A New Framework for Retirement Income Planning

by Manish Malhotra, 8/17/10

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I propose a new framework to solve many problems associated with retirement income planning, one that answers questions investors often ask, such as: “How much retirement income can I have with only a 10% chance of failure?” and “How much do I need to have now to draw $50,000 for 30 years with full certainty?”

My framework provides better answers than the current industry benchmark: safe withdrawal rates (SWRs) can be raised from 4% to 4.6% by cutting down the risky investments – not by increasing risk. My framework also brings transparency to the tradeoff between risk and income, so that investors and advisors can make decisions with which they remain comfortable throughout retirement.

The private wealth management literature is full of differing perspectives on the retirement income problem, including the benefits and inefficiencies of the 4% rule-of-thumb. Nobel laureate William Sharpe’s article and Robert Huebscher’s article cover the benefits of owning bonds and the higher withdrawal rates that result. Many articles have also been published on each aspect of the retirement income problem with analytical and empirical analysis leading to a specific recommendation for each decision, whether it be asset allocation, drawdown order, or the amount and timing of annuity purchases.

Typically, each one of those analyses comes with a useful rule-of-thumb that is applicable in isolation. The usefulness of those rules is limited, however, when trying to analyze a comprehensive asset allocation. For example, the amount of portfolio that is converted to annuities used may affect the optimum asset allocation for the rest of the portfolio. Yet, no comprehensive framework exists that synthesizes and models the asset allocation decision and other decisions during retirement distribution phase; therefore, I propose a new one.

Goal risk among the efficient portfolios

Current business practices in private wealth management rely on choosing a portfolio from an efficient frontier after assigning investors a score using a psychological risk questionnaire. This practice works very well for the wealth accumulation and growth phase, when investor goals can be expressed as an expected return with a defined volatility. When the investor moves to the decumulation phase of the portfolio, however, he or she will usually have a more specific disbursement goal, such as $50,000 in pre-tax income annually. I present an alternative way of choosing among the efficient portfolios that is more effective and at the same time intuitive for the investor and his or her advisor.

Let’s introduce a new risk metric, called goal risk, which represents the chance that a specific goal will not be accomplished. Let’s start with a counter-intuitive finding: a 20% bond and 80% stock portfolio can be half as risky (in goal risk terms) as a portfolio with 80% bonds and 20% stocks. How is that possible?

Goal Risks

Suppose one of your conservative clients wants to invest $409 towards an inflation-adjusted goal of $1,000 in 30 years. You would typically choose a conservative portfolio like an 80% bond portfolio. The $409, growing at a conservative rate of 3%, will reach the target of $1,000 in 30 years. The return of 3% is the historical average returns for this portfolio, using data from the last 84 years.

Let’s understand the implications of that decision. The chance of realizing the mean return of 3% is 50% under a random walk assumption. However, if the if $409 were invested in a 20% bond portfolio with a historical average return of 5.5% and a historical standard deviation of 16.9%, then under the same random walk assumptions, the chance that he or she will not achieve the goal is 20%. So, a portfolio with 20% bonds can be less than half as risky (a 20% versus 50% chance) in achieving the goal compared to portfolio with 80% bonds, as shown in figure 1. (Stocks and bonds referred to in this article are large-cap stocks and intermediate-term government bonds respectively. Average returns mentioned above are mean of logarithmic real returns.)

Cum. Probability

Now, let’s see the goal risk using a historical sequence of returns instead of a random walk. The goal of $1,000 with an investment of $409 implies a terminal value ratio of 2.4 ($1,000/$409). Figure 2 shows that the 20% bond portfolio has a zero goal risk of achieving that terminal value, whereas the goal risk using an 80% bond portfolio is 67%. The dark black vertical line shows the terminal value of 2.4, which touches the x-axis before the 20% bond line touches it and it intersects the 80% bond line at 67% goal risk.