In comparing the relative merits of smaller and larger portfolios, Aristotle’s ideas about virtue may provide a useful analogy. He wrote:

Virtue, then, is a state of character concerned with choice, lying in a mean, i.e. the mean relative to us, this being determined by a rational principle, and by that principle by which the man of practical wisdom would determine it. Now it is a mean between two vices, that which depends on excess and that which depends on defect; and again it is a mean because the vices respectively fall short of or exceed what is right in both passions and actions, while virtue both finds and chooses that which is intermediate. Hence in respect of its substance and the definition which states its essence virtue is a mean, with regard to what is best and right an extreme.

Likewise, most everyone would agree that a portfolio could be too large or too small and the best portfolio would be somewhere in between. But what is the appropriate “rational principle” to determine the mean and how should that balance be maintained? One solution is to impose a numerical limit on the size of the portfolio, or a limit on the percentage allocation to the product within a larger portfolio. These types of strict limits are likely to be counterproductive, leading to excessive investment at times and inadequate investment at the time of greatest opportunity.

One solution to the problem is capital. Capital allocation provides the mechanism to allow a portfolio to achieve its desired objectives. By allocating capital to a portfolio, developing risk management requirements and establishing a required return on equity, a portfolio can naturally find its appropriate size. When opportunities are greater, the portfolio can grow to take advantage of those opportunities, when opportunities are not present, or are greater elsewhere, the portfolio will shrink.

The appropriate amount of capital can be determined by considering the overall contribution of the risk of the portfolio to the overall risk of the firm. Marginal VaR (Value at Risk) provides an indication of the amount of capital required. (Other considerations may lead a firm to deviate from the amount indicated by this theory, nevertheless the theory is instructive.)

Suppose a firm has a $100 billion position in an asset that has a standard deviation risk of 5%. Suppose the firm has the opportunity to grow a portfolio of a second asset. The second asset has the same standard deviation of risk of 5%. Suppose the second asset has an 80% correlation to the first asset. What is the marginal increase in standard deviation of the portfolio per $10 billion increase in portfolio of the second asset?

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