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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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Kamakura Corporation
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Fax: 808.791.9898
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Over the three day Martin Luther King holiday in the USA, another event took place in Santiago that brought a smile to my face.  This blog is an appreciation of one of my favorite people, Sebastián Piñera, newly elected President of Chile.

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In the first 10 installments of this series on yield curve smoothing, we committed the most common sin there is in the yield curve smoothing literature.  We used one set of “made up” data instead of hundreds or thousands of real data points to judge the performance of yield curve smoothing techniques.  In this blog, we explain why the test proposed by David Shimko is essential to judging the accuracy and realism of yield curve smoothing techniques.  We dust off some old yield data from the attic to illustrate how the test works.

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After riding up Mauna Kea volcano yesterday, Lance Armstrong is getting ready to travel from the Big Island of Hawaii to Adelaide for the Tour Down Under and the start of the 2010 cycling season.  Thanks to a blog that I stumbled on over the holidays, it seems like a good time to appreciate the risk management lessons from Lance over the years.  That’s the subject of today’s post.

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The author wishes to thank Keith Luna of Western Asset Management Company for helpful comments that led to this new version.

In Part 10 of this series, we present the final installment in yield curve and forward rate smoothing techniques before moving on to smoothing credit spreads.  We introduce the maximum smoothness forward rate technique introduced by Adams and van Deventer (1994) and corrected in van Deventer and Imai (1996), which we call Example H.  We explain why a quartic function is needed to maximize smoothness of the forward rate function over the full length of the forward rate curve. The conclusion is similar to the fact that a curve constructed from twice differentiable yield curve segments produces a shorter length yield curve over the full length of the curve than a “curve” with linear segments, even though the shortest length between any two points is a linear function.

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In Part 8 of this series, we observed that it has been proven that a cubic spline, in general, produces the smoothest set of curves that one can draw between data points.  This is certainly true in the case of smoothing the yield curve. As we show in part 10 of this blog series, this is NOT TRUE in the case of a cubic spline of forward rate curves if we apply the normal constraints one needs to fit observable financial data. In this post, we ignore that insight and flail ahead, erroneously assuming that if splines work reasonably well when applied to yields, they will work even better when applied to forward rates. In Example G, we apply cubic splines to forward rates and derive the related yields.  The results clearly illustrate why a true “maximum smoothness” approach is needed. We deliver that approach in Part 10, which explains the full maximum smoothness approach first proposed by Adams and van Deventer in 1994.

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