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Equity Risk Factor Models 389 cent ($18,750/$318,750). Note that the sum of the portfolio weights does not


equal 100 percent. A popular methodology, and one used in some commercially available risk systems, measures the risk of futures by assuming a no-arbitrage condition. According to this approach, entering into a futures contract involves converting the futures position into a long spot position on the underlying asset (e.g., S&P 500) and an equivalent short cash position. This methodology assumes that holding a short-dated futures contract is equivalent (in both risk and return terms) to borrowing cash at the spot price and buying the underlying asset. For example, an S&P 500 futures position with a total market value of $500,000 would enter a portfolio as a short $500,000 cash position and a long $500,000 position in the underlying S&P 500 spot composite. By treating futures in this way, we note that: II The portfolio's market value remains unchanged. II The total market value of equity positions increases by the amount of the futures position. II Adding a futures position is indistinguishable from adding a set of the underlying assets. An alternative methodology for measuring the risk of futures positions would treat these positions as separate and distinct whose risk and return are driven by an underlying composite. Futures positions would be mapped to the underlying equity exposures, returns, and prices. Since entering into a futures contract is costless, the futures position does not affect the cash in the portfolio, except for the margin that is allocated to enter into the futures contract. To understand this approach to modeling futures, refer to the previous example of an S&P 500 futures position with a total exposure of $500,000. In this case, we would increase the portfolio's cash position by the initial margin and compute the weight on the futures contract as $500,000 divided by the portfolio's total invested capital. Exchange-traded funds (ETFs) are securities that represent underlying composite portfolios but are traded on exchanges like stocks. Two examples of ETFs are Russell iShares and Standard & Poor's Depositary Receipts, or "spiders" (SPDRs). SPDRs are exchange-traded securities, or units (like a mutual fund), that represents ownership in the SPDR unit investment trust. The SPDR trust was established to accumulate and hold a portfolio of common stocks that is intended to track the price performance and dividend yield of the S&P 500 composite index. Hence, it is reasonable to expect the market value of a SPDR to move closely with the S&P 500. SPDRs are engineered to provide a security whose market value approximates one-tenth of the value of the underlying S&P 500 index. SPDRs are created and redeemed with an actual portfolio of securities and in quantities of 50,000 SPDR creation units. SPDRs or any other ETFs should be modeled the same way as common stock. That is, an ETF takes in positions, prices, and returns, and computes weights and related risk and return statistics.