Table of Contents
2. Structured Product
2.1. Evolution of Structured Products
2.2. Developments in the market
2.3. Global Market Comparisons
3. Literature Review
4. Problem Description
5. Research question and Hypothesis
6. Theoretical Frame of Reference and Methodology
6.1. Valuation of Structured Products
6.2. Valuation of Bonds
6.3 Valuation of Options
6.3.1 The Black and Scholes Model
6.4 Advantages and Disadvantages of Black and Scholes Model
6.5 Barrier Options
6.7. Estimation of Volatility from Historical Data
6.8. Price Index
6.9. Return Index
6.10. Dividend yield
6.11. Yield Curves
6.12. Continuous compounding formula
7. Data Set
7.1.1 Types of instruments used in the empirical study
7.2 Valuation of Structured Products (Synthetic Instruments)
7.3 Formulas used to calculate the return of synthetic instruments
8. Descriptive Statistics and Results
8.1 Returns Vs Sharpe Ratio
9. Summary and Conclusions
9.1 Comparing and contrasting with the present academic literature
9.2 Limitations and future research
Lack of knowledge and high transaction costs makes it difficult for private investors to follow the investment strategies that structured products offer. The institution wants to be compensated for the pricing of these instruments because it offers these products through their economies of scale. As there is lack of competition and transparency, a question arises here whether issuing institutions are giving fair quotes to the investors to purchase these products. According to the investor’s perspective it is significant for him to form an opinion on whether the pricing of these products can be deemed to be fair. As no previous study has been conducted in the UK market for structured products, it will be useful to see pricing and back testing of these structured products issued in the United Kingdom market.
The purpose of this thesis is to perform pricing of three hybrid instruments issued by Goldman Sachs investment bank and National Saving and Investments and perform back testing on these instruments by comparing the returns of the synthetic instrument with the returns of the Treasury bond, FTSE 100 index and the actual instrument. The pricing and back testing will be calculated based on the following criteria:
1. The period considered for the analysis is between 31st December 1984 and 29th June 2007.
2. FTSE 100 is the underlying index.
3. Three hybrid instruments are selected. Two issued by Goldman Sachs investment bank and one issued by National Savings and Investment (NS&I).
2. Structured Product
A structured product is a hybrid instrument that is comprised of at least two financial components. They are composed of building blocks that can be identified as equity and debt. The equity component of the product is equivalent to a long term option and the debt component is equivalent to a bond.
We can divide the structured products into capital guarantee products and products that offer no capital guarantee. The products with capital guarantee ensure repayment of the formerly agreed portion of the capital whilst at the same point in time make it possible for investors to have some form of participation in the underlying instrument trends.
The structured products that have no capital guarantee give the investors a prospect to attain an attractive maximum return, but have no guarantee that the capital would be paid back to them. Products that offer no capital guarantee can be further classified into products with coupon payments, products without coupon payments and products that have exotic characteristics. All structured products consist of an underlying. For example at the time of maturity the price of the underlying instrument is less than or equal to the strike price, the total sum that will be paid to the investors will equal the strike price; else they will get back the underlying instrument.
The products that consist of coupon payments have similar repayments, except that a coupon is paid out for the compounded discount amount instead of the discount. The products that consist of exotic characteristics exist in different shapes. The main difference between products with exotic characteristics is that they contain an exotic option rather than j]ust a standard one that makes the pricing for these instruments complex. For example a way of customizing the payoff of an investor is to add an Asian or a Barrier option to the product rather than opting for a plain vanilla option.
This study will mainly focus on pricing and back testing of three structured products, two issued by Goldman Sachs investment bank and one issued by National Savings and Investment(NS&I). We will calculate the returns for each product and then compare the
returns with the returns of the FTSE 100 index, UK Treasury Bond and the synthetic instrument.
