Contingent claim valuation: the case of advanced index certificates.

Hernandez, Rodrigo ; Brusa, Jorge ; Liu, Pu 等

INTRODUCTION

The constant and accelerating development of new structured products--that is to create new securities through the combination of fixed income securities, equities and derivative securities--permanently challenges practitioners, academicians, and regulators. Regulators are concern with the sophistication of the products and the targeting of individual investors as primary customers (Laise, 2006; Maxey, 2006). Regulators worry about the investors' inability to understand these products (Ricks, 1988; Lyon, 2005; NASD, 2005; Simmons, 2006; Isakov, 2007).

In this paper, we study a new financial product known as "Advanced Index Certificates" (to be referred to as AIC henceforth), one of the equity-linked "structured products" issued by major banks in Europe. AICs are also known by the commercial names of "PartProtect TRACKER", "AIRBAG Notes", "Protector", "Power Pro Certificates", or "S2MART". The rate of return on the investment in the certificates is contingent upon the performance of a pre-specified underlying equity or equity index over a pre-specified period (known as term to maturity). If the price of the underlying asset goes up during the term to maturity, the investors of the certificates will receive a return equal to the return on the underlying asset. The returns on the certificates may or may not be subject to a maximum limit. If the returns on the certificates are subject to a maximum limit, they are referred to as capped certificates; otherwise, they are known as uncapped certificates. If the price of the underlying asset goes down during the term to maturity the investors of the certificates will receive a guaranteed minimum redemption amount at maturity, as long as the underlying asset price did not close on maturity date below a predetermined level referred to as the knock-in level. The guaranteed minimum redemption amount may be the same as or higher than the par amount of the certificates. Usually the knock-in level is set up as a percentage of the initial price (e.g. 75% of the initial price). A certificate with a knock-in level of, for example, 75% of the initial price, is also referred to as having a 25% downside protection.

If, however, the price of the underlying asset closes on maturity date below the knock-in level, the investor is partially exposed to the decline in the underlying asset. In calculating the return on the underlying asset, the certificate issuers will use only the change in the asset price; the cash dividends paid during the period are not included. In other words, investors in the AICs do not receive cash dividends even though the underlying assets pay dividends during the term to maturity.

The banks that issue these certificates are usually well-recognized large banks in Europe: Bayerische Hypo- und Vereinsbank AG, Dresdner Bank AG, DZ Bank AG, Goldman Sachs, ING Bank NV, UBS Investment AG, and Westdeutsche Landesbank.

The purpose of the paper is to provide an in-depth economic analysis for the AICs to explore how the principles of financial engineering are applied to the creation of such newly structured products. We also develop pricing models for the certificates by using option pricing formulas. In addition, we present an example of an uncapped AIC issued on March 14, 2003 by Bayerische Hypo- und Vereinsbank AG (to be referred to as HVB Bank henceforth), a well-recognized large bank in Germany. In this example, we price the certificate by calculating the cost of a portfolio with a payoff similar to the payoff of the certificate. Finally, we empirically examine all outstanding AICs in August 2005 and test if issuers make a profit in the primary market. We also compare the mispricing of ICs in this study with the sample of Out performance Certificates in the Hernandez et al. (2007) study and the sample of Bonus Certificates in the Hernandez et al. (2008) study. All three samples are composed of securities outstanding in August 2005.

The rest of the paper is organized as follows: The design of the certificates is introduced in Section 2. The pricing models are developed in Section 3. We present an example of AIC in Section 4 and empirically calculate the profit in the primary market for issuing the certificate using the models developed in Section 3. In Section 5, we provide detailed analyses of the AICs market and we empirically examine the profits in the primary market. We conclude the paper in Section 6.

DESCRIPTION OF THE PRODUCT

The rate of return of a certificate is contingent upon the price performance of its underlying asset over its term to maturity. The beginning date for calculating the gain (or loss) of the underlying asset is known as the fixing date (or pricing date) and the ending date of the period is known as the expiration date. The price of the underlying asset on the fixing date is referred to as the reference price (or exercise price, or strike price), and the price of the underlying asset on the expiration date is referred to as the valuation price. In the example presented in Section 4 the exercise price and the valuation price are the closing prices on the fixing date and the expiration date respectively.

