Abstract:
A method of structuring a guaranteed financial product on a risk asset using a computer comprising: a) introducing a reference asset being another risk asset having a secondary derivative market which is better developed and more liquid than said secondary derivative market of said risk asset; b) analyzing and comparing the volatility level of said risk asset and of said reference asset over a predetermined time period; c) applying an asset adjustment when said volatility level of said risk asset exceeds a predetermined level defined by said volatility level of said reference asset; and d) removing said asset adjustment when said volatility level of said risk asset falls below said predetermined level defined by the volatility level attained in c).

Description:
BACKGROUND OF THE INVENTION  
       [0001]     In recent years, market volatility has increased the popularity and usage of “capital guaranteed” financial products. Typically, investors in these products are offered the opportunity to participate in a portion or form of the upside in an underlying market, security or fund, while bearing limited or zero principal risk to their investment over a certain time period.  
         [0002]     From a structurer&#39;s (also referred as “issuer” or “underwriter,” e.g. a private bank who issues the structured product) standpoint, capital guaranteed products are often viewed as a combination of a zero-coupon bond plus a call option on an underlying financial instrument. For example, if the value of a zero-coupon bond returning 100 units of capital (any currency) in five years is currently 80 units, then the underwriter who receives 100 units from an investor can invest 20 units in a call option on the underlying instrument and 80 units in a zero-coupon bond, thereby being able to guarantee to return at least 100 units back to the investor at the end of the five years—plus the value of the call option in five years.  
         [0003]     When the underlying instrument (also referred to as asset) is liquid, e.g., a stock, basket of stocks, or an equity index such as the S&amp;P 500, the issuer can either buy the option in the open market or dynamically replicate its payoff by continuously trading the liquid underlying instrument. However, when the underlying instrument is less liquid, e.g. an actively managed hedge fund or fund of hedge funds with only monthly liquidity, or the underlying financial instrument has a very limited secondary derivative (option) market, the issuer has to devise a more sophisticated way to offer principal protection.  
         [0004]     The most common way of offering principal protection to risk assets (such as actively managed funds) is the constant-proportion portfolio insurance model, know as the CPPI model 1 . Using this model, the issuer invests in a combination of a zero-coupon bond and the risk asset, typically starting off by investing 100% of the notional in the risk asset, and subsequently reducing such investment to the risk asset and increasing the zero-coupon investment simultaneously should the risk asset&#39;s net asset value fall below a pre-defined threshold level, in a deterministic mechanical way. For example, the issuer may reduce its investment in the risk asset by 25% should the asset&#39;s net asset value fall 5% below its initial level. If the risk asset continues to appreciate in value, however, no such reduction is needed.    1 “Seeking Capital Protection through Portfolio Insurance”, Giancarlo Frugoli and Feminando Sarnaria,  A Wealth Manager&#39;s Guide to Structured Products , Risk Books, 2004.    
         [0005]     Effectively, the issuer compares the value of the risk-asset/zero-coupon portfolio to that of a pure zero-coupon investment to always maintain sufficient margin to protect itself from any potential risk asset depreciation, thereby ensuring that investors can still be paid back their full principal at maturity without an underwriting loss. The main disadvantage of the model is that the investor&#39;s participation in the upside of the risk asset (e.g. a fund) is not fixed, but is instead path-dependent. For example, if the fund suffers a substantial loss initially, then the issuer may have to decrease its investment in the fund significantly, which may then substantially reduce the investor&#39;s upside participation in a subsequent potential period of potential appreciation in the fund. As a result, it is possible that the fund appreciates over the duration of the structured product, yet the investor ends up receiving zero appreciation on their initial principal.  
       SUMMARY OF THE INVENTION  
       [0006]     The subject invention pertains to a system and method for structuring principal guaranteed products that uses a relative volatility measure to make adjustments on the underlying risk asset (e.g. an actively managed fund) when necessary, thereby ensuring that the risk asset volatility remains contained within a predefined range.  
