Reducing sequence risk using trend following and the CAPE ratio

The risk of experiencing bad investment outcomes at the wrong time, or sequence risk, is a poorly understood, but crucial aspect of the risk faced by investors, in particular those in the decumulation phase of their savings journey, typically over the period of retirement financed by a defined contributions pension scheme. Using US equity return data from 1872-2014 we show how this risk can be significantly reduced by applying trend-following investment strategies. We also demonstrate that knowledge of a valuation ratio such as the CAPE ratio at the beginning of a decumulation period is useful for enhancing sustainable investment income

General closed-form basket option pricing bounds

This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms; hence, they do not suffer from the curse of dimensionality and can be applied also to high-dimensional problems where most existing methods fail. In particular, we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate