Patent Publication Number: US-2019197627-A1

Title: System and method for portfolio optimization

Description:
FIELD OF THE INVENTION 
     The present invention relates to a system and method for portfolio optimization, and in particular, to such a system and method for portfolio optimization through optimized selection of options. 
     BACKGROUND OF THE INVENTION 
     Various methods have been described to select components of a portfolio of securities, according to different desired parameters. For example, U.S. Pat. No. 8,140,416 describes another automatic trading algorithm, in this case to seek hidden volume in a market and to trade on that basis. 
     Options are one example of an investment that can be added to a portfolio, although one that is not mentioned by the patent described above. But adding options to a portfolio brings its own set of complexities. As Avellaneda and Dobi point out (“Modeling Volatility Risk in Equity Options: a Cross-sectional approach”, ICBI Global Derivatives, Amsterdam, 2014), options have complex volatilities. Implied volatility is determined according to the option price while realized volatility is determined according to the historical price of the underlying securities. 
     BRIEF SUMMARY OF THE INVENTION 
     The present invention, in at least some embodiments, overcomes the drawbacks of the background art by providing a system and method for portfolio optimization through optimized selection of options. Without wishing to be limited by a single hypothesis, the resultant selection of options is optimized to have a similar risk profile to a selected securities benchmark, but with a superior Sharpe ratio. As used herein, unless otherwise indicated, the reference to options and to creating a portfolio of options relate to selling options. 
     In terms of the selected securities benchmark, optionally the underlying securities of the options are determined according to a securities benchmark. Also optionally, a subset of such securities is selected before optimization of the options begins. Alternatively, all securities of the benchmark are considered during selection of the options. 
     The options are preferably selected according to one of a plurality of parameters, included but not limiting to a parameter related to the option or a parameter related to the underlying security. Non-limiting examples of parameters related to the options include the expiration date for the option, whether the option is a call option or a put option, the type of call option, estimated risk of the option, estimated liquidity of the option and estimated volatility of the option. Non-limiting examples of parameters related to the underlying securities include estimated risk of the underlying security, estimated liquidity of the underlying security and estimated volatility of the underlying security. 
     The options are also preferably selected according to an overall desired level of risk for the portfolio. Alternatively or additionally, the options are selected according to an overall desired level of liquidity for the portfolio. 
     The period of time for the option, that is before it expires, is also preferably selected. For example, the period of time could optionally be 1 week, 1 month and so forth. An option with a shorter period of time provides a greater theta, so that selling 12 options sequentially, each with a one month expiry, would have a greater price than selling 1 option for 1 year. The end of such a period of time may also be referred to as the expiration date. 
     The implied volatility of the options is preferably calculated according to the option prices. Realized volatility can also be used, calculated according to the historical prices of the underlying securities. 
     Liquidity of the options may optionally be calculated according to the options themselves or according to liquidity of the underlying securities. For the later, liquidity is optionally calculated according to historic liquidity or on calculations of a dynamic liquidity, for example, based on the rate of change daily trading levels and the like. Historic liquidity is preferably determined as the bid/ask spread. 
     Preferably, the various selected parameters for selecting the plurality of options from a universe of available options include at least risk and liquidity. Preferably also volatility is included. 
     Next an optimizer optimizes the selection of options from the available options according to at least a desired level of risk and/or a desired level of liquidity. Optionally, one parameter is given more weight than the other, such that greater deference may be given to risk than to liquidity. Preferably, volatility is also included in the optimization. 
     If an absolute optimized portfolio of options cannot be selected, for example because there are too many underlying securities and/or parameters to consider, then optionally an algorithm such as a clustering algorithm or a genetic algorithm may be used for the selection. 
     Optionally, the options are put options. Alternatively, the options are call options. If call options, the options are preferably sold while the same amount of the underlying security is bought, for covered call options. 
     The term “portfolio” as used herein relates to the portfolio of options unless otherwise indicated. The term “overall investment portfolio” is used to indicate a situation in which the portfolio of options is one of a plurality of investments. 
