How Risky is the Stock Market

How Risky is the Stock Market An Analysis of Short-term versus Long-term investing Elena Agachi and Lammertjan Dam CIBIF-001 18 januari 2018

1871 1877 1883 1889 1895 1901 1907 1913 1919 1925 1937 1943 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 Stocks can be an attractive investment. At the same time, many people are reluctant to invest in stocks, as they fear big losses due to the riskiness of stock market investment. With financial crises in mind, they rather avoid suddenly losing almost half of their outlay. However, is this fear reasonable? It seems that the risk associated with stock market investing is not well understood. People are aware of the fact that stock market prices go up and down a lot, but commonly they do not grasp what to really expect in terms of risk. Financial professionals use jargon such as volatility, systematic risk, alphas and betas, etc., but many private investors often do not understand these concepts, and if they do, they may lack an intuitive understanding of what the levels of these risk measures imply in practice. In this blog, we want to shed some light on how much risk one can expect when investing in the stock market. In particular, we want to highlight and visualize the differences in risk and return between short-term and long-term investing. 900000 800000 700000 600000 500000 400000 300000 200000 100000 0 Historical Performance of the U.S. Stock Market, 1871-2013 Data Source: Shiller, R., U.S.Stock Price Data, Annual, with consumption, both short and long rates, and present value calculations. An Update of Data shown in Chapter 26 of Market Volatility, R. Shiller, MIT Press, 1989, and Irrational Exuberance, Princeton 2015. Available online at: http://www.econ.yale.edu/~shiller/data.htm The figure above shows the historical stock market performance for the U.S., if you would have invested $100 in 1871, corrected for inflation (while reinvesting the dividend payments). In 2013 you would end up with almost $800,000, roughly 8000 times the initial outlay. When people see a graph like this for the first time, they are sometimes shocked by its shape. It seems as if up until WWII nothing really happened, after which the stock market took off in the 1960s and 1970s, then exploded in the 1980s, and since the 1990s the market has been going

1871 1877 1883 1889 1895 1901 1907 1913 1919 1925 1937 1943 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 How Risky is the Stock Market 3 up and down like crazy. But eyeballing the data like this is misleading, because the scale on the vertical axis is not appropriate. If you invest money, you expect a certain percentage return, not a fixed amount of dollars. So instead of moving one unit up in the graph reflecting one additional dollar, we want the vertical axis such that moving one unit up reflects one additional percentage. To do so we show the same historical data in a figure, but now with a logarithmic scale. Each step in the vertical direction now represents a multiplication of 10. 1000000 100000 10000 1000 100 10 1 Historical Performance of the U.S. Stock Market, 1871-2013 (logarithmic scale) Data Source: Shiller, R., U.S.Stock Price Data, Annual, with consumption, both short and long rates, and present value calculations. An Update of Data shown in Chapter 26 of Market Volatility, R. Shiller, MIT Press, 1989, and Irrational Exuberance, Princeton 2015. Available online at: http://www.econ.yale.edu/~shiller/data.htm Using the logarithmic scale, we see that the recent years are not absurdly wild, and in fact the market decline by the end of the 1920s is more obvious compared to the 2008 crisis. It also shows that in the long run, the stock market has been going up steadily. The long run picture using a logarithmic scale makes the stock market look attractive and relatively safe, but of course no real single person invests for a period of 130 years. So what about shorter time frames? Below we list historical investment (net) returns for 1-year, 5-year, 10-year, and 30-year periods respectively. The periods with a positive net return are depicted in green, with a negative return in red. We see that 1-year periods vary tremendously, without a clear pattern. On a yearly basis, the market can as easily go up with 20% as it can go down with 20%. Out of the 142 years in these data, 98 years had a positive return, so about 70% of the years ended with a net gain. The biggest drop in the data was 37% down, during the 1920s crises, while the largest yearly gain of 51% happened shortly after that. Hence, even though the average yearly return on the market is 8%, if one invests only for one year, chances are that the actual realized return is much higher or much lower and pretty hard to predict.