If we denote [I.sub.0] as the underlying asset price on the fixing date, [I.sub.KI] as the knock-in level, and [I.sub.T] as the valuation price, then for an initial investment of $1 in an uncapped certificate, the total value that an investor will receive on the expiration date (known as the redemption value or settlement amount), VT, is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Alternatively, the relationship between the terminal value of an uncapped certificate and the terminal value of the underlying asset based on the change in the underlying asset price (without taking into account dividends) with a knock-in level of 75% of the exercise price (also known as a capital protection of 25%) can be represented in Figure 1. The solid line represents the terminal value of the certificate on maturity day T, as a function of the terminal value of the underlying index. The dotted line represents the terminal value of the underlying index.

[FIGURE 1 OMITTED]

The slope for the value of the underlying asset in Figure1 is, of course, one. The slope for the value of the certificate, when the price of the underlying asset goes up, is equal to one. The slope for the value of the certificate, when the price of the underlying asset goes down below the knock-in level, is equal to the ratio [I.sub.0]/[I.sub.KI].

The redemption value, VT, for a capped certificate on the expiration date is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Similarly, the relationship between the terminal value of a capped certificate and the terminal value of the underlying asset based on the change in the underlying asset price (without taking into account dividends) with a downside protection of 25% and a capped return of 30% can be represented in Figure 2. The solid line represents the terminal value of the certificate on maturity day T, as a function of the terminal value of the underlying index. The dotted line represents the terminal value of the underlying index.

[FIGURE 2 OMITTED]

THE PRICING OF ADVANCED INDEX CERTIFICATES

Uncapped Advanced Index Certificates

The terminal value from Equation (1), [V.sub.T], for an initial investment of $1in one uncapped AIC with exercise price [I.sub.0], and term to maturity T, can be expressed mathematically as:

[[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The max [[I.sub.T] - [I.sub.0]; 0] in Equation (3) is the payoff for a long position in a call with exercise price [I.sub.0]. The -max [[I.sub.KI] - [I.sub.T]; 0] in Equation (3) is the payoff for a short position in a put with exercise price [I.sub.KI]. The payoff of one uncapped AIC is exactly the same as the payoff for holding the following three positions:

1. A long position in one zero coupon bond with face value equal to $1 and maturity date same as the maturity date of the certificate;

2. A long position in call options with exercise price [I.sub.0], term to expiration T (which is the term to maturity of the certificate), and number of options of 1/[I.sub.0].

3. A short position in put options with exercise price [I.sub.KI], term to expiration T (which is the term to maturity of the certificate), and number of options of 1/[I.sub.KI].

Since the payoff of an uncapped certificates is the same as the combined payoffs of the above three positions, we can calculate the fair value of the certificates based on the value of the three positions. Any selling price of the certificates above the value of the above three positions is the gain to the certificate issuer.

The value of Position 1 is the price of a zero coupon bond with a face value $1 and maturity date T. So it has a value of $1[e.sup.-rT]. The value of Position 2 is the value of 1/[I.sub.0] shares of call options with each option having the value C1:

[C.sub.1] = [I.sub.0][e.sup.-qT]N([d.sub.1]) - [Xe.sup.-rT]N([d.sub.2]) (4)

Where r is the risk-free rate of interest, q is the dividend yield of the underlying assets, T is the term to maturity of the certificate, X([equivalent to] [I.sub.0]) is the exercise price and

[d.sub.1] = [ln([I.sub.0]/X) + (r - q + 1/2 [[sigma].sup.2])T]/[sigma][square root of T] (5)

[d.sub.2] = [d.sub.1] - [sigma][square root of T] (6)

Where [sigma] is the standard deviation of the underlying asset return. The value of Position 3 is the value of 1/[I.sub.KI] shares of put options with each option having the value P:

P = [Xe.sup.-rT]N(-[d.sub.2]) - [I.sub.0][e.sup.-qT]N(-[d.sub.1]) (7)

Where r is the risk-free rate of interest, q is the dividend yield of the underlying asset, T is the term to maturity of the certificate, X ([equivalent to][I.sub.KI]) is the exercise price, and [d.sub.1] and [d.sub.2] can be calculated using Equation (5) and (6) respectively. Therefore, the total cost, TC, for each uncapped certificate is

[TC.sub.U] = 1[e.sup.-rT] + [1/[I.sub.0]] [C.sub.1] - [1/[I.sub.KI]] P (8)

Capped Advanced Index Certificates

When investors invests in an AIC that has a cap on the return, the return to the investor is equivalent to the return on an uncapped certificate minus the return on a call option with exercise price equal to the cap level of the underlying asset. In other words, when an investor purchases a certificate with a cap on the return, he basically buys a certificate without restrictions and sells a call option with exercise price equal to the cap level simultaneously.