     In contrast to the background art, the present invention relates to a system and method in which two different types of investment components are analyzed for the purpose of building a portfolio: securities and options on such securities. Without wishing to be limited by a closed list, such an analysis enables the benefits of options to be combined with the benefits of securities, reducing risk while still providing for a beneficial upside to the investment. 
     Implementation of the method and system of the present invention involves performing or completing certain selected tasks or steps manually, automatically, or a combination thereof. Moreover, according to actual instrumentation and equipment of preferred embodiments of the method and system of the present invention, several selected steps could be implemented by hardware or by software on any operating system of any firmware or a combination thereof. For example, as hardware, selected steps of the invention could be implemented as a chip or a circuit. As software, selected steps of the invention could be implemented as a plurality of software instructions being executed by a computer using any suitable operating system. In any case, selected steps of the method and system of the invention could be described as being performed by a data processor, such as a computing platform for executing a plurality of instructions. 
     Although the present invention is described with regard to a “computing device”, a “computer”, or “mobile device”, it should be noted that optionally any device featuring a data processor and the ability to execute one or more instructions may be described as a computer, including but not limited to any type of personal computer (PC), a server, a distributed server, a virtual server, a cloud computing platform, a cellular telephone, an IP telephone, a smartphone, or a PDA (personal digital assistant). Any two or more of such devices in communication with each other may optionally comprise a “network” or a “computer network”. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention is herein described, by way of example only, with reference to the accompanying drawings. With specific reference now to the drawings in detail, it is stressed that the particulars shown are by way of example and for purposes of illustrative discussion of the preferred embodiments of the present invention only, and are presented in order to provide what is believed to be the most useful and readily understood description of the principles and conceptual aspects of the invention. In this regard, no attempt is made to show structural details of the invention in more detail than is necessary for a fundamental understanding of the invention, the description taken with the drawings making apparent to those skilled in the art how the several forms of the invention may be embodied in practice. In the drawings: 
         FIG. 1  shows an exemplary, non-limiting system for determining a balanced portfolio; 
         FIG. 2  shows calculation engine in more detail in a non-limiting, exemplary implementation; 
         FIG. 3  shows a non-limiting, exemplary method for determining a set of components in the portfolio and the price of the corresponding options; 
         FIG. 4  relates to a non-limiting, exemplary method for selecting the components and selling the options in greater detail; 
         FIG. 5  relates to a non-limiting, exemplary system, which is similar to that of  FIG. 1 , with some additional features; and 
         FIG. 6  relates to a non-limiting, exemplary method for using call options rather than put options. 
     
    
    
     DESCRIPTION OF AT LEAST SOME EMBODIMENTS 
     The present invention, in at least some embodiments, provides a system and method for portfolio optimization through optimized selection of options. Without wishing to be limited by a single hypothesis, the resultant selection of options is optimized to have a similar risk profile to a selected securities benchmark, but with a superior Sharpe ratio. As used herein, unless otherwise indicated, the reference to options and to creating a portfolio of options relate to selling options. 
     In terms of the selected securities benchmark, optionally the underlying securities of the options are determined according to a securities benchmark. Also optionally, a subset of such securities is selected before optimization of the options begins. Alternatively, all securities of the benchmark are considered during selection of the options. In each such case, the securities available are referred to as the universe of securities. 
     The selection of options, according to the universe of available securities, is then preferably performed according to a desired level of risk, liquidity, volatility or a combination thereof. Whether the calculations of each of risk, liquidity or volatility are performed with regard to the options themselves, the underlying securities or a combination thereof, preferably these parameters are optimized according to one or more criteria. For example, one or more parameters may be given preferential weight. 
     Optionally implied volatility of the options is modelled separately. Non-limiting examples of how to model such volatility include but are not limited to the approaches described in Bernales and Guidolin (“Can We Forecast the Implied Volatility Surface Dynamics of Equity Options? Predictability and Economic Value Tests”, 2013, https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2351203) and the above described paper by Avellaneda and Dobi. 