2.1. Evolution of Structured Products
Structured products became popular in the U.S. during 1980s and in Europe and UK in the 1990’s largely due to the low interest rates that these products introduced. The base of the structured product, the zero coupon bond was introduced in the U.S. by J.C. Penny Company, Inc. in the year 1981. In the U.K. however the establishment of the London International Financial Exchange (LIFFE) bought about the first shift towards the introduction of structured products.
A market for financial derivatives and options was created that allowed the buyers to take advantage of stock market movements without being exposed towards the stock market themselves. The first of such products to be launched were the guaranteed equity bonds that debuted in 1991. Between 2002 and 2003 another form of structured investment came to the limelight known as ‘precipice bonds’. Although these instruments promised bigger returns in rising markets and offered superior market participation, they provided a very low safety net if the markets fell and also cost of a harsh downside penalty. The markets did slide, and many bondholders found themselves bearing a 2% drop in their investment for every 1% of market fall (Trustnet, 2007). Due to above reasons it is very rare that we get to see precipice bonds.
2.2. Developments in the market
For the past two decades there has been a strong global growth for structured products. Many observers feel that the recent growth for structured products is due to the interest rates that are very low worldwide and there is a difficulty amongst private investors who access some part of the traditional markets such as commodities.
Traditional instruments cannot offer features that structured products can. Some of the features include providing diversification, principal protection and tailored payoffs. In the early 90’s when structured products were introduced to high net-worth individuals there was a value proposition that was set on potential for enhanced performance, innovation and access to capital markets. The structured products market since this period has gone through several changes. A wider range of standardized products has been introduced and the number of private investors using these products have increased significantly. This is apparent in the UK, Europe and Asian markets which will see in detail in the next section.
There have been several studies conducted in the past on the pricing of structured products in the Europe and US markets. This report mainly examines pricing and back testing of structured products within the UK market. We examine three different structured products. The underlying can be an index or a basket. The underlying considered for this study is the FTSE 100 index and all the products are issued under this index. For pricing in this study we choose indices over baskets because the baskets are just not the price itself, it is the correlation between different stocks. This makes the analysis more complex.
In this study we find that for the G950 product it is better for the investor to invest in the product directly as it gives him better returns as compared to investing in the 1.5 year treasury bond Vs FTSE 100 Vs Synthetic Instrument. In the case of comparison with the G994 product, the investment in the FTSE 100 gives greater returns. Last but not the least for the NS&I instrument we find that the investor gets high returns by investing in the synthetic instrument itself.
The rest of the report is organized in the following manner. The literature review is dealt within section 3, the problem description is covered in section 4 followed by the hypothesis and research question in section 5. Section 6 discusses the methodology followed by section 7 which discusses the data set. Section 8 documents descriptive statistics and the results obtained. Section 9 finally summarizes and concludes the whole report.
2.3. Global Market Comparisons
In 1990 the first retail structured investment products began appearing in the UK market. The market however developed very slowly initially.
Majority of the structured products in the UK were capital protected products and it was in the year 1996 that sales of income products took a significant share of the market. The use of gearing to provide high levels of income but with limited risk capital was a key development. A typical product would provide a 10% annual income and a full return of capital if the Index does not fall. A 5% fall would reduce the amount returned by 50% although any further fall would not have any impact.
The UK investment environment by 2002 had become part of the mainstream and now had matured into a significant feature of the UK savings market. There were over 300 individual products launched in the UK market during 2002 which was nearly 20% greater than the previous year and almost 70 different providers issued these products. This trend has continued until 2005 and is expected to continue for the forth coming years.
The chart below shows the sales figures (in GBP millions) for retail structured products in the UK market over the last decade.
Fig 1: Growth of structured products market
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The graph shows that the sales figure over the last decade grew exponentially from one billion GBP to six billion GBP.
The graph below shows us the steady growth of the retail structured products sales in Euro millions in countries like France, Spain and Italy since 2000.
Fig 2: Structured Products in the European Market
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Other active markets in Europe include Sweden, Norway, Belgium and Switzerland.
