# What Is The Net Real Annualized Return Of The S&P 500?

## Summary

Most people have heard that the average annual return on stocks is about 10%.

3 LBS professors - Dimson, Marsh and Staunton - claim that the market expectations of 12.5% nominal annual return on stocks are far beyond reality.

Calculating the CAGR of the S&P 500, I have found that the market expectations of a high annual return on stocks are overly optimistic.

I had always been curious about what the average annual return is on stocks. However, this was a very broad question, so later I started asking myself, what is the average annual return of the S&P 500 (NYSEARCA:SPY) as the most renowned stock market benchmark?

Many of us have likely heard that the index is growing at an average annual rate of roughly 10%, but what is the exact number? Countless studies have already been done on this topic, but have you ever thought of making your own calculation?

Probably one of the best works on this topic is Irrational Optimism (2003), written by three London Business School professors - Elroy Dimson, Paul Marsh and Mike Staunton. Their work is addressed primarily to pension plan sponsors and other long-term investors who are, in their view, overly optimistic about long-term returns and often overlook the risks involved in a long investment horizon. The authors claim that the market expectations of 12.5% nominal, 10% real annual return on stocks are far beyond the reality. In addition, they suggest that the U.S. stock market has performed anomalously well in comparison with other countries.

But before we focus our attention on any numbers, we should be sure that we properly understand the ambiguity of the word ''average'', especially in relation with the collocation annual return. We have to distinguish between the average calculated as arithmetic mean and the average calculated as geometric mean. The first one is frequently abused by the financial industry to make past returns look a little better than they actually were. For example, if you had a \$10,000 investment that went up 100% to \$20,000 one year and then came down 50% the next year, you certainly wouldn't say that you had an average return of 25% = (100% - 50%)/2, because your principal is back where it started. The only correct measure of an average annual return is the one based on geometric mean, which is referred to as Compound Annual Growth Rate, CAGR or Annualized Return. The more volatile the annual returns are, the more distorted arithmetic mean in view of CAGR will be. In the case of the S&P 500, the difference over a longer time period between these two means is about 1-2%.

Unlike Dimson, Marsh and Staunton, I decided to use a much shorter timeframe that does not include two World Wars and the market crash in the 1930s, but is more recent and takes into account the 2008 meltdown. Besides the CAGR of the S&P 500 and the S&P 500 Total Return (dividends reinvested), I also calculated the CAGR of the S&P 500 Net Total Return index, which reflects reinvested dividends after taxation. Finally, in order to determine real annualized returns, I deflated all nominal values by Consumer Price Index. The results are summarized in the following table:

CAGR of all S&P 500 versions, 1964-2013
 (%) S&P 500 S&P 500 TR S&P 500 NTR CAGR 6.6 10.0 8.3 CPI adj. CAGR 2.2 5.6 3.9

As is apparent from the table, the U.S. stock market generated an annualized return of 10% from 1964 to 2013. However, this is a nominal figure, and long-term investors are usually more concerned by real figures. The real annualized (dividends reinvested) return reached just 5.6%. I think that such a number barely touches the most pessimistic market expectations. Dimson, Marsh and Staunton get the real return of 6.3% with the standard deviation of 20.3% over their 1900-2002 period.

According to my calculation, the net real annualized return of the S&P 500 totals only 3.9%. Here, I would like to note that the ''net'' still does not include all relevant attributes such as capital gain tax or transaction costs. Without any doubts, many market participants are indeed irrationally optimistic about high long-term equity returns.

On the other hand, the good news for stocks is they beat inflation. Moreover, they beat other significant asset classes in my risk-reward test. Over the given period, gold CAGR reached 7.3% with an SD of 26.8% (nominal), and a CAGR of U.S. 10-year government bonds reached 6.5% with an SD of 2.7% (nominal). Gold, maybe surprisingly, cannot be recommended for the long run due to its high ex post volatility. Bonds seem to be safe, but not so generous on the return side. Therefore, stocks remain the best pick for the majority of long-term investors.