Methods for measuring hedging value-at-risk and profitability

Abstract

Methods for measuring value-at-risk and profitability of hedging in relation to BMA debt obligations are provided using rigorous, statistical solutions that address problems associated with municipalities involved in swap hedging face. Various embodiments permit users to quantify POL hedging basis risk through a VAR-style loss measurement and statistics measuring the profitability of a hedge, those statistics including gain durability and gain/loss ratio. Various aspects introduce significant innovation to risk management practices, particularly for tax-exempt issuers of debt. Certain embodiments of this disclosure facilitate better management of hedging risk, analysis of hedges using POL vs. BMA and provide guidance for analyzing the risk existing in an existing portfolio of POL swap hedges to better inform decision-making regarding use of hedging risk for profit or to lay off risk.

1 . A computer-implemented method for quantifying risk-return trade-offs, comprising:
 providing a data processing system comprising a processor, a user interface, and a memory;   using the processor, calculating a risk-weighted expected return for each of a time series of financial positions based on a risk-return statistic for said each financial position and storing the risk-weighted expected return in the memory, wherein the time series of financial positions represents a transaction.   
     
     
         2 . The method of  claim 1 , wherein each of the time series of financial positions is calculated as a cash flow projection. 
     
     
         3 . The method of  claim 1 , and further comprising calculating an average of a series of risk-return statistics, each of the series of risk-return statistics corresponding to one of the time series of financial positions. 
     
     
         4 . The method of  claim 3 , wherein the average measures the attractiveness of a transaction. 
     
     
         5 . The method of  claim 1 , wherein the risk-return statistics are provided via the user interface as Sharpe Ratios. 
     
     
         6 . The method of  claim 1 , wherein each of the risk-return statistics is expressed as a return divided by standard deviation of the return. 
     
     
         7 . The method of  claim 1 , wherein each of the risk-return statistics is provided as a probability of realizing a gain of the financial position. 
     
     
         8 . The method of  claim 7 , wherein the probability represents a level of security of potential gains. 
     
     
         9 . The method of  claim 7 , wherein the probability is measured as gain durability. 
     
     
         10 . The method of  claim 7 , wherein the probability is measured as the probability that an expected gain will be realized or exceeded. 
     
     
         11 . The method of  claim 2 , wherein each risk-return statistic quantifies the ratio of a put value of the financial position to a call value of the financial position. 
     
     
         12 . The method of  claim 11 , wherein the put value and the call value are synthesized from cash flow calculated for each financial position in the time series. 
     
     
         13 . The method of  claim 1 , wherein the risk-return statistics include Sharpe Ratios, gain durability statistics and ratios of put value of a financial position to call value of the financial position. 
     
     
         14 . The method of  claim 1  and further comprising using the processor to estimate a value-at-risk (“VAR”) representative of maximum potential loss associated with the time series of financial positions. 
     
     
         15 . The method of  claim 14 , further comprises calculating a risk-weighted expected return for each of the time series of financial positions based on the risk-return statistics. 
     
     
         16 . The method of  claim 14 , further comprising:
 simulating a BMA-Libor spread;   simulating the probability of occurrence of a tax rate change within a selected time period; and   simulating a magnitude of the tax rate change.