of handling. Specifically, an adjustment needs to be made so as to not overestimate the contribution of risk from a composite asset. This adjustment is required because a portfolio may hold an asset (e.g., IBM) and then hold a futures contract on a composite portfolio that contains that asset (e.g., S&P 500). Without such an adjustment, we are not guaranteed zero specific risk in the presence of a perfect hedge. In order to correctly measure specific risk when dealing with futures and ETFs, we need to create a new set of managed weights. These new weights-represented as an N-vector-are computed as follows: <Jt~ 1) = <fataJt-T) + "CJf- 1) x "/*(*- 1) (20.97) where w^future(£- 1) = eX "wP(t-l) = Original managed weights, excluding the futures position Managed weights on the underlying assets in the futures or ETFs Weight of the futures contract in the managed portfolio; defined as the futures market exposure divided by the portfolio's net worth To understand how (20.97) works, suppose that a portfolio held a common stock outright and its weight in the portfolio is 3 percent (excluding the futures). In addition, the portfolio holds futures contracts on a composite portfolio. The weight of the futures contract in the portfolio is 5 percent and the weight of the asset in the composite portfolio is 4 percent. In this case, we have "/£(£- 1) =4%; tvfct]iie(t - 1) = 5%:andw/* (f-1) = 3%. ' ex tuture * ' Note that when a futures position is not held with respect to a particular asset, then wf (t - 1) = 0 and wp At - 1) =ivp , It - 1). and the modified weights are future* ' mod* ' ex tuture * " " the same as the original portfolio weights without the futures. How Does Cash Affect Tracking Error? At some point, an equity portfolio will hold some amount of cash. In this section we study the role that cash plays in the tracking error of an equity portfolio. First, we need to be clear on the definition of cash. By cash, we mean the local risk-free investments. Investments in foreign risk-free assets (i.e., foreign cash) have currency risk associated with them and, therefore, do not fall under our definition of cash. Second, we need to be clear on the definition of risk. While it is straightforward to understand the impact of changes in cash to a portfolio's volatility, it is not so simple when it comes to understanding the role of cash in affecting tracking error. As explained in the section on cash, an increase (a decrease) in the amount of cash in a portfolio decreases (increases) the weights of the equity positions. Hence, since cash is assumed to be a riskless asset (it has zero volatility and zero correlation), increases in cash tend to reduce a portfolio's volatility. This effect comes basically from reducing the weights in the risk positions and increasing the weight in the riskless position. This is an intuitive result. Now, when measuring tracking error, we need to understand how changes in