Question

1. Explain how a mean variance strategy could be used as a retirement income drawdown strategy. (Financial planning)

Answer 1

A retirement income stream strategy that is optimal under the mean-variance criterion involves splitting the lump sum into two parts. The first part purchase is a guaranteed indexed medium-term annuity while the remainder is invested in the national bourse accumulation index. The principle involved is analogous to the Tobin Separation Theorem or Mutual Fund Theorem of Modern Portfolio
Theory, which asserts mean-variance optimality of an investment portfolio comprising only cash and the market portfolio (a proof of the extended separation theorem applicable to annuity and other bonds is available on request from the author or, for a similar result, see Guay 2008). As with the Tobin result, the precise investment term remains unspecified.
Retirees may adopt pragmatic criteria to determine a suitable initial term (size of lump sum, the required annual pension, the long-term expected return on the market index) or, with longevity risk in mind, the probability that the market investment reinstates the entire original lump sum (in real terms) at the end of the guaranteed income years.
Over a 12-year annuity term, the accumulation in an Australian market index fund is expected to replace the entire original capital in real terms at the end of the guaranteed income years in a high proportion of realisations. Pensions funded in this way are referred to in the remainder of this article as mean-variance efficient (MVE) or annuity/ market fund retirement income streams.
For a retiree with $600,000 able to purchase a 12-year annuity at a yield of 4% p.a., it would cost $11.1467 per starting dollar of indexed annuity ($267,520 for a 12-year annuity of $24,000 p.a. payable monthly, indexed at 3% p.a.). Based on a large simulation sample of 12-year terms, the remaining $322,480 invested in the index will replace the real capital ($855,457) in more than 70% of cases.
If the annuity can be purchased at a yield of 5% p.a., the annuity cost is reduced to $10.5382 per starting dollar; the total cost is $252,917 for $24,000 p.a., leaving $347,083 to invest in the index. The proportion of such 12-year terms in which the indexed capital is replaced increases to 72.5%.