The terminal value from Equation (2), VT, for an initial investment of $1 in one capped AIC with exercise price [I.sub.0], knock-in level [I.sub.KI], cap level [I.sub.C] (e.g. 130% of [I.sub.0]), and term to maturity T can be expressed mathematically as:

[V.sub.T] = [1/[I.sub.0]] [[I.sub.0] + max[[I.sub.T] - [I.sub.0];0] - [[I.sub.0]/[I.sub.KI]] max [[I.sub.KI] - [I.sub.T];0] - max[[I.sub.T] - [I.sub.C];0]] (9)

The first three terms in Equation (9) are exactly the same as those in Equation (3). The payoff -max [[I.sub.T] - [I.sub.C]; 0] in Equation (9) is the payoff of a short position for a call on the underlying asset with an exercise price [I.sub.C]. The value of Position 4 is the value of 1/[I.sub.0] shares of call options with each call value of [C.sub.2] calculated using Equation (4) with the exercise price set equal to the cap level, X ([equivalent to] [I.sub.C]). Therefore, the total cost, TC, for each capped certificate is

[TC.sub.X] = [TC.sub.U] - [1/[I.sub.0]][C.sub.2] (10)

If we denote [B.sub.0] as the issue price of the certificate, any selling price above the fair value is the gain to the certificate issuer. And the profit function for the issuer of certificates is

[PI] = [B.sub.0] - TC (11) (11)

EMPIRICAL TEST

In this section, we empirically examine an AIC issued by HVB Bank on March 14, 2003 using the Dow Jones Euro STOXX 50 as the underlying asset. The AIC is the "HVB Advanced Index Certificate 2003/2008" (ISIN DE0007873671), and the major characteristics of the certificate are listed in Appendix I of the paper.

Based on the information in Appendix I, the certificate has a participation rate of 100% on the positive returns of the underlying asset, and a 25% downside protection on the negative returns of the underlying asset. The fixing date HVB Bank set for the certificate was March 14, 2003 and the issue price of the certificate was 1,030 [euro] per 1,000 [euro] nominal value. The expiration date (i.e. the date on which the closing price of the underlying asset will be used as the valuation price) was set on March 14, 2008, 5 years later. Therefore, the payoff to the investor of on maturity date, T, is:

1,000 [euro] x [1 + max[[[[I.sub.T] - [I.sub.0]]/[I.sub.0]];0] - (max[[[0.75 x [I.sub.0] - [I.sub.T]]/[I.sub.0]];0] x (1/0.75))] (12)

1,000 [euro] + [1,000 [euro]/[I.sub.0]]max[[I.sub.T] - [I.sub.0];0] - [1,000 [euro]/0.75]max[0.75 x [I.sub.0] - [I.sub.T];0] (13)

Equation (13) is the payoff to be received by the certificate investor, which is also the cash flow to be paid by the certificate issuer, and the [I.sub.0] ([I.sub.T]) in Equation (13) is Dow Jones Euro STOXX 50 Index value on March 14, 2003 (March 14, 2008).

The cost of the payoff of 1,000 [euro] in Equation (13) is 1,000 [euro] [e.sup.-r5], the cost of the payoff (1,000 [euro]/[I.sub.0]) x max [[I.sub.T] - [I.sub.0]; 0] is 1,000 [euro]/[I.sub.0] call options with an exercise price [I.sub.0], and the cost of the payoff (1,000 [euro]/0.75 x [I.sub.0]) x max [0.75 x [I.sub.0] - [I.sub.T]; 0] is 1,000 [euro]/0.75 x [I.sub.0] put options with an exercise price 0.75 x [I.sub.0]. The call premium can be calculated from the following equation:

C = [I.sub.0][e.sup.-q5]N([d.sub.1]) - [I.sub.0.sup-r5]N([d.sub.2]) (14)

