Thursday, February 21, 2013

Compound Interest and Wealth Accumulation: It's Not As Easy as You Think

The Magic(?) of Compound Interest
One of the very basic staples of personal finance is the idea that by starting save when young, one can become very wealthy watching their investments multiply over time. I surely agree that starting to save young is ideal, but a lot of the personal-finance literature can take things way too far. 

For example, and I don't mean to single out anyone out in particular (though the title of the book sets itself up for overinflated expectations), I recently read I Will Teach You To Be Rich by Ramit Sethi.  In the book, he likes to use 8% as a portfolio growth rate assumption when providing examples about the power of compounding interest. Surely, if someone can earn 8%, getting rich becomes a lot easier. But let's try to break this assumption down a bit.

Historical Data

The 8% number is seemingly derived from US historical data. Using historical averages is pretty popular both for savings and for studying safe withdrawal rates in retirement. One key resource about the historical data is Morningstar and Ibbotson Associates SBBI database. From it, we can learn that the S&P 500 on average since 1926 earned an 11.8% return, while intermediate term government bonds earned 5.5% on average. However, these are not the numbers we should be using. 

For starters, when talking about wealth accumulation over a long period of time, we should be removing inflation from the numbers in order to make the results is more meaningful. We should be looking at wealth accumulation in today's dollars, not future dollars. Sethi, in particular, makes this mistake on page 170 when talking about historical returns. He provides nominal returns and seemingly gets it backwards by saying that the numbers do not include inflation, when in fact they do. Step #1 is to remove inflation from these numbers so that we can talk about them in terms that we can understand: today's dollars. Having $1 million in 40 years will not mean the same thing as it does today. I'm a multimillionaire in Japanese yen, but that won't get me so far when lunch costs 1,000 yen.  

With inflation removed, the historical average stock return is 8.6%, and it is 2.6% for bonds.  

We are not finished yet.
Compounding Growth over Long Periods

The next step is that we need to switch to compounded returns rather than arithmetic returns. These historical averages represent a possible best guess about what you can earn over the next year. But when talking about accumulated wealth over a long period of time, we cannot use these single period returns. We have to account for portfolio volatility. Sometimes the portfolio grows and sometimes it shrinks. 

The way to understand this point is to consider what happens if your portfolio loses 50% of its value. How much does it need to gain in order to get back to its original starting point? The answer is not 50%. It is 100%. The portfolio needs to double to get back to where it started.

To make this more clear, suppose your portfolio is worth 100. Losing 50% means that the portfolio value drops to 50. The next year suppose your portfolio gains 50% in value. Well, 50% of 50 is 25 and so your portfolio would only grow to 75. The portfolio would need to grow by 50 to get back to 100 and that represents a 100% growth rate on top of its current value of 50.

This asymmetry must be incorporated into the analysis when talking about compounded returns over a long period of time. Stocks are volatile, and even though they earned 8.6% after inflation historically, with volatility one's wealth would've only grown at a rate of 6.5%. Bonds are less volatile and so their hair cut is smaller, but still the compounded returns for bonds falls from 2.6% down to 2.3%.

Asset Allocation

Another issue to consider is one's asset allocation. Back to that 8% assumption that is so popular to use, I don't know what the discussant has in mind for the asset allocation. Let's be charitable and say they are talking about it as a growth rate for stocks after removing inflation. Historically that was 8.6%, and perhaps the person is a bit conservative and reduces it down to 8%. Is this where the assumption comes from?

Nonetheless, this assumes that a person will hold 100% stocks over their entire working life and into retirement! Someone may start their career with a more aggressive asset allocation, but by the time they are approaching retirement and their wealth is hopefully grown to its largest value, where a given percentage return has the biggest effect in terms of dollars, the person is probably going to have an asset allocation far removed from 100% stocks. 

In trying to choose one asset allocation to represent an entire lifetime, it's not exactly clear what to assume, but we do need to put more weight on what the asset allocation will be around the retirement date. That is when a given return will have the biggest overall impact on the portfolio. And that is when the asset allocation is likely to be more conservative and less weighted to stocks. Since bonds have a lower compounded return, this pulls the compounded return away from its loftiest values. 

Adjusting for Current Market Conditions

There is one more adjustment we must make. It is that in today's current market environment, it borderlines on ridiculous to assume that the US historical averages will still apply in the future. Today bond yields are very low, and they are the best predictor of subsequent returns for bonds. That assumption of 2.3% inflation-adjusted compounded returns is really way too high, especially for those close to retirement who will be drawing down their portfolios. 

As for stocks, even if they can provide the same risk premium over bonds as they have historically, the low starting position for bonds implies lower returns for stocks as well. Likewise, stocks are still considered overvalued by the cyclically adjusted price-earnings ratio, and that further implies lower future returns than average.

Joseph Tomlinson recently investigated these issues at Advisor Perspectives, and he found that popular software packages had assumed compounded inflation-adjusted returns for a 50/50 portfolio of 2.95%, while Tomlinson's own estimates for this portfolio are 1.13%.

Personally, I use a 2% compounded and inflation-adjusted return assumption in my own planning spreadsheet. I could always change the assumption to 8%, and this would let me imagine that I will be very rich, indeed, when I reach my 60s. But it would just be an illusion and I would need to prepare myself for becoming very disappointed. 

I don't think that 8% assumption was all that well thought out. I do know that is not a good assumption.