There are two essentially different kinds of rigidity . "'Finite "'or "'macroscopic rigidity "'means that the structure will not flex, fold, or bend by a positive amount . "'Infinitesimal rigidity "'means that the structure will not flex by even an amount that is too small to be detected even in theory . ( Technically, that means certain differential equations have no nonzero solutions . ) The importance of finite rigidity is obvious, but infinitesimal rigidity is also crucial because infinitesimal flexibility in theory corresponds to real-world minuscule flexing, and consequent deterioration of the structure.
12.
Its vertical intercept represents a portfolio with 100 % of holdings in the risk-free asset; the tangency with the hyperbola represents a portfolio with no risk-free holdings and 100 % of assets held in the portfolio occurring at the tangency point; points between those points are portfolios containing positive amounts of both the risky tangency portfolio and the risk-free asset; and points on the half-line beyond the tangency point are leveraged portfolios involving negative holdings of the risk-free asset ( the latter has been sold short in other words, the investor has borrowed at the risk-free rate ) and an amount invested in the tangency portfolio equal to more than 100 % of the investor's initial capital.
