A Note on the Myers and Read Capital Allocation Formula

The Myers and Read capital allocation formula is an important new actuarial result. In this paper, we give an overview of the Myers and Read result, explain its significance to actuaries, and provide a simple proof. Then we explain the assumption the allocation formula makes on the underlying families of loss distributions as expected losses by-line vary. We show that this assumption does not hold when insurers grow by writing more risks from a discrete group of insureds--as is typically the case. Next, we discuss whether the inhomogeneity in a realistic portfolio of property casualty risks is material. We show how to decompose the relevant partial derivatives into homogeneous and inhomogeneous parts and examine the behaviour of each. We then apply the theory to some realistic examples. These clearly show that the lack of homogeneity is material. This failure will severely limit the practical application of the Myers and Read allocation formula.