Where

[d.sub.1] = (r - q + [1/2] [[sigma].sup.2]) x 5/[sigma][square root of 5] (15)

[d.sub.2] = [d.sub.1] - [sigma][square root of 5] (16)

The put premium can be calculated from the following equation:

P = 0.75[I.sub.0][e.sup.-r5]N(-[d.sub.2]) - [I.sub.0][e.sup.-q5]N(-[d.sub.1]) (17)

Where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

[d.sub.2] = [d.sub.1] - [sigma][square root of 5] (19)

The total cost of the certificate, TC, is

[TC.sub.U] = 1,000 [euro][e.sup.-r5] + [1,000 [euro]/[I.sub.0]] C - [1,000 [euro]/[0.75 x [I.sub.0]]] P (20)

U ' [I.sub.0] 0.75 x [I.sub.0]

Where C is the call premium calculated in Equation (14) and P is the put premium calculated in Equation (17). The issuer sells the certificate for 1,030 [euro], therefore the profit for issuing the certificate, [pi], is equal to

[PI] = 1,030 [euro] - (1,000 [euro][e.sup.-r5] + [1,000 [euro]/[I.sub.0]] C - [1,000 [euro]/[0.75 x [I.sub.0]]] P) (21)

In order to calculate the issuer's profit, we need the following data for the certificate: 1) the price of the underlying asset, [I.sub.0], 2) the cash dividends to be paid by the underlying assets and the ex-dividend dates so we can calculate the dividend yield, q, 3) the risk-free rate of interest, r, and 4) the volatility of the underlying asset, o. Since the dividends from the underlying security are discrete and Equations (14) and (17) are based on continuous dividend yield, we calculate the equivalent continuous dividend yield for underlying security that pays discrete dividends. For an underlying asset which is an index with a price [I.sub.0] at t=0 (the issue date) and which pays n dividends during a time period T with cash dividend [D.sub.i] being paid at time [t.sub.i], the equivalent dividend yield q will be such that

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

The prices and dividends of the underlying asset are obtained from Bloomberg; the risk-free rate of interest is the yield of government bonds (alternatively, swap rates) of which the terms to maturity match those of the certificate. If we cannot find a government bond that matches the term of maturity for a particular certificate, we use the linear interpolation of the yields from two government bonds that have the closest maturity dates surrounding that of the certificate. The volatilities ([sigma]) of the underlying assets are the implied volatility obtained from Bloomberg based on the call and put options of the underlying asset. When the implied volatilities are not available, we use the historical volatility calculated from the underlying securities prices in the previous 260 days.

The five-year rate of interest, r, on March 14, 2003, the issue date of the certificate, based on the Euro swap rates is 3.632%. The dividend yield, q, on the Dow Jones Euro STOXX 50 Index is 5.23%. The Dow Jones Euro STOXX 50 Index value on the issue date of the certificate, [I.sub.0], is 2,079.71. The volatility of the Dow Jones Euro STOXX 50 Index based on the index call (put) options is 35.89% (53.05%) on the issue day. The historical volatility of the Dow Jones Euro STOXX 50 Index based on the previous 260 days is 40.10%. We use the historical volatility to take a more conservative approach in the calculation of the issuer's profit. Therefore, the d1 and [d.sub.2] in Equation (15), (16) are,

[d.sub.1] = [(3.63% - 5.23% + [1/2] [(40.10%).sup.2])[square root of 5]]/[40.10%[square root of 5]] = 0.3591 (23)

[d.sub.2] = 0.3591 -0.4010 x [square root of 5] = -0.5376 (24)

N([d.sub.1]) = 0.6403 (25)

N([d.sub.2]) = 0.2954 (26)

The [d.sub.1] and [d.sub.2] in Equation (18), (19) are,

[d.sub.1] = [0.28768 + (3.63% - 5.23% + [1/2][(40.10%).sup.2])[square root of 5]]/[40.10%[square root of 5]] = 0.6780 (27)

[d.sub.2] = -0.2167 (28)

N(-[d.sub.1]) = 0.2483 (29)

N(-[d.sub.2]) = 0.5858 (30)

Substitute Equations (25), (26) into Equation (14) and Equations (29), (30) into Equation (17), we obtain the cost of issuing the AIC, TC,