     According to at least some embodiments of the present invention, there is provided a system and method for using a particular type of option sales in a balanced portfolio to achieve a certain level that is desired of both risk and liquidity. The present invention is described with regard to both “put options” and “call options”, as the system and method described herein are operative for both types of options. A put option is an option contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying security at a specified price within a specified time. This is the opposite of a call option, which gives the holder the right to buy shares. Either type of option may be sold as an investment for a balanced portfolio, as described in greater detail below. 
     Briefly, regardless of the type of option sold, the balanced portfolio is constructed by selecting a plurality of options to be sold from a particular universe of options, to achieve a desired balance of risk and liquidity. The selected options may differ according to whether put options or call options are sold. 
     Turning now to the drawings, as shown in  FIG. 1 , there is a provided an exemplary, non-limiting system  100  for determining a balanced portfolio. System  100  comprises a user computational device  102 , which is in communication with a server  104  through a computer network  106 , such as the internet, for example. User computational device  102  operates a user interface  108 , which might optionally be a stand-alone software, alternatively, which may be a web browser, or the like. 
     Server  104  operates a server interface  110 , which is a software interface for communicating with user interface  108 , for example, for receiving commands from user interface  108  and for sending information to be displayed by the display of user computational device  102 . Server  104  also features a calculation engine  112  for calculating such parameters as the amount of risk and liquidity in the selected portfolio. Additionally or alternatively, calculation engine  112  may calculate such parameters as the desired length of time for which the option should be sold. For example, for a put option, the length of time would represent the period of time during which the underlying security could be bought at the specified price. For a call option, the length of time would represent the period of time during which the underlying security could be sold at the specified price. For example, the period of time (that is, the expiration date of the option) could optionally be 1 week, 1 month and so forth. An option with a shorter period of time provides a greater theta, so that selling 12 options sequentially, each with a one month expiry, would have a greater price than selling 1 option for 1 year. 
     Server interface  110  is preferably in communication with a database  114 . Database  114  preferably stores such information as historical prices, relative amounts of liquidity, if such information is available, or the parameters for calculating liquidity, if in fact the absolute liquidity is not known. Shorter option periods result in more liquidity. 
     Through user computational device  102 , the user interacts with user interface  108  and sends various commands to server  104 . Such commands may request information to determine the total amount of risk in a particular portfolio, and/or to determine the desired option period. Optionally, the user may also select particular components for the portfolio, and/or may adjust the portfolio manually. In that case, calculation engine  112  would need to recalculate the remaining portfolio to maintain balanced parameters. 
     Calculation engine  112  then performs calculations to determine which options, when selected for a particular portfolio from a universe of options, would be best according to the desired parameters. These parameters may comprise the level of risk, the actual liquidity, and the like, for example, by using information taken from database  114 . The user may then optionally choose to place an order through user computational device  102  and/or such an order may optionally be placed automatically through server  104 . For example, an automatic order may be placed to a market, as shown in  FIG. 5 . 
     Turning now to  FIG. 2 , calculation engine  112  is shown in more detail in a non-limiting, exemplary implementation. Tracking engine  112  preferably features an optimizer  200 , which receives information of various types, and uses such information to select the best portfolio from the universe of components. Optimizer  200  may also optionally select the best length of time during which the option should be sold, when the option should be rebalanced, such that this period of time is optionally optimized for the amount of risk and/or liquidity. 
     Optimizer  200  features a volatility calculator  202  for calculating volatility of the selected portfolio. Volatility information can be purchased for example, regarding the particular securities, to determine the implied volatility surface for the underlying securities. A back calculation is performed to determine the realized volatility of the underlying securities. Optionally, if a particular level of volatility is desired, optimizer  200  may consider various combinations of the different portfolio components before selecting a combination which supports the constraint of the desired volatility or volatility range. 
