Multi-Period Planning and Asset Allocation

This post has been cited in the Carnival of Personal Finance, hosted by Stretchy Dollar.

This is the seventh in a series of posts on investment planning. For those who haven’t read the first post (or have forgotten), I’m soliciting feedback (tips, tricks, links, etc.) that I will cite and use in the final post of the series. Here’s a list of the other posts in the series:

  1. Investment Planning: The Series
  2. Household Budgeting the Easy Way
  3. Budget Tracking and Projections (with Quicken Tricks)
  4. Willingness, Ability, and Need
  5. Estimating a Retirement Budget
  6. Need for Risk: The Details
  7. Multi-Period Planning and Asset Allocation [this post]
  8. Investment Planning: Reader Tips, Tricks, and Links

In the prior post in this series I illustrated how to compute the real return required to meet a future investment goal given a fixed real monthly amount to invest. Because downside risk increases with expected return (no free lunch), it is sensible to take more risk at a younger age than at an older age. At a younger age one has more time and ability to recover from a loss (one can work harder, take on another job, forego expenses, etc.). In the years just before retirement those options are more limited.

Translating this notion into expected return, it is sensible to aim for greater return (and more risk) in the earlier years of one’s investment plan and to settle for lower return (and lower risk) in the later years. To illustrate how this might be done, let’s consider a two-period plan with equal length periods. Generalizing to more periods and/or periods of varying length is straight forward.

Using the example of the prior post, suppose a 35 year old investor needs to build a $626,800 nest egg over a 30-year span with $725 to invest per month. We used the savings calculator iteratively to determine that he required a 5.4% real return over that span. Now let’s break this plan into two periods of 15 years, one for ages 35-50 and one for ages 50-65. The investor wishes to take less risk in the second span and more in the first.

Suppose he expects to achieve a 7% real return in the first period (one can debate whether this is realistic). At this rate he can build up $229,798 by age 50 (calculated using the MSN Money savings calculator). With this much saved by age 50, he can settle for a real return of about 4.5% in the second period to reach $626,800 by age 65 (calculated using the savings calculator). The astute reader will have noticed a degree of arbitrariness in this exercise. How should one allocate return (risk) across periods? Should the investor described above aim for a lower (more realistic) return in the first period, requiring a higher one in the second? I do not think logic alone can answer this question. One has to use one’s own subjective judgment.

With the next step we penetrate even deeper into the jungle of subjectivity. How does one select investment vehicles expected to obtain the return(s) computed in the preceding step? The ways are manifold; it is an underdetermined problem. This is the question of asset allocation about which a great deal has been written and many debates waged. The equity/bond ratio is the most basic decisions, but there are many others: the domestic/international mix of equity, the nominal/inflation-adjusted mix of bonds, whether or not to use market capitalization weights, whether or not to use index or managed funds, the placement of funds for tax efficiency, among others.

To my mind, some issues are settled, either by reason or empirics, or both. For instance, I’m convinced of the superiority of diversification, low fees, certain tax efficiency strategies, and indexing. Even with these as necessary constraints on choices, there is a lot of room for variation.

Ideally, one would like the portfolio expected to provide the required after-expenses, after-tax return with the lowest expected risk. In principle, with a precise definition of risk one could back test a wide range of strategies and select the optimal one. By equating risk with variance modern portfolio theory specifies an optimal (efficient) portfolio. To find the optimal portfolio one needs to estimate future asset correlations (recent past asset correlations can be found at However, asset correlations fluctuate, and predicting future correlations with useful precision is problematic (as discussed on the Bogleheads Investment Forum). This approach is just not practical, at least not for the average non-institutional, do-it-yourself investor.

The best one can do is to select a style of portfolio according to one’s taste and tune the percentage allocations to match an expected return. Fortunately, there are plenty of places to learn more about asset allocation issues. My favorites are the Bogleheads suite of sources: The Bogleheads’ Guide to Investing (new edition expected out in the fall of 2009), the Bogleheads Investment Forum, and the Bogleheads Wiki. TFB has reviewed many other relevant books. Using these (or others) as guides, one can select a class or style of portfolio that suits one’s taste and that is consistent with the constraints implied by the analyses presented in this series.

With that, I conclude my portion of this summer project on investment planning. The next post will be based on your assignment (given in the first post of the series). In it I will share reader inquiries and comments and provide any tricks, tips, and links that have been sent to me by others throughout this series.

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