[TC.sub.U] = 1,000 [euro][e.sup.r-5] + [1,000 [euro]/2,079.71] C - [1,000 [euro]/[[0.75 x 2,079.71]]] P = 836.62 [euro] + 246.54 [euro] - 233.58 [euro] = 849.58 [euro] (31)

The profit for issuing each AIC, [pi], is

[PI] = 1,030 [euro] - 849.58 [euro] = 180.42 [euro] (32)

So the profit for issuing each AIC with a par value of 1,000 [euro] is approximately 180.42 [euro]. There are several ways to examine the reasonableness of the profit (or the quality of the model). One way to test the quality of the model is to examine the profit on the AIC. Since the AIC requires a minimum purchase amount of 1,030 [euro] (per nominal value of 1,000 [euro]), the cost of issuing such an AIC is about 849.58 [euro], and then a profit of 180.42 [euro]--seems reasonable. Alternatively, we can examine the rate of return on such a transaction. A profit of 180.42 [euro] on a transaction that requires an investment of 849.58 [euro] over a five-year period translates into an annual rate of return of 3.93%. Based on HVB Bank's 2003 Annual Report, the return of 3.93% is almost identical to by HVB Bank's return on total risk assets of 3.13% if we take into account the marketing costs (e.g. sales commissions and promotion expenses) associated with the issue of the AIC. The 3.93% return on risk assets calculated from the pricing model in the paper can also be translated into a return on equity of 12.89% using by HVB Bank's 30.5% of Tier One Capital ratio (by HVB Bank, 2003 Annual Report). The calculated 12.89% return on equity is also in line with by HVB Bank's reported return on common stockholder's equity, which is 13.86% if we take into account the marketing costs for issuing the AIC. The remarkable consistency between the empirical results calculated from the pricing model developed in the paper and the reported financial data in HVB Bank's Annual Report suggests the model developed in the paper is sound and robust.

ADVANCED INDEX CERTIFICATES MARKET

The sample of AICs in this study includes all AICs outstanding in August 2005 issued between August 2001 and August 2005. We developed our sample from final term sheets published on web pages of each bank (the banks' websites are available from the authors upon request). In Table 1 we present the descriptive statistics for both the uncapped and the capped certificate samples. The total value issued is 1.39 [euro] billion on 36 issues of AICs. The median issue size is 27.75 [euro] million with 500 thousand certificates in each issue. The median knock-in level and cap level are at 80.00% and 184.91% of the reference price respectively. The median dividend yield and volatility (taking in account the volatility surface) of the underlying assets are 2.66% and 35.68% respectively. In Table 1 we also present the profitability for issuing PCs. The profitability is measured by the profit ([product]) as a percentage of the total issuing cost (TC), i.e.

Profitability = [[PI]/TC] x 100%

= [[[B.sub.0] - TC]/TC] x 100% (33)

The results in Table 1 show that average (median) profit for all the 36 issues is 10.46% (5.75%) above the issuing cost. The result in the paper provided additional evidence that issuers of newly structured products price the securities above the issuing cost in the primary market. Several studies have reported that structured products have been overpriced, 2%-7% on average, in the primary market based on theoretical pricing models: King and Remolona (1987), Chance and Broughton (1988), Abken (1989), Chen and Kensinger (1990), and Chen and Sears (1990), Baubonis et al. (1993), and Hernandez et al. (2010) for Equity Linked Certificates of Deposit; Burth et al. (2001), Benet et al. (2006) and Hernandez et al. (2010) for Reverse Convertible

Bonds; Hernandez et al. (2007) for Outperformance Certificates, Hernandez et al. (2008) for Bonus Certificates, Wilkens et al. (2003), Grunbichler and Wohlwend (2005), and Stoimenov and Wilkens (2005) for various products.

Given that issuing AICs is a profitable business, three interestingly related questions arise in terms of the mispricing: First, it is interesting to know whether uncapped AICs are more or less profitable than capped AICs. In order to answer this question, the profitability of the uncapped sample of AICs is compared with the sample of capped AICs. The average profit for all the 26 issues of uncapped AICs is 6.34% and the average profit for all the 10 issues of capped AICs is 17.87%. The results of the test of equal means suggest that the issuance of capped AICs is more profitable that the issuance of uncapped AICs. Results are reported in Table 1.