     Liquidity analyzer  204  analyzes the amount of liquidity in any given combination of portfolio components. For example, to be certain that the overall set of selected components have at least a certain minimum amount of liquidity. Optionally, liquidity analyzer  204  bases this information on historic liquidity or on calculations of a dynamic liquidity, for example, based on the rate of change daily trading levels and the like. Historic liquidity is preferably determined as the bid/ask spread. 
     Risk analyzer  206  determines the total of risk for a selected set of components, and may optionally also suggest to optimizer  200  in regard to particular components whether perhaps certain components should be included or not included. Optimizer  200  balances all of this information, modeling, in various ways, different sets of portfolio components. In case there are a very large number of components, making an absolute selection by calculating all possibilities would be difficult. Optionally, optimizer  200  relies on any suitable optimization algorithm, including but not limited to any constrained non-linear optimization algorithm, such as Active-Set from Matlab, a clustering or genetic algorithms, or other algorithms, for selecting a set of components from a large set of components, while preferably avoiding problems such as local minima. 
     Portfolio selector  208  then interacts with optimizer  200  to determine which portfolio components may be selected. Again, optimizer  200  may instruct portfolio selector  208  to keep various options, for example, to increase liquidity, to reduce risk, or to reduce volatility. In cases where certain components are felt to track each other too closely, portfolio selector  208  may be instructed by optimizer  200  to locate portfolio components which do not track each other so closely. 
       FIG. 3  shows a non-limiting, exemplary method  300  for determining a set of components in the portfolio and the price of the corresponding options. Optionally, put options are sold according the described implementation, although a similar implementation may be made for call options. For selling call options, a covered call is preferably used, so that for each option sold, the underlying security is purchased. This provides the desired balanced of an equity portfolio with reduced risk (although selling the covered call also reduces the upside). This is not required for selling a put option. In stage  302 , the desired risk in determined. The desired risk may optionally be determined through instructions from the user or, alternatively, may be determined through calculation, for example, according to a previously constructed portfolio which had a certain level of risk. Also, optionally, the level of desired risk may be determined according to an overall portfolio for a particular customer. In this case, a portfolio of selected options is determined so as not to increase the overall risk of the complete portfolio of the customer. 
     Next, the potential portfolio components are determined in stage  304 . This is the universe of components from which components may be selected for the options. For example, the user may set certain parameters, such as only options or stocks available on the S&amp;P 500 or another stock index, only stocks for which a certain amount of liquidity is available when options are sold, and so forth. 
     In stage  306 , the implied volatility is calculated according to the option prices, as available in the market, as previously described. In stage  308 , the actual historical prices are preferably received. Next, in stage  310 , the risk, volatility, and prices are preferably analyzed. According to this analysis, the optimized, actual portfolio components are selected in stage  312 . Again, if the universe of components is too large to make an absolute analysis of every potential combination, then alternatively the optimized, actual portfolio components are selected to an algorithm, such as a cluster algorithm, a genetic algorithm, and the like, which provide a heuristic measure for a particular selection and which seek to avoid such problems as local minima. 
     Once the components have been selected, the actual portfolio risk is determined in stage  314 . This portfolio risk is relative for the options. For example, such risk is determined according their length, and so optionally it may be determined that in order for the portfolio risk to not be excessive, the options should be a relatively short period of time, such as one week. Alternatively, if a certain minimum level of risk is desired, then the options may be sold for a longer period of time, such as one month or more. In stage  316 , the options are sold. 
       FIG. 4  relates to a non-limiting, exemplary method  400  for selecting the components and selling the options in greater detail. Again, the desired risk is calculated in stage  402 , but now so is the desired return in stage  404 . It may be necessary to balance the risk and return against each other at later stages. 
     Next, the expected liquidity is determined in stage  406 , for example, from the universe of components, which has been previously determined. The expected volatility is also then calculated in stage  408 , again, optionally for the entire universe of components from which selections may be made. In stage  410 , the components are selected according to the desired risk, the desired return, the expected volatility, and the expected liquidity, for example, to meet a certain balance between these factors. Optionally, if certain factors are more important than others, then the components are selected to best relate to those more important factors. For example, if liquidity must be at least a certain level or liquidity is considered more important than other parameters, than the components are selected in order to fulfill the desired level of liquidity, potentially at the expense of fulfilling the other parameters. 
