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Financial Engineering PrinciplesA Unified Theory for Financial Product Analysis and Valuation phần 8

chúng tôi có thể cố gắng để tái tạo hồ sơ cá nhân chi trả được hiển thị trong hình 5,10. Nếu thời gian Macaulay của phiếu giảm giá mang hai-năm Kho bạc tại chỗ là 1,75 năm, tất cả số tiền mặt trị giá 1 triệu USD của Kho bạc hai năm đó được mua, chúng tôi đi dài bảy tương lai hóa đơn Kho bạc với ngày hết hạn so le. | Risk Management 193 venience can create a unique volatility-capturing strategy. By going long both Treasury bill futures and a spot two-year Treasury we can attempt to replicate the payoff profile shown in Figure 5.10. If the Macaulay duration of the spot coupon-bearing two-year Treasury is 1.75 years for every 1 million face amount of the two-year Treasury that is purchased we go long seven Treasury bill futures with staggered expiration dates. Why seven Because 0.25 times seven is 1.75. Why staggered So that the futures contracts expire in line with the steady march to maturity of the spot two-year Treasury. Thus all else being equal if the correlation is a strong one between the spot yield on the two-year Treasury and the 21-month forward yield on the underlying three-month Treasury bill our strategy should be close to delta-neutral. And as a result of being delta-neutral we would expect our strategy to be profitable if there are volatile changes in the market changes that would be captured by net exposure to volatility via our exposure to convexity. Figure 5.11 presents another perspective of the above strategy in a total return context. As shown return is zero for the volatility portion of this strategy if yields do not move higher or lower from their starting point. Yet even if the volatility portion of the strategy has a return of zero it is possible that the coupon income and the income from reinvesting the coupon cash flows from the two-year Treasury will generate a positive overall return. Return Price profile for a 3-month Treasury bill 21 months forward and leveraged seven times Price level Price profile for a spot 2-year Treasury Starting point and point of intersection between spot and forward positions also corresponds to zero change in respective yields This gap represents the difference between duration alone and duration plus convexity the strategy is increasingly profitable as the market moves Yields lower Yields higher Changes in yield .