Multi-Period Planning and Asset Allocation

August 25, 2009 · by Austin Frakt · Posted in Personal Finance · 1 Comment

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:

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 Bankrate.com 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 Bankrate.com 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 assetcorrelation.com). 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.

Tags: <investment planning, risk, summer project>

Need for Risk: The Details

August 18, 2009 · by Austin Frakt · Posted in Personal Finance · 3 Comments

This post has been cited in the Carnival of Personal Finance #219, hosted by Your Money Relationships.

This is the sixth 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:

This post builds on prior ones in the series and I assume the reader has read them. So far I’ve covered the development of a current household budget, discussed how to use it for tracking and projections, related the surplus it indicates to ability for risk, and used it to estimate a retirement budget. The retirement budget indicates how much investment income (which includes the possibility of spending principal) one expects to need in retirement (in current dollars). What will be the source of this investment income?

The source I will focus on is a portfolio of securities, or what I will call a retirement nest egg. Other sources include various types of annuities, which I will not discuss. To keep things simple, let’s assume you expect to live for up to 30 years in retirement and you do not wish to leave funds to your heirs. In this case, how big a nest egg do you need to generate a specific level of income?

A key concept is the notion of a safe withdrawal rate (SWR): the inflation adjusted percentage of your nest egg value (at time of retirement) you can withdraw annually with very small risk of out-living your money. In the now classic “Trinity study,” Cooley Hubbard, and Walz found, based on back-testing, that a 3% SWR was safe for a wide range of asset allocations.

By definition of SWR,

[Eqn. 1] investment income = SWR x (initial nest egg),

where “investment income” is in constant dollars. Thus the initial nest egg (at time of retirement) must be

[Eqn. 2] initial nest egg = (investment income) / SWR

for a given investment income.

In the example of the previous post (see spreadsheet), an investment income of $1,567 per month or $18,804 per year was required. Using Eqn. 2 and an SWR of 3%, this translates into an initial nest egg of $626,800 in current dollars.

We have now established the necessary inputs for designing a retirement investment plan: ability to invest (the surplus of the current household budget), dollar goal (initial nest egg), and time span (between now and date of retirement). What return on investment is required to satisfy these constraints? This classic finance problem is easily solved using a financial calculator, spreadsheet, or any number of online savings calculators.

Let’s solve the specific problem implied in this spreadsheet and referenced above. Assume the budgets in the spreadsheet are for an investor age 35 years wishing retire at 65, a 30 year span. He needs to build a $626,800 nest egg and has $725 (his budget surplus) to invest per month (assuming he’s investing nothing via a payroll deduction). Using, the Bankrate.com savings calculator iteratively, we find that he will need an annual return of 5.4% to reach his goal. This is the real rate of return required. The nominal rate required will be this rate plus the inflation rate. Assuming inflation of around 3%, a rate of 5.4% + 3% = 8.4% will be required.

The investor will need to inflate his monthly investment as well: $725 is the real amount. This reflects the virtue of budget tracking. By tracking one’s budget, one can periodically reassesses one’s needs and income as they grow with inflation and be sure one’s surplus is growing at a sufficient rate.

Is the 5.4% real rate determined above reasonable to expect? If the hypothetical investor of the example thinks not then he should go back to his budget and see if he can find ways to scrape together some additional funds to invest and re-compute the necessary rate of return. What’s a reasonable maximum real rate of return? Real rates of return are expected by Rick Ferri and William Bernstein to be no higher than 7%, depending on asset class. So 5.4% does seem like a reasonable goal.

Once one has determined the necessary rate of return, the next step is to develop a plan to achieve it. That’s the topic of the next post in the series.

Tags: <investment planning, risk, summer project>

Willingness, Ability, and Need

August 4, 2009 · by Austin Frakt · Posted in Personal Finance · Comment

This post has been cited in the Money Hacks Carnival #79, hosted by Modern Tightwad.

This is the fourth 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:

It is standard advice that one should only take risk commensurate with one’s willingness, ability, and need. But what does this really mean? I am not satisfied with the definitions I have found elsewhere (to the extent any are given) so I thought it through for myself. Here’s my take.

Willingness

Willingness is all about a gut feeling of comfort. It is a non-quantitative concept. A common test for willingness to take risk is the “sleep test”. If you can’t sleep at night because of an investment decision, either actually made or in consideration, then you may have exceeded (or are considering exceeding) your willingness to take risk. On the other hand, if your decisions do not cause you unrest, your investments are probably in line with your willingness for risk.

Thus, willingness to take risk reflects your level of comfort with loss of your investment. For instance suppose you’re considering investing $10,000. Your willingness for risk is how readily you would take the chance of losing some of it for the chance of earning an expected profit. For example, you might not be comfortable taking the risk of a 50% probability of losing $5,000 (half the principal) in exchange for a 50% probability of earning $10,000 (doubling the principal). But, perhaps you might readily risk a 25% probability of losing half for a 75% probability of doubling it. Your willingness for risk is exceeded in the first example but not the second.

Ability

While your willingness for risk may be vague, your ability to take risk is quantifiable. It is based on your budget (if you don’t have one, see my prior post on the topic). To be able to take risk you have to have something you can afford to place at risk. Thus, your ability for risk is your surplus, i.e. your income less all necessary and regular expenses. By definition you do not require your surplus to support your current lifestyle. If you do, then you haven’t constructed a proper budget.

(By the way, I am assuming you already have an emergency fund of appropriate size and no high-interest debt. Having an emergency fund and ridding oneself of high-interest debt are prerequisites. Some would argue putting emphasis on ridding oneself of all debt, event low-interest fixed-rate mortgage debt. That’s debatable and I’m not taking that position here. You may decide for yourself.)

Need

Like ability, need for risk is quantifiable but the process of doing so will take many more words to develop. In short, your need for risk is based on your future requirements for money. Some of these requirements are large and a long time from now (e.g. retirement) so pinning down their relationship with risk is tricky (and is the topic of many books and a large industry). Need for risk, more than anything else, drives one’s required asset allocation. Subsequent posts in this series will delve into this further into this topic.

Tags: <investment planning, risk, summer project>