This paper derives formulas for higher order duration measures, including D(1) (i.e. Macaulay duration), D(2) (i.e., slope duration), D(3) (curvature duration), etc. We develop a general iterative method to obtain formulas for any higher order measure D(m), for an arbitrary positive integer...

VaR_Delta-Normal fails in two counts: subadditivity and potentially producing losses larger than its portfolio value. This paper solves the second inconsistency developing formulas derived from a put option, named PVaR_Delta-Normal and Put_Expected_Shortfall, PSF_Delta-Normal; the latter also...

This paper presents a critical review of the different versions of the LIBOR market model (LMM). Based on the new taxonomy of the term structure models (see Nawalkha, Beliaeva, and Soto [2007a, 2007b]) the typical application of the LMM are shown to triple-plus type, exposing these to the...

The 30-year U.S. swap spreads have been negative since September 2008. We offer a novel explanation for this persistent anomaly. Through an illustrative model, we show that underfunded pension plans optimally use swaps for duration hedging. Combined with dealer banks' balance sheet constraints,...

The 30-year U.S. swap spreads have been negative since September 2008. We offer a novel explanation for this persistent anomaly. Through an illustrative model, we show that underfunded pension plans optimally use swaps for duration hedging. Combined with dealer banks' balance sheet constraints,...

In recent years many US corporate pension plans have closed and entered their “end-state.” As end-state plans have become more prevalent, their special portfolio management challenges, including asset allocation, have gained attention.Pure immunization with public fixed income assets...

Institutional investors have increased their allocation to private assets to capture a potential return premium over public assets and diversification benefits. However, an allocation to private assets, which typically are less liquid than public assets, raises questions: “How does an...

We introduce a new approach to model the market smile for inflation-linked derivatives by defining the Quadratic Gaussian Year-on-Year inflation model -- the QGY model. We directly define the model in terms of a year-on-year ratio of the inflation index on a discrete tenor structure, which,...

Movements in prices depend both on innovations to cashflows and changes in discount rates, which can be modelled as fluctuations in the cross-sectional distribution of wealth across an unchanging set of investment objectives. This paper explores the risk that arises when investors do not have...

Recently, commodity index investing has come under attack. A Staff Report by the U.S. Senate Permanent Subcommittee on Investigation (hereafter, the "subcommittee report") "…finds that there is significant and persuasive evidence to conclude that these commodity index traders, in the...