         [0007]     Structured products on liquid underlying risk assets such as broad market indices are issued in large numbers and large notional amounts by a number of issuers such as private banks. The subject invention significantly expands the opportunity to underwrite structured products on less liquid assets, including assets for which a secondary derivative market is limited or does not exist, such as actively managed funds. Specifically, the subject invention allows the issuer to effectively transfer the hedging of its volatility risk to a broader and more liquid market, where a variety of option instruments can be used to offload such volatility risk. Using the subject invention, pricing of a structured product on an asset for which a secondary derivative market may not even exist then effectively becomes as easy as pricing a standard call option on a liquid market with developed traded derivative products such as the S&amp;P 500.  
         [0008]     The CPPI model is not well suited for structuring principal guaranteed products on highly volatile assets for which a secondary derivative market is limited or does not exist. As mentioned before, the CPPI model may force the underwriter to substantially decrease its investment in the risk asset in the event the risk asset sharply depreciates in value at the initial phase of the duration of contract embedded in the structured product, thereby potentially limiting or eliminating the opportunity to fully recover such losses even if the underlying asset fully recovers its losses by the end of the contract. This potential for limited upside participation is less of a risk for products in which the underlying asset is not very volatile. The subject invention is indifferent to the volatility of the risk asset as long as this volatility is contained within a range fixed relative to the volatility of a liquid reference asset. As a result, the subject invention significantly broadens the universe of risk assets that can be handled by issuers in their structured product offerings.  
         [0009]     In addition, the subject invention allows the issuer to offer a fixed upside participation (e.g. 60%) on the appreciation of the underlying risk asset. In contrast, the CPPI model can only offer principal protection; upside participation is variable.  
         [0010]     Finally, the subject invention allows the issuer to hedge unexpected future changes (“gaps”) in the volatility of the risk asset resulting from unexpected and potentially large changes in future financial market volatility. Using a volatility transaction, such as a volatility swap, the issuer can effectively “lock-in” a level of expected volatility on the risk asset in pricing the product, offsetting gains/losses in the embedded call option of the structured product (resulting from the actual risk asset volatility being different than the level used in pricing the product) by corresponding losses/gains in a volatility transaction such as a volatility swap on the reference asset, as the two volatility levels are linked by design.  
         [0011]     The subject invention specifically contemplates:  
         [0012]     A method and system of structuring a guaranteed financial product on a risk asset using a computer comprising: a) introducing a reference asset, i.e. another risk asset having a secondary derivative market which is better developed than the secondary derivative market of the primary risk asset; b) analyzing and comparing the volatility levels of the primary risk asset and of the reference asset over a predetermined time period; c) applying an asset adjustment when the volatility level of the risk asset exceeds a predetermined level defined by the volatility level of the reference asset; and d) removing the asset adjustment when the volatility level of the risk asset falls below a predetermined level defined by the volatility level attained in c).  
         [0013]     A method and system of structuring a guaranteed financial product on a risk asset using a computer comprising: a) introducing a reference asset, i.e. another risk asset possibly having a secondary derivative market which is better developed than that of the primary risk asset; b) analyzing and comparing the volatility levels of the primary risk asset and of the reference asset over a predetermined time period; c) applying an asset adjustment when the volatility level of the risk asset exceeds a predetermined level defined by the volatility level of the reference asset d) removing the asset adjustment when the volatility level of the risk asset falls below a predetermined level defined by the volatility level attained in c); and e) entering a volatility transaction such as a volatility swap to hedge (i.e. protect from) unexpected changes in the volatility of the reference asset beyond the predetermined level defined in c) which is used to price the structured product.  
         [0014]     A method and system of structuring a guaranteed financial product on a risk asset using a computer comprising: a) analyzing historical volatility levels and correlations between the risk asset and potential reference asset candidates to select one of the reference asset candidates as the reference asset; b) introducing a reference asset, i.e. another risk asset possibly having a secondary derivative market which is better developed than that of the primary risk asset; c) analyzing and comparing the volatility levels of the primary risk asset and of the reference asset over a predetermined time period; d) applying an asset adjustment when the volatility level of the risk asset exceeds a predetermined level defined by the volatility level of the reference asset; and e) removing the asset adjustment when the volatility level of the risk asset falls below a predetermined level defined by the volatility level attained in c). 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]     These and other subjects, features and advantages of the present invention will become more apparent in light of the following detailed description of a best mode embodiment thereof, as illustrated in the accompanying Drawings.  
