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Most discussions of risk seem to be rather superficial, focusing in on the supposed risk-return continuum and ignoring all else. But if you define your investment activity in terms of a particular objective, then there are lots of different factors that can affect your ability to achieve your goals.

Objective: Accumulate enough assets to support yourself (and any dependents) without relying on employment income, or government largesse.

Goal 1 (Leave inheritance): Accumulate sufficient assets by proposed retirement date so that annual investment gains equal or exceed anticipated living expenses (i.e. retirement is fully endowed, children receive kick-start on asset accumulation).

Goal 2 (Die broke): Accumulate sufficient assets by proposed retirement date so that annual living expenses are partially met by annual investment gains and partially by capital depletion. The depletion rate must be low enough to ensure that your funds have > 95% probability of outliving you (and/or your spouse or other dependents). Requires less capital, but involves difficult assumptions about longevity.

For Goal 1, I'm assuming that a necessary nest egg will be 25 times larger than anticipated annual expenses. Hence, I'm assuming a 4% annual draw (real return), and a nominal return of 4% plus inflation.

During asset accumulation, for t = 1 to k:

A(t) = [A(t-1) + S(t)]^[r + e(t) – I(t)]

After retirement, for t = k to z:

A(t) = [A(t-1) - C(t)]^[r + e(t) – I(t)]

where t = years (1,2,3….k)
k = projected years of asset accumulation (i.e. k years until retirement)
z = projected maximum lifespan beyond retirement
A(t) = inflation-adjusted assets ($) at the end of year t
A(k) = inflation-adjusted assets at retirement
S(t) = amount saved in year t (savings assumed to occur in Jan for simplicity)
C(t) = living expenses in year t (ditto on Jan assumption)
r = targeted nominal rate of return, e.g. 7% = 1.07
e(t) = annual deviation from targeted return; e.g. + 3% = 0.03
I(t) = inflation rate in year t; e.g. 4% = 0.04

I'll assume that individual investors can plug in their best estimates of time to retirement (k), annual living expenses (C), annual savings rate (S), anticipated return (r), and anticipated inflation (I), and verify that their goals are achievable. If not, one or more of the previous parameters will need to be altered.


1) You could die or become disabled prior to reaching A(k). If you're single with no dependents, this isn't a risk. But if you have dependents, then your savings rate becomes zero and cost-of-living withdrawals begin immediately. Strategy: Carry enough life and disability insurance on you and/or your working spouse to provide A(k)-A(t) worth of assets upon death or disability. Cost: insurance premiums reduce the amount of annual savings that would otherwise be possible. These costs accelerate rapidly after age 40. Anyone with dependents who has lifestyle risks and/or waits until after age 50 to begin serious asset accumulation will face enormous friction from insuring against loss of earnings/savings power.

2) Insufficient savings rate. Persistent inability to meet the annual targeted savings rate. This implies a concurrent inability to budget for annual living costs, and suggests that annual expenses during retirement are likely underestimated as well. This could be due to unrealistic goals regarding savings rates and living expenses, or more likely due to lack of sufficient cost controls. Repair strategy: Implement rigorous budget planning and monitoring over next five years, adaptively managing both goals and results. Revise retirement plan accordingly.

3) Targeted nominal return rate (r) is too optimistic (i.e., mean e is negative, reflecting not only variance, but bias as well). A recent survey by Vanguard showed that most 401(k) investors still think that the stock market will return > 15% per year over the long term. Needless to say, most investors are going to be in for a rather rude shock. This positive bias in r leads to poor planning (e.g. insufficient savings rate, overly optimistic retirement date). Strategy: Under promise (but over deliver). Based on arguments extended by Buffett & Gross, I think that anyone who sets r higher than 6-8% is setting themselves up for potential disappointment. Paradoxically, I've found it's psychologically much easier to earn superior rates of return if you've got the patience to be content with below average returns. And I think it's important to remember that r is a necessary finite rate of return. It's not beating the S&P 500 on a consistent basis, which may or may not also happen. Beating the S&P has to be the most over-rated investment goal of all time.

4) Successive negative deviations in annual returns [e(t)] lead to substantial impairment of capital. Aside from bias (addressed in point 3), the investment strategy may simply be too volatile, resulting in a temporary impairment of capital that is nevertheless of long enough duration to affect your economic well being. If r represents the geometric mean return and e represents log-normal variance, then the mean expected value of retirement assets will be independent of e. But for smallish time frames, the Central Limit Theorom isn't always going to pull you through.

Suppose you have $100 k in current assets, save $10 k per year, intend to retire in 25 years, and need $1 million in retirement assets. A 6% annual return on investments will just get you there ($1.01 M). But suppose that you achieve a lumpy 6%, with standard deviations about the mean of 1%, 2%, 3%, or 5%. On average, over 30 different 25-year trials, each strategy will still return $1 M. But the high variance strategy will return less than $1 M 13 times out of 30, < $900 k 7 times out of 30, < $800 k 5 times, and once it even returned $588 k. Never mind that the high variance strategy once returned $1.62 M. You don't need the extra $0.62 M, but you absolutely can't afford to finish up with only $588 k. Variance reduction may make sense, especially as one approaches retirement date and there is less time to make up for random shortfalls.

5) Inflation rate (I) exceeds expectations. If inflation is higher than anticipated, then living costs are going to be higher than projected. If salary doesn't keep pace with inflation during the accumulation years, then neither will annual savings. Nominal rates of return, after correcting for inflation, won't provide sufficient asset growth. Although retirement goals might be reached in absolute $ terms, they won't be reached in real (inflation-adjusted) terms. Strategy: Unlike return rate, where underestimating seemed prudent, it's probably best to overestimate likely long-term inflation rates. Like solasis, I expect we'll see 10% inflation rates sometime again in my lifetime--given recent trends in money supply and deficit spending, perhaps sooner rather than later. Whenever I've used formal retirement calculators I've always assumed 2.5% inflation, but bumping that up to 3.5% might be more reasonable. Inflation can take on added risk if, in attempting to reduce volatility of returns (i.e. Point 4), you lock in long-term fixed rates of return that, though attractive at the time, are nullified by rising inflation. Hyperinflation (i.e., monetary collapse) probably deserves some consideration as a risk factor, but this is long enough post already.

Most discussion of risk focuses on r, e, and the implied correlation between the two. And I'm not trying to say that isn't a worthy point of discussion. But in your total game plan, you should realize that there are a lot of other factors within your control besides the risk-return continuum. And they shouldn't be ignored.


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Goal 2 (Die broke)

There are plenty of insurance companies out there offering annuity products that will meet that goal exactly. At some of them you can choose inflation-adjusted withdrawals.
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