We are lost, but making excellent progress

Steve Covey’s exhortation used as the title of this piece is particularly relevant for investors. One of the common mistakes investors make is to see investing as a series of short term gains that hopefully add up to long term success. This is like trying to climb a mountain by staring at your boots.

Consider the situation of John and Natasha who want to invest $50,000 now to pay for their child’s education in 10 years, which will then cost $80,000. They attach a great deal of importance to not losing the principal in pursuit of their $80,000 target. Similarly, providing a succession of annual income streams for future retirement often involves setting a minimum amount while hoping for additional upside.

Their advisor presents them with two options:

• Investment  A  with an expected  annual return of 4%
• Investment B with an expected annual return of 6%.

Simple math suggests that they need an annual return of 4.8% to reach their goal of 80,000. So obviously, they choose Investment B. Role forward ten years and John and Natasha are reviewing their education fund. The actual returns were as shown in Table 1 below. The actual annualised return is -1% and the final value at the end of 10 years is only $46,399, well short of their desired outcome. What went wrong?

The most obvious problem is that the annual returns varied from year to year. When expected annual returns are quoted they are averages that smooth out a lot of annual variability.

The chart of the US Market above shows that the average return, as represented by the dotted line is a very rare occurrence. Well, you might say, but after ten years these fluctuations should smooth themselves out? The answer to this is given by the chart below. Each bar represents an average return over the previous ten years.

The good news is that negative returns over ten years are quite rare but the actual return still shows considerable fluctuation. Looking at the chart, it is easy to forget that the returns are annual returns which compound over ten years.  For someone thinking of retiring in 10 years it is not very comforting for them to be told that their $100,000 nest egg will be worth somewhere between  $74,000 (-3% annual return over 10 years)  and $523,000 (18% annual return over 10 years)**.

What other information should John and Natasha seek before making their investment choice? Often investment risk is presented in terms of a measure of price volatility, usually something called standard deviation. A higher standard deviation means a higher fluctuation in price.

Suppose their investment advisor came back with this additional information:

• Investment A with an expected  annual return of 4%, and a annual risk of 4%
• Investment B with an expected annual return of 6%, and an annual risk of 12%

In both cases we are told that the risk measure is the standard deviation. Does this help? Certainly John & Natasha can now see that Investment B is “riskier” than Investment A. But the question they want to address is "What is the risk, after ten years, that the portfolio value is less than $80,000?"

Before we answer that question let us consider Investment A in more detail. Investment A is a bond  (for example, from the Province of Ontario) that matures in ten years and pays an annual interest of 4%.  It is not a bond fund or bond index, but an individual bond with a fixed maturity date. The difference is important because the value of bond funds is sensitive to changes in interest rates, but the maturity value of the bond does not change. The price of the bond will vary during the next ten years,  but we know (unless the bond issuer  goes bust, a risk we will ignore) that after ten years John & Natasha will get their initial $50,000 back plus 4% interest every year, a total of $74,012*. In this case, the price volatility (standard deviation) is no help whatsoever in assessing whether Investment A is a good choice. The problem with Investment A is that we can be 100% certain that it will not achieve the goal of $80,000. In other words, it has a very high (certain) shortfall risk.

Let us go back to our previous question about Investment B.  Suppose Investment B is a Canadian Index fund, tracking Canadian equities. We have seen one example above where the sequence of returns did not turn out well for John and Natasha. But maybe this is a rare occurrence – what is the shortfall risk for Investment B?

Using a statistical simulator, we can compute that there is a 62% chance that Investment B will exceed John & Natasha’s goal of $80,000 in ten years, and that there is an 8% chance that the value will be less than $50,000. At last we have some useful information! But John and Natasha may feel that the 8% chance of ending up with less than $50,000 is too high. Can we do better?

Suppose we build a portfolio with 50% of Investment A and 50% of Investment B. We can calculate that the $25,000 invested in Investment A (the bond) will generate $37,006 at maturity, with a 4% return. To make sure the portfolio achieves the desired minimum of $50,000 we only require $12,994 from Investment B, the equity index. Our simulator tells us that there is a 99% chance of Investment B not achieving this goal but the chance of reaching the goal of $80,000 has fallen to 48%. Thus to be more certain about protecting the downside we have traded some of the potential upside.

Conclusion

Investors often have specific future income goals. They may be for a lump sum expenditure for education as in the example above, or they could be an annual income stream for future retirement. Meeting the income objectives with a high degree of certainty can’t usefully be determined using annual risk and return data but requires a prediction over the entire investment period. Such predictions lead to better decisions about the right mix of bond and equities today, to meet the income requirements of tomorrow.

* We assume interest is reinvested at 4%.
** The returns illustrated are in excess of one month T-Bill returns.