Financial Derivatives Toolbox

Portfolio Rebalancing

As a final example of user-specified constraints, rebalance the portfolio using the second hedging goal of hedgeopt. Assume that you are willing to spend as much as $20,000 to rebalance your portfolio, and you want to know what minimum portfolio sensitivities you can get for your money. In this form, recall that the target cost ($20,000) is treated as an inequality constraint during the optimization process.

For reference, invoke hedgeopt without any user-specified linear inequality constraints.

• [Sens, Cost, Quantity] = hedgeopt(Sensitivities, Price,... 
  Holdings, FixedInd, [], 20000);
  
  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 result corresponds to the $20,000 point along the Portfolio Sensitivities Profile shown in Figure 3-3, Rebalancing Cost,.

Assume that, in addition to holding instruments 1, 4, 5, 7, and 8 fixed as before, you want to bound the position of all instruments to within +/- 150 contracts (for each instrument, you cannot short more than 150 contracts and you cannot long more than 150 contracts). These bounds disallow the current position in the second and third instruments (-151.86 and -253.47). All other instruments are currently within the upper/lower bounds.

As before, you can generate these constraints by first specifying the lower and upper bounds vectors and then calling portcons.

• LowerBounds = [-150 -150 -150 -150 -150 -150 -150 -150];
  UpperBounds = [ 150  150  150  150  150  150  150  150];
  ConSet = portcons('AssetLims', LowerBounds, UpperBounds);
  

To impose these constraints, again call hedgeopt with ConSet as the last input.

• [Sens, Cost, Quantity] = hedgeopt(Sensitivities, Price,... 
  Holdings,FixedInd, [], 20000, [], ConSet);
  
  Sens =
  
        -8818.47        434.43      -4010.79
  
  Cost =
  
        19876.89
  
  Quantity' =
  
          100.00
         -150.00
         -150.00
           80.00
            8.00
          -28.32
           40.00
           10.00
  

With these constraints hedgeopt enforces the lower bound for the second and third instruments. The cost incurred is $19,876.89.

Setting Constraints

Hedging with Constrained Portfolios