Following up on my post from November 1, here is a matrix of the Macaulay durations for a range of equity portfolios. The conclusion is obvious: the amount of the upfront payment is far more significant in determining equity duration than the growth rate. The incremental growth rate, and the incremental expected return or discount rate, ends up being almost trivial in the calculation. Cash is king.
| Macaulay Duration Matrix for Equity Portfolios | ||||||||||||||||
| The “Dividend” Market | The Stock Market | The “Dividend Growth” Market | ||||||||||||||
| Yield | 4.0% | 4.0% | 4.0% | 2.0% | 2.0% | 2.0% | 2.0% | 2.0% | 3.0% | 3.0% | 3.0% | 3.0% | 3.0% | |||
| Div Growth | 4.0% | 4.5% | 5.0% | 6.0% | 7.0% | 8.0% | 9.0% | 10.0% | 5.0% | 6.0% | 7.0% | 8.0% | 9.0% | |||
| IRR | 8.0% | 8.5% | 9.0% | 8.0% | 9.0% | 10.0% | 11.0% | 12.0% | 8.0% | 9.0% | 10.0% | 11.0% | 12.0% | |||
| Macaulay Duration | 27.00 | 27.13 | 27.25 | 54.00 | 54.50 | 55.00 | 55.50 | 56.00 | 36.00 | 36.33 | 36.67 | 37.00 | 37.33 | |||
| Assumptions | ||||||||||||||||
| 1 | Based on cashflows in perpetuity, with no terminal value as is typical in equity duration exercises. | |||||||||||||||
| 2 | Uses Gordon Constant Growth model to determine expected rates of return, despite excessive simplicity, and logic issues associated with assuming high div growth rates in perpetuity. | |||||||||||||||