Thursday, May 30, 2013

Return Expectations

Steadyhand recently released a report on the Five Essential Elements to Being a Better Investor. It’s an excellent report that focuses on mindset and qualitative factors. I highly recommend giving it a read. However, the part on return expectations irked my quantitative side.

The report’s basic message about having realistic return expectations is sensible. You shouldn’t be too optimistic expecting 20% returns every year. You shouldn’t be too pessimistic either; you’re unlikely to actually lose money over a long period of time. Wild swings can happen in any one year, but average returns over a long period of time tend to settle down.

However, the report includes the following figure:

I had one of those moments where Daniel Kahneman would say that my System 1 kicked in and I knew that something wasn’t right even though I wasn’t sure what was wrong at first.

The left side of this figure is some sort of equity price chart or portfolio size chart. Such charts give overall returns. If you average a 6% return for 10 years, such a chart would show that this compounds to an overall return of about 79%. However, the right side of the figure gives ever tighter ranges for average yearly returns (not overall returns). Just following the figure from left to right, the reader gets the impression that returns may fluctuate, but the destination is a small point in the upper right corner of the figure to be reached with certainty. This is not the case.

It’s true that the range of average yearly returns shrinks as we look further into the future, but the range of overall returns keeps getting larger. If we changed the figure so that the bars on the right indicated ranges of possible overall returns, the bars would keep getting longer the further into the future we go.

The important thing is that even though we can’t predict a final portfolio value with any certainty, we know that the odds of a low-cost broadly-diversified portfolio outperforming safe investments goes up the longer we stay invested. Over a week or a month the probability of stocks beating short-term government bonds is little better than 50%, but over 25 years it is almost 100%.

It could be that Steadyhand are actually doing investors a service by giving them the impression that future portfolio size is more certain than it actually is. Investors are too fearful of short-term fluctuations with their long-term savings. Perhaps they need to be calmed in this way.

A small quibble I have with the numbers in the figure is that ranges do not tighten up by a factor of 3 from 5 to 10 years of investing. If the 5-year range is 0 to +12% per year, then the 10-year range is closer to +2% to +10%. A rough rule of thumb is that it takes 4 times as long for the yearly return range to tighten up by a factor of 2. So, the 20-year range would be roughly +3% to +9%.

Once again, it could be that Steadyhand are doing investors a service by presenting a safe-looking narrow range of 10-year returns. However, I’m comfortable with realistic levels of volatility as long as I’m being compensated with a higher expected return.


  1. Oddly enough, this chart may be good enough for the average person. If we look at overall returns, the lower bound should increase in time since a loss or small gain is more likely over a short period than a long period. The chart does show the lower bound going up.

    The upper bound probably increases a lot more, since you can get greater total return in 20 years than you can in 1 year. The chart shows the upper bound increasing but under-represents that.

    Most of the missing information seems to be on the upside, so removing that can't hurt in managing expectations. Anyone who can truly understand that in the right perspective probably figured it out just like you did.

    1. @Value Indexer: I agree that this chart serves a useful purpose for many average people. I suspect that there is a large gap of people between those who are well served by this figure and those who are able to see what is wrong with it.

    2. It was our intention to keep the chart simple, but we didn't mean to make it inaccurate or fundamentally unsound. Mike, Scott and I think get your critique and are going to redo the slide. I think we all understand the point we're trying to make, but for the sake of simplicity, we've made the chart deceiving and confusing. Thx for the feedback.

    3. @Tom: It's not easy to simplify messsages while keeping them accurate. Steadyhand does this well.