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In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates (duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change in ...
Merton's portfolio problem is a problem in continuous-time finance and in particular intertemporal portfolio choice. An investor must choose how much to consume and must allocate their wealth between stocks and a risk-free asset so as to maximize expected utility .
Convexity is a geometric property with a variety of applications in economics. [1] Informally, an economic phenomenon is convex when "intermediates (or combinations) are better than extremes". For example, an economic agent with convex preferences prefers combinations of goods over having a lot of any one sort of good; this represents a kind of ...
In the Arrow–Debreu approach, convexity is essential, because such fixed-point theorems are inapplicable to non-convex sets. For example, the rotation of the unit circle by 90 degrees lacks fixed points, although this rotation is a continuous transformation of a compact set into itself; although compact, the unit circle is non-convex.
Any discussion of fixed-income attribution therefore requires an appreciation of how changes in the curve are described, and their effect on the performance of a portfolio. If one is only interested in gross changes in the yield curve at a particular maturity, then one can read yields off the various datasets, using interpolation where ...
The model is a short-rate model.In general, it has the following dynamics: = [() ()] + ().There is a degree of ambiguity among practitioners about exactly which parameters in the model are time-dependent or what name to apply to the model in each case.
Examples [ edit ] In the LM model of interest rate determination, [ 1 ] : pp. 261–7 the supply of and demand for money determine the interest rate contingent on the level of the money supply, so the money supply is an exogenous variable and the interest rate is an endogenous variable.
For example, assuming 3.88% inflation over the course of one year (just about the 56 year average inflation rate, through most of 2006), and a real yield of 2.61% (the fixed US Treasury real yield on October 19, 2006, for a 5 yr TIPS), the adjusted principal of the fixed income would rise from 100 to 103.88 and then the real yield would be ...