         [0016]      FIG. 1  is a logic process flow chart embodying the system and method of the subject invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0017]     The subject invention pertains to a system and method for structuring principal guaranteed products that uses a relative volatility measure to make adjustments on the underlying risk asset (e.g. an actively managed fund) when necessary, thereby ensuring that the risk asset volatility remains contained within a predefined range.  
         [0000]     Definitions  
         [0000]     Investors  
         [0018]     A variety of investors use structured products in their portfolios. These investors include high-net worth individuals, institutions such as corporations, endowments, foundations and pension plans, family offices, money managers, private partnerships and companies.  
         [0000]     Issuer  
         [0019]     Also known as structurer or underwriter, a legal entity that offers structured products to investors and backs its principal guaranteed obligation by its own credit or the credit of an affiliate or partner. Such issuers include commercial and investment banks, insurance companies, private banks and other financial institutions and their subsidiaries and partners.  
         [0000]     Risk Asset  
         [0020]     A financial instrument such as an equity index, commodity index, fund, or a combination of financial instruments underlying a structured offered by the issuer to investors. The performance of this instrument is used to define the potential appreciation of the structured note, as promised by the issuer. The issuer may make investments in the risk asset continuously or at preset time intervals, or liquidate part of its investment in the risk asset as the issuers feels necessary relative to its obligation to deliver a level of upside participation at a future date, i.e. the expiration date of the structured note.  
         [0000]     Reference Asset  
         [0021]     A financial instrument whose volatility is used by the issuer to define an acceptable range of volatility for the risk asset underlying a structured note. The issuer will provide an adjustment (or remedy) at times when the volatility of the risk asset exceeds such acceptable range.  
         [0000]     Asset Adjustment  
         [0000]     A mechanism introduced by the issuer of the note to restrict the volatility of the risk asset. For example, if the risk asset is an actively managed fund, the adjustment can be a reduction in the net exposure of the fund.  
         [0000]     Volatility Measurement  
         [0022]     A process used by the issuer to compare the volatility of the risk asset to a level defined by the volatility of the reference asset. For example, the issuer may continuously measure the risk asset volatility calculated over a trailing one-month window and compare it against the volatility of the reference asset over the same rolling time window.  
         [0000]     Volatility Linked Transaction  
         [0023]     A financial transaction, such as a volatility swap, initiated by the issuer to hedge its volatility risk, i.e. the risk of having the actually volatility of the risk asset, realized over the duration of the structured product, be materially different than the volatility level used initially in pricing the structured product.  
         [0000]     Description  
         [0024]     Referring to  FIG. 1 , an important aspect of the subject invention is the monitoring of the underlying risk asset  206  volatility  212  relative to the volatility  214  of another asset called the “reference asset  208 ,” typically a more liquid asset than the risk asset  206 , and one for which a secondary derivative market is well developed. The issuer  202 , who issued a structured product to investors  204 , compares the volatility  212 ,  214  of the risk  206  and reference  208  assets periodically over a certain rolling time period (the “measurement window” e.g. a month) and directs an adjustment (or remedy)  210  to the risk asset  206  should the volatility  212  of the risk asset  206  exceed a certain level (or a function of) the volatility  214  of the reference asset  208 . In that event, a remedy  210  is then imposed for a certain adjustment time and the volatility comparison between the two assets  206 ,  208  is performed again. The process is repeated until the risk asset&#39;s  206  volatility  212  falls below a level of function of the reference asset&#39;s  208  volatility  214  at which point the remedy  210  is removed.  