Although the retail structured product market in Asia is currently expanding to new levels, Asia-Pacific is still lagging behind.
With relation to structured products the regulatory environment in Asian markets such as India, China, Hong Kong and Taiwan are changing in a positive way and a strong growth forecast is predicted in these markets.
3. Literature Review
This section details prior research that was carried out in the areas of pricing and back testing of structured products within the European and US markets. Little emphasis was paid to structured products in the literature although they have emerged in the US market in 1987. There have been only a handful of investigations in the US concerning valuation of structured products, all of which go back to a time when these products were first launched (Wohlwend et al, 2003).
Market Index Certificates
There was an investigation done for Market Index Certificates of Deposit (MICD) by Chen and Kensinger (1990). These certificates of deposit offered a variable interest rate and a guaranteed minimum interest rate when tied to the growth of the S&P 500 index.
In their sample they included 25 of these products in January 1989 and 18 in January 1988. These products were issued by Murray Savings and Chase Manhattan. The authors reveal significant positive and negative differences between market and theoretical values by making a comparison of the implied volatility of the embedded MICDs with the implied volatility of the S&P 500 option.
Chen and Kensinger (1990) find inconsistencies in the pricing of MICDs of different types and different maturities offered by the same issuer (Wilkens et al, 2000).
The Salomon Brothers issued the “S&P 500 Index Note” (SPIN). Chen and Sears (1990) made an analysis on this note. The SPIN has a 2% coupon bond and a maturity of four years that pays the holder:
1. The accrued interest and the principal amount.
2. The excess of the index value of the S&P 500 over the initial value of the index times a multiplier that is predetermined. It is a combination of a long- term plain vanilla call option on the S&P 500 index and a low coupon bond.
Chen and Sears (1990) analyze differences between theoretical and market prices using long-term and average implied volatilities that were ex-post over three sub-periods in the lifecycle of the product spanning from September 1986 upto December 1987.
In the first sub period they find an overpricing of approximately 5% whereas the product was underpriced in the second and third sub periods. The market was going through a learning process as suggested by Sears and Chen in pricing this unique and new type of security (Chen and Sears, 1990)
Products with no principal protection
There was a study conducted by Chen and Chen (1995) on the valuation of structured products on the secondary market with no principal protection and offering investors high interest payments in exchange for a cap on the underlying stock’s growth. The authors find persistent evidence that the product is overvalued at some 5 percent (Grunbichler et al, 2003).
Discount Certificates and Reverse Convertibles
Wilkens, Röder, and Erner (2003) carried out a study on structured products in the European market and analysed 906 structured products that linked to the stock indexes NEMAX (high-tech segment) and DAX in Germany. Discount certificates and reverse convertibles were the main structured products examined by them.
Reverse convertibles basically have a coupon as well as a fixed nominal value. For corresponding bonds the coupon typically exceeds the market interest rate. The investor at maturity can choose either delivery of pre-determined number of shares or redeem the nominal value of the bond. The discount certificates are very similar to the reverse convertibles. From the current market value they offer shares at a discount. At maturity the owner of the certificate receives shares that are physically delivered.
Wilkens, Röder and Erner (2003) find a significant pricing in favour of issuing institutions when comparing the theoretical values with market prices. The driving factors of the issuers pricing policies are analyzed by the authors. For their formulated hypothesis they tend to find strong evidence that issuers orient their pricing towards the risk of redemption of shares given by the moneyness of the option and the lifetime of the product. Their study reveals that average mispricing increases with the moneyness of the option and decreases with time to maturity (Wilkens et al, 2000).
Stoimenov and Wilkens (2005) analyze the pricing of ‘plain-vanilla’ structured financial products such as discount certificates and reverse convertibles. They also study structured financial products with embedded exotic options (rainbow and barrier options) on the DAX and the DAX stocks in the secondary and primary market. The term rainbow option is applied to an entire class of options which are written on more than one underlying asset. Rainbow options are usually calls or puts on the best or worst of n underlying assets, or options which pay the best or worst of n assets. A good example for a type of rainbow option is a spread options. Barrier options are similar to standard options except that they are extinguished or activated when the underlying asset price reaches a predetermined barrier or boundary price.
