIBOR itself (and examples are given from Taqi Usmani's allowance of Murabaha markups related to many other more-complex payoffs).

Notably missing from their discussion are:

1. Should consideration be permissible in a wa'd? Can you pay for a wa'd?
2. Can bilateral wa'd (muwa'adah) be allowed? (Most jurists would disagree with this as a means of circumventing prohibitions on forward-starting contracts).
3. Should wa'd be legally enforceable only if there is detrimental reliance on the part of the promissee? (Maliki view). Is Wa'd the same a Promissory Estoppel?
4. Actual details of the structure of Shariah Compliant Swaps

Wa'd: Shariah-Specific Details
Wa'd, or unilateral promise has the following features/restrictions

1. Consideration is not permissible with Wa'ad. You cannot pay for a promise. (we will find an striking exception to this permitted by some scholars with Promissory Notes!)
2. Bilateral wa'd (muwa'adah) is not allowed. (Most jurists would disagree with this as a means of circumventing prohibitions on forward-starting contracts). (Note: We have already seen exceptions to this with Short-Sales Contracts using Muwa'adah)
3. Is wa'd legally enforceable only if there is detrimental reliance on the part of the promissee? (Maliki view). Is Wa'd the same a Promissory Estoppel? (this is dismissed and rather it is claimed Wa'd should be legally, not just morally upheld even if there are no damages).

For more on wa'd and on the wa'd swap, please see the following:

• al Masri, R, The Binding Unilateral Promise (wa’d) in Islamic Banking Operations: Is it Permissible for a Unilateral Promise (wa’d) to be Binding as an Alternative to a Proscribed Contract?
  
• Nurdianawati Abdullah, The Status of Wa’ad and its Implications in Contemporary Islamic Banking
  
• Aznan Hassan, Pengertian Al-Wa’ad, Al-Wa’dan Dan Al-Muwa’adah (dalam Bahasa Melayu)
• Islamic laws of Contract and Sale and purchase, Iqra University (pp 14-16)
  
• Vogel & Hayes, Islamic Law and Finance: Religion, Risk & Return (pp 125-8)
• Islamic Bankers Blog: Is Wa'ad the Next Star of Islamic Banking
• Barakat & Mehrej: The Structure and Use of Wa'ad
  
• Humayon Dar, Islamic Economist, Sharia Advisor and Transformational Thinker (for details of his seminal input from the man, the myth, the legend)
  
• Humayon Dar, Incentive Compatibility of Islamic Financing, Handbook of Islamic Finance, pp 85-96 (for a very western critique of Islamic contracts as not being "incentive compatible" except for the amazing Wa'ad swap, a matter of much possible disagreement. One might even say Islamic Finance in its current incarnation, just plain sucks according to Humayon. (sorry Humayon, but it really does sound like that!). Perhaps we can ask Mahmoud El-Gamal to critique the view that the Wa'd swap is doing a great service to Islam by allowing access to all these amazing products?)

Note that with this amazing swap, anything and everything is possible. As one Belgian banker said with excitement, "yes, it is possible to have Shariah Compliant pork bellies" (Astaghfirullah!).

For the pious, this should already raise red flags. And, presumably this should have raised red flags for the Structurers, for the Shariah board (the esteemed Dr Hussein Hamed Hassan, Dr Ali al Qaradaghi, Dr Abdul Sattar Abu Ghuddah, Dr Mohamed Elgari, and Dr Mohammed Daud Bakar) and for the Investors (which were terribly slow to take it up, and now are a bit hush-hush about it, but we suspect these include some large name public hedge funds, and DIB has been documented) .

Just given the controversial nature of this Islamic "wrapper" there is much more Shariah risk, including the risk of a change of heart of a scholar (please see: Global Islamic Funds & Sukuk, Linked In Discussion on this topic).

Please stay tuned for more details on the Shariah Compliant Swap, and the Criticisms. We will also detail other methods for constructing Shariah Compliant PRS (Profit Rate Swaps) in later posts, InshAllah.

Shariah Compliant Swap I: Shariah "conversion" or subversion?

Ernst & Young - Islamic Funds & Investments Report

Islamic Funds & Investments Report 2009

Here is the latest report from Ernst & Young on Shariah compliant investment funds (please follow the link to their site). Worth checking their breakdown of market sizing (individuals, insitutional, quasi institutional, etc) as well as their analysis on existing/evolving asset manager business models. This goes hand in hand with their global Takaful reports.

Ernst & Young - Islamic Funds & Investments Report

Islamic Banks and Financial Stability: An Empirical Analysis

We kickoff this month with a variety of empirical studies on Islamic finance, complementing theoretical discourse with hard facts & figures. The following working paper arrives from the IMF, scrutinizing the impact that Islamic banks have on financial stability. A very noteworthy finding is that small Islamic banks are more stable than their larger counterparts. This raises the question of whether the "mega Islamic bank" concept being touted around is actually valid! The authors argue that "as the scale of the banking operation grows, monitoring of credit risk becomes rapidly much more complex. That results in a greater prominence of problems relating to adverse selection and moral hazard [for large Islamic banks]. Another explanation is that small banks concentrate on low-risk investments and fee income, while large banks do more PLS [Profit-and-Loss Sharing] business". This further raises the issue of how robust is the risk management system of IFI's and how different should it be from that of conventional banks which focus on other metrics - such as PD (probability of default) and LGD (loss given default).

Islamic Banks and Financial Stability: An Empirical Analysis
Martin Čihák and Heiko Hesse
IMF Working Paper
Monetary and Capital Markets Department

Abstract: "We find that (i) small Islamic banks tend to be financially stronger than small commercial banks; (ii) large commercial banks tend to be financially stronger
than large Islamic banks; and (iii) small Islamic banks tend to be financially stronger than large Islamic banks, which may reflect challenges of credit risk management in large Islamic banks. We also find that the market share of Islamic banks does not have a significant impact on the financial strength of other banks."

- The paper is also discussed in the May 2008 edition of the IMF Survey Magazine.
- PWC has a further discussion on this topic within their Islamic finance blog.

Islamic Banks and Financial Stability: An Empirical Analysis