         [0025]     For example, assume that the risk asset  206  is a hedge fund and the reference asset  208  is the S&amp;P 500 index. In this example, the hedge fund  206  is restricted to have its average daily volatility  212 , calculated over a rolling one-month measurement window, always be less than the corresponding S&amp;P 500  208  volatility  214  over the same time period. Once the fund&#39;s  206  average volatility  212  exceeds the S&amp;P 500  208  volatility  214 , then the portfolio manager is directed to take remedy  210  by, for example, de-leverage  206  the fund by a fixed percent. The remedy  210  is applied to the fuid  206  for a predefined time period (e.g. a two-month window, called the “remedy window”) at the end of which volatilities  212 ,  214  are compared again over the measurement window. At that point, the fund  206  will be permitted to again increase leverage to its original level (remove remedy  210 ) should the fund&#39;s  206  volatility  212  drop below the S&amp;P 500  208  level  214  over the measurement time window; otherwise the fund  206  is de-leveraged  210  again by the fixed percent over another remedy window. The process is repeated until the fund&#39;s  206  volatility  212  drops below that of the S&amp;P 500  208 , at which point the remedy  210  is removed.  
         [0026]     The system and method of the subject invention uses a personal computer to monitor the volatilities  212 ,  214  of the risk  206  and reference  208  assets. A non-limiting example of the personal computer that can be employed to implement the system and method of the subject invention is an I.B.M.-type personal computer having, for example, a 3.2 GHz Intel Pentium 4 processor, commonly manufactured by Intel, Inc., 1 GB of memory, and 250 GB of internal hard drive storage. In order to accommodate a higher number of users a more powerful computer, or a grid of computers connected to each other in order to carry out parallel processing and load balancing, can be utilized. The computer, or computers, use an operating environment such as Enterprise Linux ES manufactured by Red Hat, Inc. or Windows Server 2003 manufactured by Microsoft Corp. Databases are managed using database software such as 10 g manufactured by Oracle Corp. A statistical software package (such as, for example SAS/STAT manufactured by SAS) will be used to calculate the volatility (variance)  212 ,  214  of a return series (e.g. daily returns) for the two assets  206 ,  208  over certain time windows (e.g., month). The same statistical software package will be used by the issuer to compare the historical volatility  214  and correlation of various reference assets  208  to that of the risk asset  206 . The objective of this statistical analysis is to, first, select a reference asset  208  that is best correlated to the risk asset, and second, define the level of volatility  212  of the risk asset  206  (relative to the reference asset  208 ) that the risk asset  206  will be permitted to carry.  
         [0027]     The subject invention offers a unique advantage to the issuer of the product. Specifically, the issuer can hedge its volatility risk  212  associated with the risk asset  206  underlying the structured product by transacting in another market, often more liquid, i.e. the market of the reference asset  208  for which a secondary derivative market often exists and is well-developed. Effectively, the subject invention is designed to “guarantee” that the volatility  212  of the risk asset  206  will not exceed a level related to the reference asset  208  over the duration of the product.  
         [0028]     Embedded in the structured product is a call option on the underlying risk asset  206 . Generally, any call option is dependent of five variables: the price of the underlying asset, the strike price, the risk-free interest rate, the time to expiration and the expected (implied) volatility of the risk asset. While the first four variables are deterministic the last one (implied volatility) is dynamic and the most difficult to assess for various risk assets  206 . For example, the risk asset  206  may be dynamically managed (i.e. a managed fund) and its future volatility  212  may materially differ from its historical volatility.  
         [0029]     Moreover, the volatility  212  of the risk asset  206  can also be difficult to dynamically hedge through trading, as the risk asset  206  may not be as liquid. Using the subject invention, however, the issuer  202  can price a structured product underwritten on a less liquid risk asset  206 , or one for which a secondary derivative market is limited or does not exist, by transacting in the market of the reference asset  208 .  
         [0030]     As an example of a volatility transaction, the issuer may enter a volatility swap on the reference asset  208 . In this example we further assume that the volatility of the volatility of the risk asset is restricted to be less than the volatility of the reference asset over the duration of the structured product. A volatility swap would allow the issuer  202  to hedge the risk of unexpected changes in future volatility  214  of the reference asset  208 , and consequently unexpected changes in future volatility  212  of the risk asset  206  (whose volatility is linked to that of the reference asset  208 ). A volatility swap would have a payoff at expiration of: 
 