The study reveals large implicit premiums charged by the issuing banks in the primary market for majority of the products (Stoimenov and Wilkens, 2005). According to them the product life cycle is found to be an important pricing parameter for the secondary market. They find that products with embedded exotic options give higher premiums compared to the common ‘classic products’ (Stoimenov and Wilkens, 2005).
Szymanowska, Horst and Veld (2004) study the pricing of reverse convertible bonds issued on the Amsterdam Stock Exchange between 1999 and 2002. They chose the Dutch market on the basis of the popularity of long-term options and reverse convertibles with the investors. These reverse convertible bonds carry coupon payments that are very high.
Their study reveals no overpricing of knock-in reverse convertibles but indicate an overpricing of plain vanilla reverse convertible bonds by 6%. They conduct an experiment to check what role do behavioral factors such as cognitive errors and framing play in the pricing of reverse convertibles and ask participants to price a simple financial product having similar characteristics as a reverse convertible(Szymanowska et al, 2006). Their analysis shows that in the pricing of simple financial products the cognitive errors play an important role.
Baule, Entrop and Wilkens (2006) carried out a study in the German Secondary market for structured products that are exchange traded. These products mainly emphasized on the influence of the bank’s credit risk. They used three models and made a comparison between them to value discount certificates They made a comparison between quoted and theoretical prices by applying a structural model that allowed incorporation of correlation effects between market and credit risk. Although there was a previous study conducted for discount certificates in Germany, this study finds out that the total margins are found to be comparatively lower, whereas the portion which draws back to credit risk appeared to be a material part of the total margin.
They mainly divided their analysis into two parts. The theoretical part presented a structural model to evaluate discount certificates that took into account the risk of issuer defaulting. The empirical part investigated quoted prices of discount certificates on the DAX stocks of five major issuers.
They found that compared to the earlier studies, total margins were found to be comparatively low whereas the credit risk margin appeared to be a material part of the total margin. The reason for this decline was the rising competition among the issuers.
Plain vanilla concave products and products with no capital protection
Concave strategies retain the downside risk, give up a portion of the upside, but pay a fixed return in a stable or rising market that is well above the yield on ordinary bonds (Burth et al, 2001). Individual investors like these payoffs, but cannot construct them easily on their own using traded instruments.
There have been three important studies conducted in the Swiss market so far. Schenk and Wasserfallen (1996) analyze the pricing of thirteen structured products having principal protection, listed on the Swiss Market Index (SMI) between the years 1991 to 1992. They examined a span ranging from 21 to 80 trading days for each product. The results showed that the structured products are undervalued in the secondary market and tend to be overvalued when they are issued for the first time. They do not find any systematic differences between model prices based on implied and historical volatilities. They conclude that the products are fairly priced by finding the root mean square error above 3% only in two cases and the range of error below 10% for all instruments (Wasserfallen et al, 1996).
A second study was conducted in the primary market by Burth, Kraus and Wohlwend (2001) who investigated 275 products without principal protection. They discussed for the first time the study of concave products. Products that have a concave payoff function can be seen as a position in the underlying asset in combination with a short position in a call option on the same asset. They find that the price differences with issuing institutions are approximately 1.91% significant at all conventional levels of confidence. The authors tend to find differences in the pricing on the basis of product category and issuing institutions. The mispricing can be seen in structured products without a coupon payment rather than those with a coupon.
Further they also emphasize on the role of co-lead managers and the important role they play in the primary market for structured products. The products are not managed by colead managers as they are smaller banks. A major player is found by these small banks from which they can look for the best deal to issue the product jointly. The study reveals that the structures show a smaller dispersion of pricing error and are significantly better priced when they are co-lead (Burth et al, 2001).