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Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura. Read More

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President Obama’s pay czar Kenneth Feinberg has a daunting task.  He has to intervene and override “market forces” to establish “fair pay” for the CEOs of major institutions that are reliant on government support for their survival.  The difficulty in this process is a simple fact: football coaches are paid for their skill, but large company CEOs are not.  Large company CEOs, with a few exceptions, are winners of a lottery that entitles them to huge payouts during their brief tenure.  On behalf of the shareholders, the Boards of Directors of these firms have to do a better job of separating luck from skill.

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In Part 6 of our series on the basic building blocks of yield curve smoothing, we learn from our results in Part 5 (linear forward rates).  We found in Part 5 that, for forward rates to be continuous and linear, we induced too much of a saw-tooth pattern in forward rates, even though the yields implied by these forward rates looked reasonable. In this post, we turn to Example D, in which we seek to “take the teeth out of the saw tooth pattern” by requiring that the first derivatives of the curve segments we fit be equal at the knot points.  We use a quadratic spline of yields to achieve this objective, and we optimize to produce the “maximum tension/minimum length” yields and forwards consistent with the quadratic splines. Finally, we compare the results to the popular but flawed Nelson-Siegel approach and gain still more insights on how to further improve the realism of our smoothing techniques.

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In Part 5 of our series on the basic building blocks of yield curve smoothing, we make another adjustment of the constraints we’ve imposed on the “best” yield curve.  We find that our criterion for best implies linear segments for forward rates, as in the linear yield example in Part 4. The related yields, however, are not linear. The other difference in Example C, which we explain here, is that we require the forward rates to be continuous to avoid the unrealistic jumps in forward rates at the knot points which we saw in Example B, the case of linear yields. We again compare the results to the popular but flawed Nelson-Siegel approach and gain still more insights on how to further improve the realism of our smoothing techniques.

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In Part 4 of our series on the basic building blocks of yield curve smoothing, we tweak our constraints on the “best” yield curve and find that our criterion for best implies linear segments for both yields and forwards.  We compare the results to the popular but flawed Nelson-Siegel approach and gain insights on how to further improve the realism of our smoothing techniques, a step forward we will make in part 5 of this series. 

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In this installment of our yield curve smoothing series, we choose a common definition of “best” yield curve or forward rate curve and a simple set of constraints. We derive from our definition of “best” and the related constraints the fact that the “best” yield curve in this case is stepwise constant yields and forward rates.  We then show that even this simplest of specifications is more accurate and “better” by our definition that the popular but flawed Nelson-Siegel approach. 

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