There’s nothing worse that investing with no clear sense of direction. You may end up just holding cash (the default asset for many people) or you tread in and out of the stock market like a short-term punter looking for a jackpot. By definition, lottery winners are few and far between.

Cash is an expensive asset to hold in the long run because over time, inflation takes a big chunk of its purchasing power. For example, an annual inflation rate of 4% is enough to cut the purchasing power of a dollar by half in just 18 years

Among liquid assets, only stocks or **equities** rise to the occasion in beating inflation over long periods of time. This is because every share of a stock represents a fractional ownership in a firm whose earnings are intimately derived from real economy (both domestic, and increasingly in a globalized world, outside the country where the firm’s stock is listed). So, if real economic growth is above inflation, theoretically, stock returns should also be above inflation. The following confirms this relationship for a globally diversified stock portfolio (16 developed countries). The bottom of the table shows that over the 40-years from 1969 to 2009, there is a close correspondence between the average real GDP growth of the world economy and the average real stock price return.

So, stocks provide higher real returns than either cash or bonds. Unfortunately, as discussed in my previous blog, many Singaporeans prefer to hold most of their wealth outside property in cash. Research evidence also shows that those who do invest in stocks do not hang on to their investment long enough to harvest the “equity risk premium” (the average excess return in stocks over bonds). They give up too easily when the going gets rough.

The lesson is clear. To be a successful investor, you must have the patience of a long-term investor who does not flinch even in stormy times. Measure yourself in terms of decades, not weeks or months.

With this caveat in mind, let’s consider the question of formulating a concrete investment target to aim for. To frame this discussion, I will use retirement planning as the context, but the key points are more general. Here’s the problem.

Suppose you are now 30 years old and wish to retire at 65 with sufficient wealth to enjoy for the rest of your life. For concreteness, suppose you will spend 25 years in retirement, and that you do not intend to leave any of this wealth behind as a bequest.

The above assumptions lead to two broad periods: (a) an accumulation or investment period of 35 years from now to age 65 and (b) a decumulation or spending period of 25 years from 60 to 90. Both periods will play a part in determining your investment goal.

We need a few more assumptions to quantify your wealth goal. Suppose you figure that you will need the future equivalent of $36,000 in your first year of retirement. In other words, you wish to spend $36,000 in today’s dollars when you reach 65.

Due to inflation, the future value of $36,000 will be much larger. I will assume that the inflation rate during the accumulation period is 3% a year. Thus, at 65, you will actually need to spend $36,000 x 1.03^35 or $101, 299. What about the other 19 years?

To be conservative, suppose the inflation rate during the decumulation period is 4% while your nominal rate of return during this period is 3%. The TOTAL amount of money you require at 65 to last 25 years is equal to the present value of all your expenses during this period. This present value is your RETIREMENT GOAL.

Given the above assumptions, we are now ready to calculate this retirement goal with the help of time value of money concepts (in particular, the concept of a growing annuity).

YOUR RETIREMENT GOAL = $101,299 x PVIFGA(T, g, r)(1+r)

Here, PVIFGA stands for the **present value interest factor for a growing annuity**, where T is number of years (25), g is the inflation rate during retirement (4%) and r is your rate of return earned during this period (3%). We need to multiply PVIFGA by 1+r as shown to reflect the assumption that you will withdraw the first year amount ($101,299) immediately upon retirement.

The formula for the cryptic PVIFGA formula is shown in the accompanying explanatory note. Plugging the relevant numbers into this formula and solving the above equation gives the solution to your retirement goal. The solution is $2,850,705

Now that you have quantified your investment goal, the next step is to design an **investment plan** to achieve your goal. The shape of your investment plan depends critically on your risk tolerance (i.e., how timid or brave you are when facing losses particularly in the short run).

If you are a timid person, you will most likely park your savings in bank deposits or bonds. But as mentioned, cash and bonds lose out to inflation in the long run, so conservative investment plans will be sub-optimal for your needs.

To meet multi-million wealth targets such as illustrated above, you will need to include riskier assets like stocks as part of your overall portfolio, and the temperament to hang in there when the going gets rough.

**Further Analysis**

Here is the spreadsheet for calculating future retirement goal. And here is explanatory note for the calculations.