Second, whether the issuance of structured products with exotic options (e.g. Bonus Certificates) is more or less profitable than the issuance of structured products with plain vanilla options (e.g. Advanced Index Certificates). In other words, are certificates with options that more difficult to understand, price and hedge mispriced more? In order to answer this question, the profitability of the sample of Bonus Certificates outstanding in August 2005 from the Hernandez et al. (2008) study is compared with the sample of AICs in this study. The average profit for all the 5,560 Bonus Certificates is 2.64% and the average profit for all the 36 AICs is 10.46%. The results of the test of equal means suggest that the issuance of AICs is more profitable than the issuance of Bonus Certificates. Results are reported in Table 2. We find similar results when controlling by type.

Third, it is also interesting to know whether the issuance of structured products with partial capital protection and plain vanilla options (e.g. Advanced Index Certificates) is more or less profitable than the issuance of structured products without any capital protection, plain vanilla options and participation greater than 100% (e.g. Outperformance Certificates). In other words, how is priced the capital protection versus the participation rate greater than 100%? In order to answer this question, the profitability of the sample of AICs outstanding in August 2005 is compared with a sample of Outperformance Certificates also outstanding in August 2005 from the Hernandez et al. (2007) study. The average profit for the 36 AICs is 10.46% and the average profit for all the 1,597 Outperformance Certificates is 3.83%. The results of the test suggest that the issuance of AICs is more profitable. Results are reported in Table 2. We find similar results when controlling by type.

CONCLUSION

In this paper we introduce a newly structured product known as AICs and we provide detailed descriptions of the product specifications. We further develop pricing models for two types of certificates--uncapped and capped certificates. We also apply the pricing model for AICs to a certificate issued by HVB Bank, as an example, to examine how well the model fits empirical data. Moreover, a detailed survey of the 1.4 [euro] billion Advanced Index Certificates market for 36 issues outstanding on August 2005 is presented and the profitability in the primary market is examined. We find that issuance of the certificates is profitable for the issuers. The result is in line with previous studies pricing other structured products. Finally, we compare the mispricing in our sample of AICs with the sample of Outperformance Certificates from the Hernandez et el. (2007) study and the sample of Bonus Certificates from the Hernandez et al. (2008) study. All three samples are composed of securities outstanding in August 2005.

The study provides insights into the design, the payoff, the pricing and the profitability of the newly designed financial product. The methodology and approach used in this paper can be easily extended to the analysis of other structured products.

APPENDIX 1: EXAMPLE OF AN UNCAPPED ADVANCED INDEX CERTIFICATE

The uncapped certificate in Appendix 1 was issued by investment bank HVB using the Dow Jones Euro STOXX 50 as the underlying asset. The fixing date HVB set for the certificate was March 14, 2003 and the issue price of the certificate was 1,030 [euro]. The expiration date (i.e. the date on which the closing price of the underlying asset will be used as the valuation price) was set on March 14, 2008.

HVB ADVANCED INDEX CERTIFICATE 2003/2008

Issuer Bayerische Hypo- und Vereinsbank AG
Index Dow Jones Euro STOXX 50
Type Advanced Index Certificate
Subscription Period 21 February 2003
Valuation Date 14 March 2003
Maturity Date 14 March 2008
Issue Size 12,000 certificates
Issue Price 1,030 [euro]per certificate
Denomination 1,000 [euro]
Repayment

1,000 [euro] x [1 + max[[[[I.sub.final] - [I.sub.initial]]/
[I.sub.initial]];0] - (max[[[0.75 x [I.sub.initial] -
[I.sub.final]]/[I.sub.initial]];0] x (1/0.75))]

[I.sub.initial] is the index value on March 10, 2003

[I.sub.final] is the index value on March 10, 2008

Listing Open Market--Frankfurt Stock Exchange
Smallest Unit 1 certificate
WKN 787,367
ISIN Code DE 000 787 367 1

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Rodrigo Hernandez, Radford University

Jorge Brusa, Texas A&M International University

Pu Liu, University of Arkansas

Table 1: Descriptive statistics for the uncapped and the capped
Advanced Index Certificates samples

Type Issue Size Issue Size Maturity Knock-In
 (Mill. [euro]) (Certif.) (Years) Level (%) (b)

