Thinking About the Long Term Real Return You Need to Earn to Achieve Your Goals

One of the surest ways to cause an anxiety attack is to ask someone (or yourself), how much they need to save for retirement. The panic most people feel when they hear this question is triggered by some combination of three underlying fears most of us have: Either we will outlive our retirement savings, we'll see our purchasing power severely eroded by inflation, and/or we won't end up leaving as much money to our heirs as we'd like. One of the best ways to overcome these fears is to better understand the issues and trade-offs that underlie them. 

Saving for retirement is an issue that is not only very important, but also one that too many people don't understand as well as they should. Back in 2001, the United States Retirement Confidence Survey found that while 67 percent of current workers report that they have saved something for their retirement, only 32 percent had tried to calculate how much money they actually will need to have saved so that they can live comfortably after they retire. Given this, it comes as no surprise that only 23 percent of current workers believed they were doing a good job of preparing financially for their retirement. And after the tremendous destruction of wealth in 2008, even fewer probably believe that today.

Why haven't more people tried to calculate how much money they need to save to pay for the retirement they want to enjoy? Former Federal Reserve Chairman Alan Greenspan suggested one reason, when he noted in one of his appearances before the U.S. Congress that "one of the most complex economic calculations that most workers will ever undertake is without doubt deciding how much to save for retirement." In short, many people may simply find the calculation too difficult to do on their own. Academic research by Professor Annamaria Lusardi has also suggested another potential explanation: people are afraid of what they may find out.

Avoiding this issue, however, may only compound future problems. Using data from the Health and Retirement Study, Professor Lusardi found that 54 percent of retirees who had not planned for their retirement rated their retirement years as not as good as their working years, while 79 percent who had thought a lot about retirement rated it as better or about the same as their working years. In summary, the data suggest that, painful or not, understanding how much we need to accumulate for our retirement (and what we need to do to get there) is an issue that all of us are better off confronting now rather than putting off until later.

Here is the way we approach it. The first question to ask is how much annual income will you need to have the lifestyle you want after you retire? To make things easier, this entire discussion will be in so-called "real" terms, assuming the effects of inflation have been removed. For example, a number of studies suggest that people generally desire replace 70% to 90% of their pre-retirement income. If we assume that amounts to $100,000 today, a target post-retirement income might be $80,000.

The second step is to subtract from this the annual income an investor expects to receive from non-portfolio sources, including a state pension (e.g., Social Security in the United States), a company pension (if you are in a defined benefit plan) and part-time work. Let's say these sources amount to $30,000. That leaves $50,000 in annual income (i.e., $80,000 less $30,000) that our investor's portfolio of financial assets must provide after he or she retires.

The third step is to determine the size of the bequest, if any, that our investor wants to leave after he or she dies (and note that for many people, this target bequest also serves as precautionary savings for unanticipated health care costs not covered by insurance). One way to think of this is in terms of a multiple of your annual portfolio income. Let's say, for example, that our investor wants to leave a bequest equal to ten times his or her annual portfolio income, or $500,000.

The fourth step is to estimate the number of years the investor expects to live in retirement. A "mortality table" provides the expected years of remaining life for people at different ages. However, these estimates are simply the midpoints of distributions that can be quite wide; some people will die sooner than the mortality table's estimate, while some people will die later.

Interestingly enough, other researchers have found that individual's own estimates of their remaining years of life are often more accurate than a simple random guess (probably because they are based on a knowledge of family and personal health histories). In this example, we will use an estimate of 25 years of life to be spent in retirement.

The fifth step is to estimate the real (after inflation) compound rate of return an investor will earn on his or her financial investment portfolio after retirement. In this example, we will use 4%.

Armed with these estimates, you can calculate the real value (i.e., the value in today's dollars, or whatever currency you are using) of the amount of money an investor must accumulate by the time he or she retires, in order to meet his or her expected needs.

The actual calculation is a two-part process. The first discounts a 25 year stream of $50,000 payments at 4% to their present value of $781,104. The second discounts a one-time payment of $500,000 at the end of 25 years at 4% to its present value of $187,558. Adding these two together yields an accumulation goal (in today's dollars) of $968,662.

Of course, this analysis has some important caveats. The first caveat is based on a common fear: "but what if I live longer than 25 years after I retire?"

Technically, this is called "longevity risk;" practically it is called "outliving your savings." There are four ways to manage this risk.


The easiest is buy longevity risk insurance. Products which offer longevity insurance are known as "annuities." Annuities promise to make payments to you over some period of time. These payments can be either fixed (i.e., not increase with inflation to keep their real value constant) or variable (i.e., payments rise with inflation). By investing in a real annuity, you avoid the risk of having inflation erode the purchasing power of your income over time. Hence, in this article, we focus only on real return (inflation indexed) annuities.