     Next, the options period is determined in stage  412 . One reason for determining the options period is, for example, to be able to regulate the level of risk, so as to bring the level of risk closer to the desired risk. The potential return is then calculated in stage  414 . In stage  416 , the components are optionally adjusted to account for all of these different factors, including desired risk, desired return, expected liquidity, and expected volatility. 
     In stage  418 , the components are rebalanced and/or the options period is redone. This is necessary in order to provide a comprehensive portfolio that fulfills all of the requirements in a balanced manner. In stage  420 , the options are sold. 
     One non-limiting example of a method that can be used for optimization of the selection of the options is as follows. The goal of the method is to find the options portfolio that maximize the “Semi Implied Diversification Ratio”—SIDR. The SIDR is defined as the sum of the weighted implied volatilities of the constituents of the portfolio divided by the portfolio expected realized volatility. 
     
       
         
           
             
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     Where w is the weights vector of the portfolio constituents&#39; universe, s is the implied volatilities of the portfolio constituents&#39; universe, V is the covariance matrix and σ(w)is the realized portfolio volatility for a vector w. 
     The implied option volatility is optionally calculated by inversing Black-Scholes formula. For this calculation to be performed, the price of the option, the expiration date, dividend yield, interest rate, strike price and underlying price of the security are input into the inverse formula, to obtain the volatility. The price for the options is the market price (that is, the price offered by the market for the particular option and expiration date). 
     The covariance matrix is preferably calculated according to the standard calculation, optionally plus one or more weights. For example the matrix may be exponentially weighted for a more recent time period than for data from a period that is farther back in the past. 
     Weights for portfolio are determined according to how much of the portfolio is taken up by each option. The maximum amount of any given option or group of options may be limited. 
     In this implementation, the optimizer seeks to create a portfolio with the biggest SIDR ratio, optionally as constrained by other factors (such as liquidity, volatility and/or overall risk levels). 
     The method provides exposure to more than just price with implied volatility, thereby bringing in other risk factors, which may be adjusted according to the desired weight of the above factors. 
       FIG. 5  relates to a non-limiting, exemplary system  500 , which is similar to that of  FIG. 1 , with some additional features. Optionally, a command is given to purchase interface  502  to automatically execute the selling and/or buying commands, which are then transmitted to purchase server  504 , which may be, for example, on a particular stock exchange or other market, or a plurality of such exchanges. The connection to purchase server  504  may optionally be described as a market interface. 
       FIG. 6  relates to a non-limiting, exemplary method  600 , in relation to using call options rather than put options. Calculated risk is calculated in stage  602 . Desired return is calculated in stage  604 . Expected liquidity is determined in stage  606 , and expected volatility is determined in stage  608 . Because of the slightly different nature of what is being purchased, it is possible that these factors will be affected by this. 
     In stage  610 , the components are selected and then the period is determined in stage  612 . Again, because of the different nature of what is being sold, it is possible that this period will need to be adjusted. Of course, the potential return in stage  604  may differ, and hence the need to adjust components in stage  606  may differ. Rebalancing of the components and of the period is also expected to be different in stage  618 . The options are then sold in stage  620 A, while the underlying securities are purchased in stage  620 B, for covered call options. These two stages are preferably performed in parallel. 
     It is appreciated that certain features of the invention, which are, for clarity, described in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention, which are, for brevity, described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. 
     Although the invention has been described in conjunction with specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, it is intended to embrace all such alternatives, modifications and variations that fall within the spirit and broad scope of the appended claims. All publications, patents and patent applications mentioned in this specification are herein incorporated in their entirety by reference into the specification, to the same extent as if each individual publication, patent or patent application was specifically and individually indicated to be incorporated herein by reference. In addition, citation or identification of any reference in this application shall not be construed as an admission that such reference is available as prior art to the present invention.