Financial Derivatives Toolbox

Example: Minimize Portfolio Sensitivities

To illustrate using hedgeopt to minimize portfolio sensitivities for a given maximum target cost, specify a target cost of $20,000 and determine the new portfolio sensitivities, holdings, and cost of the rebalanced portfolio.

• MaxCost = 20000;
  [Sens, Cost, Quantity] = hedgeopt(Sensitivities, Price,... 
  Holdings, [1 4 5 7 8], [], MaxCost);
  
  Sens =
  
        -4345.36        295.81      -6586.64
  
  Cost =
  
         20000.00
  
  Quantity' =
  
          100.00
         -151.86
         -253.47
           80.00
            8.00
          -18.18
           40.00
           10.00
  

This example corresponds to the $20,000 point along the cost axis in Figure 3-1, Figure 3-2, and Figure 3-3.

When minimizing sensitivities, the maximum target cost is treated as an inequality constraint; in this case, MaxCost is the most you are willing to spend to hedge a portfolio. The least squares objective matrix C is the matrix transpose of the input asset sensitivities

• C = Sensitivities'
  

a 3-by-8 matrix in this example, and d is a 3-by-1 column vector of zeros,
[0 0 0]'.

Without any additional constraints, the least squares objective results in an under-determined system of three equations with eight unknowns. By holding assets 1, 4, 5, 7, and 8 fixed, you reduce the number of unknowns from eight to three. Now, with a system of three equations with three unknowns, hedgeopt finds the solution shown.

Example: Fully Hedged Portfolio

Example: Under-Determined System