Some empirical studies suggest that the computation of certain graph structures from a (large) historical correlation matrix can be helpful in portfolio selection. In particular, a repeated finding is that information about the portfolio weights in the minimum variance portfolio (MVP) from classical Markowitz theory can be inferred from measurements of centrality in such graph structures. The present article compares the two concepts from a purely algebraic perspective. It is demonstrated that this heuristic relationship between graph centrality and the MVP is not inner-mathematical, at least not significantly strong. This means that empirically found relations between both concepts depend critically on the underlying historical data. Repeated empirical evidence for a strong relationship is hence shown to constitute a stylized fact of financial return time series, rather than the expected outcome of a heuristic similarity between both approaches.
The negative basis is an annualized earnings figure that measures the expected excess return of a bond investment over a reference discounting rate, after credit risk has been hedged away via credit default swap (CDS) protection. Unfortunately, the most appropriate measurement of the negative basis is in terms of a root of a non-trivial decreasing function. The goal of the present article is to derive closed proxy formulas for the negative basis, at least in special situations. Under the assumption that a credit event before maturity of bond (and CDS) is certain, i.e. conditioned on default before maturity, we are able to derive a very simple formula. Furthermore, a small enhancement of the formula provides a proxy formula for the (unconditional) negative basis. The availability of such closed formulas allows to study qualitative properties of the negative basis, such as dependence on the recovery rate assumption or leg prices
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