The simplest inflation-indexed annuity promises to pay you a fixed real income for as long as you live. More complicated products will also make payments for a period of time after you die (e.g. until a spouse dies). However, annuities come with two potential costs: first, they require a large up front premium payment, which is not available for use as a bequest if you die earlier than you expect. While annuities that guarantee a payout for a minimum number of years to some extent limit this potential cost, the financial consequences of dying too soon have caused many people to decide against purchasing an annuity and instead look for other ways to manage longevity risk. Second, as the 2008 crisis made clear, since annuities are issued by insurance companies, they also carry some amount of credit risk. If the issuing insurance company goes bust, there may be little or no payout under the annuity (though there has yet to be a major insurance company bankruptcy where we have seen how this scenario would actually play out).

The second way to hedge the risk of outliving one's assets is to use a long expected life in your calculations. However, this has two potentially adverse consequences: it leads to a higher accumulation goal (which implies reduced consumption before you retire), and, if you die sooner than expected, it results in a higher than desired bequest.

The third way to manage longevity risk is to use your bequest goal as a buffer, drawing it down if you live longer than expected. Of course, this means that, depending on the returns you earn on your investments after retirement, you may not achieve your bequest goal if you live longer than you expect.

The fourth way to manage longevity risk is to assume a relatively low real rate of return on your investments after you retire. The lower the assumed rate of return, the easier it is to achieve. We believe that the four percent real compound rate of return we have assumed in our example is prudent for someone with a normal risk preference. Expected real rates of return above this would, in our estimation, imply a higher than normal tolerance for investment risk, as well as a higher probability of not achieving one's portfolio income and bequest goals.

The second caveat is that this analysis does not explicitly take into account residential property owned by an investor.

This is because different investors will treat this in different ways. For example, one investor may enter into a "reverse mortgage" to generate post-retirement income that does not depend on the returns on her investment portfolio. Another may sell his large house, purchase a smaller one, and add the profits realized (technically the "equity extraction") to his financial investment portfolio. And still another may consider her house as her bequest, and thereby reduce the size of the bequest she expects her financial investment portfolio to fund.

With those two caveats in mind, let’s move from the target accumulation goal of $968,662 to the real return on your portfolio that you will need to earn in order to reach it. Once again, answering this question is not as easy as it first seems.

Let’s assume that you would like to retire (i.e., reach your accumulation goal) 25 years from today, and that you already have $100,000 in savings. And let’s further assume that you believe you can save an additional $10,000 per year, as your income and expenses evolve over time. Obviously, there is a lot of irreducible uncertainty around these assumptions, but that’s life. You have to make the best estimate you can with the information you have available (and later update it over time).

The minimum required real portfolio return that you are solving for is the rate that, in 25 years makes the future value of your current savings and your expected annual savings equal to your accumulation target of $968,662. The answer is 5.95%.

So should you therefore seek an asset allocation that has an expected return of 5.95%? No — because actual asset class returns will vary around that average.

Consider a simple example. Your starting capital is $100,000 and you add no additional savings. Based on your asset allocation, your portfolio’s expected return is 5.95%. Let’s assume the expected variability of returns around that average (i.e., the standard deviation) is 11.90% (twice the average, which is pretty conservative). The first year, you earn 5.95%. The next year, 17.85% (the expected return plus one standard deviation). The next year, minus 5.95% (the expected return less one standard deviation). In year four, you 29.74% (the expected return plus 2 standard deviations). And in year five, minus 17.85% (the expected return less 2 standard deviations).

At the end of year five, what is your compounded portfolio rate of return? It is 4.59%, well below the 5.95% compound return you need to reach your accumulation goal.

In sum, the variability of returns, plus the fact that downside losses hurt more (both mathematically and emotionally) than upside gains help, means that you have to aim for a higher expected average return than the minimum return you need to reach your goals. How much higher? That depends on the size of the expected portfolio standard deviation.

It also depends on how effective you are at avoiding large downside losses.

As you can see, investors face a complicated set of trade-offs between desired accumulation goals, savings rates, time to retirement, and acceptable levels of risk (i.e., the probability of falling short of one's goals, and the potential size of this shortfall, should it occur).

Indeed, most investors probably have in their head two scenarios: one ideal, and one that is the minimum outcome that is acceptable to them. We do not believe that there is any single "right" way to make these tradeoffs - investors differ in too many ways. What we do believe is that investors who explicitly explore these tradeoffs, and make logical, well informed decisions about them, are likely to feel much less anxious and ultimately much more satisfied with the results they achieve

Let us now turn to a review of the different asset classes that you can potentially include in your portfolio.

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