How Risky is the Stock Market 4

1871 1875 1879 1883 1887 1891 1895 1899 1903 1907 1911 1915 1919 1923 1927 1935 1939 1943 1947 1951 1955 1959 1963 1967 1971 1975 1979 1983 1871 1876 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 1871 1876 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 1871 1876 1881 1886 1891 1896 1901 1906 1911 1916 1921 1926 1936 1941 1946 1951 1956 1961 1966 1971 1976 1981 1986 1991 1996 2001 2006 2011 How Risky is the Stock Market 5 U.S. Stock Market 1871-2012, 1-Year Returns 100% 50% 0% -50% 400% 200% 0% -200% U.S. Stock Market 1871-2008, 5-Year Returns 600% 400% 200% 0% -200% U.S. Stock Market 1871-2003, 10-Year Returns 2000% 1500% 1000% 500% 0% U.S. Stock Market 1871-1983, 30-Year Returns Data Source: Own calculations based on: Shiller, R., U.S.Stock Price Data, Annual, with consumption, both short and long rates, and present value calculations. An Update of Data shown in Chapter 26 of Market Volatility, R. Shiller, MIT Press, 1989, and Irrational Exuberance, Princeton 2015. Available online at: http://www.econ.yale.edu/~shiller/data.htm

How Risky is the Stock Market 6 5-year returns and 10-year returns show a lot of variation as well, and clearly investing longer gives you higher average returns, namely 45% and 111% respectively. So investing for 10 years means that on average you will more than double your money. We also see that tripling (200% net return) or quadrupling (300% net return) the outlay happens quite often as well after ten years. Yet, almost no return, or even a negative return, is not unlikely either after a longer period. However, the number of red data points is lower compared to 1-year investments; 80% of the 5-year investment periods had a positive return, 87% of the 10-year period had a positive return. This sounds much better, but the flipside is that there is 13% chance that you will actually have lost money on the stock market after 10 years. The 30-year returns show what the best thing to do is in this case wait longer. Of all the 30-year periods between 1871 and 1983, not one of them resulted in a loss. The lowest gain was 158%, or roughly 1.3% a year, and took place during WWI, the crisis years of the 1930s, followed by WWII. This shows that even in the worst historical 30-year scenario, investing in the stock market beats the historical average (and current) low interest rates; note that these data are adjusted for inflation. At the same time, the upward potential after a long period is tremendous. The largest 30-year return is 1600%. Someone lucky enough having invested during this particular period only needed an initial $60,000 to become a millionaire 30 years later. On average you will have about 7 times your initial amount after 30 years. Again, the differences in the range of returns are large, but the good news is that the downside risk is much lower after longer periods of investing. To represent the wild range of possible returns, financial specialists use the concept of return volatility, which basically is the statistical standard deviation of returns. For historical yearly returns, this number is 18%. It implies that even though the average yearly return was 8%, you were just as likely to end up with a gain of 26% (8%+18%) as with a loss of 10% (8%-18%). In the data, roughly 2.5 standard deviations above and below the mean have been historical extremes the aforementioned -37% and +51% (compared to 8% - 2.5 x 18% = -37% and 8% +2.5 x18% =53%). Scholars initially believed that this risk, or volatility, would simply amplify over time without any memory of what happened in the past (sometimes referred to as a random walk in returns). Otherwise this would make stock markets predictable, and indeed in the short run, stock markets are very unpredictable. But by now there are also many scholars who feel that the data suggests that a phenomenon labeled mean reversion is present in the stock market for longer time horizons. Basically, mean reversion implies that after a drop in stock market prices, the market is more likely to bounce back up over a longer period of time, rendering longer periods of investing relatively safer and more predictable. To investigate this, we calculated standard deviations of returns over one year, two years, three years, etc. up to 30 years. We then translated these numbers back to the one-year equivalent and plotted these annualized standard deviations in a

