It has been said [2, 4, 5, 6, 7, and 8], and it seems to be widely accepted, that the geometric mean of the price relatives of a group of securities can be interpreted as the return which would have been earned on a portfolio of those securities, managed continuously over time to maintain an equal money investment in each security. This is a theoretical concept which could not be implemented literally by a portfolio manager, but it can still be treated rigorously in a mathematical sense. In a recent paper in this journal Rothstein [8] defined continuous reallocation as the limiting case of a policy which does have an operational definition. He showed that the index corresponding to a policy of the equalization of dollar investments approaches the geometrically averaged index as its limiting value. We shall argue that this interpretation of the geometric mean is a misleading one, since it depends upon assumptions which imply serious market inefficiencies.

The paper explores the economic value of being able to span market outcomes through the use of options. We model an economy with a single risky asset. Consumption takes place at one date, corresponding to the horizon of all investors. Options on the consumption good are not redundant securities in the economy because volatility is uncertain. The model enables us to examine the benefits to investors of using options to optimize their investments. Within this model, the gains from the use of options appear to be relatively minor.

Much attention has been devoted to understanding and modeling the dynamics of implied volatility curves and surfaces. This is crucial for both trading, pricing and risk management of option positions. We suggest a simple, yet flexible, model, based on a discrete and linear Kalman filter updating of the volatility skew. From a risk management perspective, we assess whether this model is capable of producing good density forecasts of daily returns on a number of option portfolios. We also compare our model to the sticky-delta and the vega–gamma alternatives. We find that it clearly outperforms both alternatives, given its ability to easily account for movements of different nature in the volatility curve.

ABSTRACT In this paper, we examine leasing as a tax‐arbitrage instrument. Analysis of a sample of UK leases presented in this paper suggests that lessors earn large positive NPVs. Our theoretical model seeks to explain these positive NPVs in terms of a market price for a scarce resource that we identify as scarce taxable earnings. Using these prices, the model permits a lessor to determine whether the profitability of a proposed set of lease contracts can be improved by writing a different set of contracts that makes better use of the lessor's taxable earnings. There may be two reasons why an initial portfolio of contracts may be suboptimal. Either there may be clienteles or the leasing market may be inefficient. Subsequently, we discuss reasons why the leasing market may be characterized by clienteles, and, using two different samples of leases, we test whether the leasing market is segmented and efficient.