Property funds: how much diversification is enough?

t is well known that when assets are randomly-selected and combined in equal proportions in a portfolio, the risk of the portfolio declines as the number of different assets increases without affecting returns. In other words, increasing portfolio size should improve the risk/return trade-off compared with a portfolio of asset size one. Therefore, diversifying among several property funds may be a better alternative for investors compared to holding only one property fund. Nonetheless, it also well known that with naïve diversification although risk always decreases with portfolio size, it does so at a decreasing rate so that at some point the reduction in portfolio risk, from adding another fund, becomes negligible. Based on this fact, a reasonable question to ask is how much diversification is enough, or in other words, how many property funds should be included in a portfolio to minimise return volatility.

Closed form approximations for spread options

This article expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new closed form approximation for the price of a European spread option and a corresponding approximation for each of its price, volatility and correlation hedge ratios. Our approach has many advantages over existing analytical approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur costs. Simulations quantify the accuracy of our approach; we also present an empirical application to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996, Correlation in energy markets. In: V. Kaminski (Ed.), Managing Energy Price Risk, pp. 71–78 (London: Risk Publications)), which is commonly used by traders.

Rational speculative bubbles: an empirical investigation of the London Stock Exchange

In recent years, a sharp divergence of London Stock Exchange equity prices from dividends has been noted. In this paper, we examine whether this divergence can be explained by reference to the existence of a speculative bubble. Three different empirical methodologies are used: variance bounds tests, bubble specification tests, and cointegration tests based on both ex post and ex ante data. We find that, stock prices diverged significantly from their fundamental values during the late 1990's, and that this divergence has all the characteristics of a bubble.