How Risky is the Stock Market 7 graph for each investment period 1. If the long run is indeed just as risky as the short run, we expect to see a straight horizontal line; a volatility of 18% per year irrespective of the number of years of investing. But instead of a straight horizontal line, the figure below shows something else. The longer one invests, the lower the annualized risk. For 30-year period investments, the annualized risk has been reduced by half, to a level of annual volatility of just below 10%. Risk Comparison of Short-term vs. Long-term investing: Buy-and-Hold Returns 20% 18% 16% Anualized Volatility (Risk) 14% 12% 10% 8% 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 Investment Period in Years Data Source: Own calculations based on: Shiller, R., U.S.Stock Price Data, Annual, with consumption, both short and long rates, and present value calculations. An Update of Data shown in Chapter 26 of Market Volatility, R. Shiller, MIT Press, 1989, and Irrational Exuberance, Princeton 2015. Available online at: http://www.econ.yale.edu/~shiller/data.htm Stocks are indeed much safer investments over a longer period of time, and the figure implies that after price drops the market is likely to climb back up. For practical investment purposes there is one caveat though. The analysis behind the figure assumes that an investor sets aside a large amount of money once, at the beginning of the investment period, and never adds additional funds to his investment a so called buy-and-hold portfolio. In practice, investors usually set aside smaller amounts of money each month or each year. 1 We adjust for the overlapping data in multi-year returns following the methodology in Cochrane, J. H. (1988). How big is the random walk in GNP?. Journal of political economy, 96(5), 893-920.

How Risky is the Stock Market 8 Risk Comparison of Short-term vs. Long-term investing: Annual Investments 20% 18% 16% Anualized Volatility (Risk) 14% 12% 10% 8% 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930 Investment Period in Years Data Source: Own calculations based on: Shiller, R., U.S.Stock Price Data, Annual, with consumption, both short and long rates, and present value calculations. An Update of Data shown in Chapter 26 of Market Volatility, R. Shiller, MIT Press, 1989, and Irrational Exuberance, Princeton 2015. Available online at: http://www.econ.yale.edu/~shiller/data.htm Therefore, we recreated the same figure, but in our analysis we assumed that an investor invests, say, an additional $1000 each year, while letting this amount grow with inflation (to represent larger income, for example). We still observe a decline in the long-term risk, but not as sharp compared to the buy-and-hold returns. The reason is simple. The money that the investor puts aside at the beginning of the 30 years enjoys the long run risk decline, but the money invested in, say, the last 5 years is subject to the larger short-run risk. As a result, the strategy with annual investments ends up being somewhat more risky compared to a buy-and-hold strategy because it is a mixture of more risky short-run and safer long-run investments. How can we translate our volatility measure back into realistic expectations? Well, we can calculate a bad scenario, a good scenario, and an average scenario based on these numbers. We assume that an investor puts aside $300 each month, or $3600 a year, and invests it in the stock market. We also compare it to the alternative, the total amount invested so far, labeled sock as if the investor could have also put his money in an old sock and not run any stock market risk.

How Risky is the Stock Market 9 Data Source: Own calculations Let us first look at the scenarios for a 10-year period investment. $300 a month after 10 years implies that the investor has put up $36,000 in total over this period. The bad scenario falls behind the sock strategy, an investor would have lost about $7000 dollars of his outlay. But at the same time, on average he can expect to do better at $49,350, and with an approximate maximum upside potential of $93,509 almost three times the size of his original investments. Nevertheless, even though the bad scenario is highly unlikely, one can understand that an investor with a 10-period investment horizon may shy away from the stock market if he or she is very risk averse. Data Source: Own calculations Finally, we show a figure of the same analysis, but continuing the same strategies for 30 years. Now we see the benefit of long-run investing in the stock market.

How Risky is the Stock Market 10 For periods of 22 years or more, investing in the stock market always beats putting money in a sock; even in the bad scenario. When investing in the stock market, you can expect to triple your money, with an upside potential of almost eight times your initial investment. In sum, yes, investing in the stock market can be risky. Investors facing an investment horizon of five or ten years are likely to do well, but should accept the risk that they end up with somewhat less than they initially invested. But for a 20 to 30 year investment horizon, the stock market risk comprises almost exclusively upside risk not downside risk. It is extremely likely that your return will be far better compared to putting your money in a sock, or in a bank account with a low (real) interest rate. So if you are in your 30s or 40s and want to save for retirement at 65 or 70, realize that the risk of stock market investing is not as severe for such a long time period compared to the craziness in daily price fluctuations.