# Have Your Cake and Eat it To? Risk vs. Return

What is more important, getting the most return, or not losing anything? For many, getting the highest possible return is the biggest goal. They obsess over return. But higher returns warrant more risk, and more risk can have a hidden villain not always discovered until it is too late. The villain – geometric return, or more correctly termed in statistician land – geometric mean.

According to Wikipedia, Geometric Mean is a type of mean or average,…similar to the arithmetic mean, which is what most people think of with the word “average”, except that… the geometric mean of a data set is less than or equal to the data set’s arithmetic mean, unless you are using the same data set.

Translation = Actual Returns May Differ from Average Returns.

I first ran into Geometric Mean or Return when talking to another advisor. We agreed that if a \$100,000 portfolio went down 50% one year to \$50,000, it would take a 100% return (\$50,000) the next to get back to even. The total return over those two years would be 50%. (-50% + 100% = 50%) The average return over the two years would be 25%. (50% / 2 ) But clearly the investor has only gotten back to even. His actual gain is zip.

Let’s apply this to more realistic investment returns. Here are two 4 year average return scenarios.

 Bond \$100,000 Equity \$100,000 Year Returns Investment Returns Investment 1 5% \$105,000 30% \$130,000 2 5% \$110,250 -50% \$65,000 3 5% \$115,763 50% \$97,500 4 5% \$121,551 -10% \$87,750 Total 20% Total 20%

Both return series  total 20%. Over 4 years they average 5% per year. But their actual return tells a different story. You can clearly see that the actual investment results differ because of the volatility of the portfolios. The bonds made \$21,551, while stocks lost \$12,250 ending with \$87,750.

Actual return of the bonds were 21.55%, 1.55% more than the 20% total return. The extra 1.55% was due to compounding of return.  The actual return of the stocks were -12.25%, averaging negative 3.05% per year. The problem is that in the long run, bond returns do not keep up with inflation. We know we need stocks in our portfolio in order to keep up with inflation. Most of us also need higher than bond returns to achieve our goals. So how do we invest in stocks to keep pace with inflation while minimizing risk?

Asset Allocation

Asset allocation is a combination of stocks, bonds, and cash that can help take extreme peaks and valleys out of your returns.  Let’s look at returns without the peaks and valleys.

 Allocation \$100,000 Year Returns Investment 1 25% \$125,000 2 -25% \$93,750 3 25% \$117,188 4 -5% \$111,328

The average return is still 20%, or 5% per year. But less volatility produced a total return of 11.32% or 2.83% a year. How does this apply over longer periods? All Financial Matters.com did a really nice blog on the S&P 500 returns from 1986 to 2005. The average return was 13.17%. The geometric return was 11.94%.

How does this apply to planning for your retirement?

By looking at a series of returns applied to your actual portfolio over time, you get a more clear picture or your likelihood of success. Unfortunately most online calculators that many do-it-yourself investors are using only use average returns. They don’t account for geometric “actual” returns. As advisors, we have access to the Monte Carlo Analysis. Monte Carlo analysis runs not 1, but 10,000 series of returns on your portfolio based on historical or projected returns. This gives you a more clear picture as to your likelihood of success given your investment allocation. It also allows your to see the impact of reduced volatility on a portfolio as you shift investments from stocks to bonds to find the right mix.

In conclusion, you may not have bragging rights for the biggest returns at the company social with a lower risk, less volatile portfolio, but your long term results may be better off because of it. Remember that there are no guarantees when investing in the stock market. Historical returns are not indicative of future returns.