Quantify Your Portfolio Goals

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
What rate of return does your portfolio have to earn to achieve your target income and savings/bequest goals? Sadly, too many retired investors cannot answer this question. So let's deal with it straight away. Given these goals, as well as your expected remaining years of life, you can derive the minimum compound annual real rate of return your portfolio must earn to meet them. To make this process even simpler, we've calculated the following table. 

Here is how to use it. In the upper left cell of each section, "Exp =" refers to your estimate of your remaining years of expected life. The top line of each section contains a series of numbers, ranging from 3% to 10%. These represent your target income, expressed as a percentage of the starting value of your portfolio. Along the left side of each section is a series of numbers ranging from 0% to 200%. These represent your target bequest/savings goal, also expressed as a percentage of the starting value of your portfolio.

Within each expected life section, at the intersection of each target income and target bequest goal, you will find the minimum compound annual real return that your portfolio must earn. If, over your expected remaining life, your portfolio earns this compound annual rate of return, it should end with a value of zero after your bequests are paid out. For example, suppose you expect to live for twenty more years. The target income you want your portfolio to produce equals 5% of its initial value. You also would like to leave bequests equal to 100% of your portfolio's current value after you die. The table shows that achieving these goals requires that you earn a compound annual real rate of return (also called the geometric average) of at least 5.42% on your portfolio over this period.

There are three key points to keep in mind about these returns. First, they are real returns, and do not include inflation. We use real returns because it focuses attention on maintaining the purchasing power of your income and savings over time. When people focus on nominal returns, high inflation can cause them to think they are doing quite well, even as the purchasing power of their portfolios shrink. Second, these returns are after-tax. To convert these returns to a pre-tax basis, divide them by an amount equal to 1 less your marginal tax rate. 

Third, in order to achieve this 5.42% compound annual return, your average annual return will have to be significantly higher than this amount, because you will be investing in risky assets. When the standard deviation of annual returns (a proxy for risk) on an asset or portfolio is greater than zero, its simple (arithmetic) average annual rate of return will be higher than its compound average rate of return over time (also known as its geometric average return). This is due to a phenomenon called either "variance drain" or "volatility drag."

This is an important concept that too few investors clearly understand.

Here's another example that should help make it clear. Consider an investment that over five years earns annual returns of 10%, 5%, (20%), (5%), and 25%. Over this five year period, the arithmetic average return on this investment was 3.00%. The standard deviation of these returns was 16.81%. Because of this variability, the compound average annual return over this five year period was only 1.87%.

A quick (if not perfectly accurate) estimate of the impact of volatility drag (that is, the difference between the arithmetic average annual return on an investment and the actual compound annual return you are likely to earn) is that it is equal to one half the square of volatility (that is, it is equal to one half the variance, which is the same thing as the standard deviation squared). In our example, this method yields an estimated compound return of 1.59%, which is reasonably close to the actual 1.87% figure. 

One last point: The shaded cells in the table show real compound annual rates of return that, based on our view of historical experience, seem imprudent to expect in the future. In general, the lower the required compound annual real rate of return, the higher the probability that wise asset allocation and investment selection will result in its achievement.

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** Note: The compound annual real returns shown in this table are calculated using the internal rate of return method. We assume that the next year's target income requirement is taken out at the end of each year.

Hence, a portfolio initially worth $1,000 and a target income of 5% starts the first year of our simulation with a value of $950. A portfolio that achieves its target compound annual real rate of return ends up with a zero balance after its bequest goal has been met at the end of the expected lifetime.

Once you have quantified the goals for your portfolio you need to implement a plan to achieve those objectives. The allocation of your assets is critical.

Let's proceed to 
What Asset Allocation is Right for You?
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