(S−D)*n 
 
 where, S is the actual volatility  214  of the reference asset  208  over the life of the contract (ideally set to be equal to the life of the structured product), D is the volatility specified by the swap (e.g. a level equal to the implied (market) volatility  214  of the reference asset  208  at the time when the structured product was priced), and n is the notional amount of the swap (in any currency) per a unit of volatility. 
 
 Having entered a volatility swap, the issuer  202  can effectively hedge unexpected large changes in the future volatility  212  of the risk asset  206  resulting from market events or external events (e.g. catastrophic events such as wars) that would result in large increases in overall equity market volatility because the effect of such events can be captured by the volatility  214  of a market index than can be used as the reference asset  208 . Such “gap” risk would have been difficult to hedge by dynamically trading the risk asset  206  even if the risk asset  206  was liquid enough. Using a volatility transaction, such as a volatility swap, the issuer  202  can effectively “lock-in” a level of expected volatility  212  on the risk asset  206  in pricing the structured product, thus offsetting gains/losses in the embedded call option of the structured product by corresponding losses/gains in the volatility swap on the reference asset  208  because the two volatility levels are linked by design. 
 
       EXAMPLE  
       [0031]     USD 100% Principal Protected Note on Fund ABC  
                                             Terms and Conditions                                    Issuer   Bank XYZ, New York           Rating   AA           Notional Amount   USD 50,000,000           Issue Price   100%           Trade Date   10 Aug. 203           Issue Date   11 Sep. 2003           Maturity Date   14 Sep. 2008           Coupon   Zero           Redemption   100% plus capital appreciation           Capital Appreciation   65% × Max{0%, [(ABC_Final −               ABC_Initial)/ABC_Initial]}           Calculation Agent   Bank XYZ, New York           Business Days   New York           Minimum Trade Size   USD 1,000,000           Governing Law   New York                      
 
         [0032]    
       
         
               
             
               
               
             
           
               
                   
               
               
                   
               
               
                 Investment Restrictions 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Monitoring Agent 
                 Bank XYZ, New York 
               
               
                 Securities 
                 US-exchange listed only 
               
               
                 Concentration 
                 Single Security less than 10% of ABC Fund&#39;s 
               
               
                   
                 Net Asset Value (NAV) 
               
               
                 Leverage 
                 ABC Fund&#39;s net long exposure less than 100% 
               
               
                   
                 (Permitted Leverage) of Fund&#39;s NAV 
               
               
                 Variance 
                 ABC Fund&#39;s Variance less than 100% of 
               
               
                   
                 S&amp;P 500 Variance 
               
               
                 Measurement Window 
                 25 business days 
               
               
                 Remedy Window 
                 25 business days 
               
               
                 Asset Adjustment 
                 10% Reduction in ABC Fund&#39;s net long exposure 
               
               
                   
               
             
          
         
       
     
         [0033]     ABC Fund&#39;s  206  trailing 25-day (Measurement Period) average variance  212  is compared to S&amp;P 500  208  trailing average variance  214  at the end of each business day. If ABC Fund&#39;s  206  variance  212  exceeds the variance  214  of the S&amp;P 500  208  then Permitted Leverage  210  is reduced by 10% over the ensuing 25-day period (Remedy Period), at the end of which the variances of ABC Fund and the S&amp;P 500 are compared again over a Measurement Window. Then if the Fund&#39;s  206  average variance  212  falls below the variance  214  of the S&amp;P 500  208  over the Remedy Period then Permitted Leverage  210  is reset to its initial level of 100% (Remedy is removed), otherwise Permitted Leverage is reduced by another 10% over a second Remedy Window. The process is repeated until ABC Fund&#39;s variance falls below that of the S&amp;P 500, at which point the Remedy is removed and permitted leverage is reset to its initial level of 100%.  
         [0034]     In this example, the structured note is priced to offer 65% participation on the appreciation of ABC fund  206  over a five-year period. The fund  206  needs to follow the above set of investment restrictions. Following issuance, the issuer  202  of the note will be monitoring the fund&#39;s  206  investment restrictions daily and will notify the manager of the fund  206  of any violations, which must then be immediately corrected. Should the manager fail to comply with such notification, the issuer  202  has the right to terminate the note early.