Uncapped

Mean 45.29 552,202 4.23 76.92
Median 50.00 500,000 4.01 80.00

Amount Issued (a)

Number of Issues

Capped

Mean 21.25 424,500 2.30 78.51
Median 13.62 200,000 2.91 78.08

Amount Issued (a)

Number of Issues

Pooled Sample

Mean 38.61 516,729 3.69 77.36
Median 27.75 500,000 3.25 80.00

Amount Issued (a)

Number of Issues

Test of Means

p-value 0.043 0.432 <0.001 0.627

Type Cap Level Issue Price Volatility Div.
 (%) (b) (%) (b) (%) Yield (%)

Uncapped

Mean n.a. 101.81 32.18 3.16
Median n.a. 101.50 30.42 2.98

Amount Issued (a)

Number of Issues

Capped

Mean 172.19 100.07 44.95 2.34
Median 184.91 100.00 51.41 2.30

Amount Issued (a)

Number of Issues

Pooled Sample

Mean 172.19 101.33 36.74 2.87
Median 184.91 101.50 35.68 2.66

Amount Issued (a)

Number of Issues

Test of Means

p-value n.a. 0.577 0.040 0.087

Type Profit
 (%)

Uncapped

Mean 6.34 **
Median 4.85

Amount Issued (a) 1,177

Number of Issues 26

Capped

Mean 17.87 **
Median 16.33

Amount Issued (a) 212

Number of Issues 10

Pooled Sample

Mean 10.46 **
Median 5.75

Amount Issued (a) 1,390

Number of Issues 36

Test of Means

p-value 0.009

(a) in million Euros b as a percentage of the reference price **
significant at the 0.01 level

Table 2: Comparison between Advanced Index Certificates, Bonus
Certificates and Outperformance Certificates

Type Amount Issued Issue Size Maturity
 (Mill. [euro]) (Mill. [euro]) Years)

Adv. Index Cert.
Uncapped (n=26) 1,177 45.29 4.23
Capped (n=10) 212 21.25 2.30
Pooled (n=36) 1,389 38.61 3.69

Bonus Cert.

Uncapped (n=5,078) 108,567 21.38 3.11
Capped (n=482) 14,064 29.18 2.48
Pooled (n=5,560) 122,631 22.06 3.06

Outperformance Cert.

Uncapped (n=596) 14,944 25.20 2.34
Capped (n=911) 28,263 31.02 1.39
Pooled (n=1,597) 43,207 28.72 1.77

Type Knock-In Cap Level Issue Price
 Level (%) (b) (%) (b) (%) (a)

Adv. Index Cert.
Uncapped (n=26) 76.92 n.a. 101.81
Capped (n=10) 78.51 172.19 100.07
Pooled (n=36) 77.36 172.19 101.33

Bonus Cert.

Uncapped (n=5,078) 74.37 n.a. 100.18
Capped (n=482) 72.49 136.37 100.29
Pooled (n=5,560) 74.21 136.37 100.19

Outperformance Cert.

Uncapped (n=596) n.a. n.a. 100.29
Capped (n=911) n.a. 130.26 99.78
Pooled (n=1,597) n.a. 130.26 99.98

Type Volatility Div. Yield Profit
 (%) (%) (%)

Adv. Index Cert.
Uncapped (n=26) 32.18 3.16 6.34 **
Capped (n=10) 44.95 2.34 17.87 **
Pooled (n=36) 36.74 2.87 10.46 **

Bonus Cert.

Uncapped (n=5,078) 20.47 3.22 2.60 **
Capped (n=482) 20.62 2.86 3.08 **
Pooled (n=5,560) 20.50 3.19 2.64 **

Outperformance Cert.

Uncapped (n=596) 19.40 3.21 3.31 **
Capped (n=911) 21.24 2.64 4.29 **
Pooled (n=1,597) 20.51 2.87 3.83 **

 Test of Means p-values

AICs vs. OCs <0.001
AICs vs. BCs <0.001
Uncapped AICs vs. Uncapped OCs 0.004
Uncapped AICs vs. Uncapped BCs 0.020
Capped AICs vs. Capped OCs <0.001
Capped AICs vs. Capped BCs <0.001

(a) as a percentage of the reference price ** significant at the 0.01
level