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High-convexity portfolios outperform low-convexity portfolio

a) Whether the bond market moves up or down, high-convexity portfolios will for all time outperform low-convexity portfolios of equal duration and yield." Elucidate the argument supporting this statement and the connection to the classical immunization strategy. What factors would tend to undermine the validity of the statement?

b) An important drawback of "traditional yield spread analysis" is the "failure to take into account future interest rate volatility that would affect the expected cash flow" of a fixed income security. How does option adjusted spread analysis correct for the "failure" of traditional yield spread analysis in the valuation of bonds with embedded option features? Once the choice adjusted spread has been determined, how can the cost of option be calculated? What are some important pitfalls of using option adjusted spread analysis to value mortgage backed securities and other collateralized debt obligations?

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