Financial report and comments for NASDAQ, DJIA, AND S&P500 index

Background

Stock indexes were created to measure the value of specific parts of the stock market. Investors use stock indexes as tools to analyse the markets and calculate the return on investment. Among some of the most well-known indexes are the NASDAQ Composite, S&P 500, and Dow Jones Industrial Average (DJIA). In order to understand the index, investors use statistical measures. One of the key statistical measures is volatility.

This paper explores the three indexes—NASDAQ Composite Index, S&P 500 and DJIA—in different time periods, identifies how their levels of volatility differed, and examines the implications for investors. Volatility identifies the change rate of the index in the given time period: the higher the volatility of the stock is, the higher the implied risk can be.

Analysis of the historical data for NASDAQ, S&P 500 and DJIA yields three main observations. First, while the time series or a box plot can support the analysis, each method can often lead to incorrect observations and therefore should be approached with caution. Second, the volatility of indexes varies over time. The same index can have low volatility in one year, but have high volatility in another year. One example of this is DJIA: in 2012, its volatility was as low as 2.1%, while three years earlier, in 2009, it reached 12.2%. The third observation is that it is important to perform a proper investigation of key statistical measures and normalize the volatility in order to compare the volatility correctly across time and indexes. If the indexes being compared have significantly different values, the results will be difficult to compare before they are normalized.

Stock indexes were created to measure the value of specific parts of the stock market. They can be organized either around particular areas (for example, technology) or around markets. Investors use stock indexes as tools to analyse the markets and calculate the return on investment. The higher the volatility of the stock is, the higher the risk can be.

This paper analyses the volatility of three indexes: NASDAQ Composite Index, S&P 500, and DJIA.

The NASDAQ Composite Index was launched in 1971. It measures both domestic (U.S.) and international NASDAQ common-type stocks that are listed on the NASDAQ Stock Market. It currently comprises over 3000 different securities. In order to qualify for the NASDAQ Composite Index, a security must meet several criteria. Once listed on the NASDAQ Composite Index, if the security ceases to meet any of the criteria, it is removed from the index. This ensures the stability and low volatility of the NASDAQ Composite Index (NASDAQ Composite Index, n.d.).

The S&P 500 Index includes 500 leading companies and covers approximately 80% of the available market capitalization. According to Spindices (S&P 500 Index, n.d.), “there is over USD 5.14 trillion benchmarked to the index, with index assets comprising approximately USD 1.6 trillion of this total.” It is highly followed in the U.S. as an indicator of the performance of the stocks of technology companies and growth companies. However, since both U.S. and non-U.S. companies are listed on the S&P 500 Index, it is not exclusively a U.S. index.

The Dow Jones Industrial Average (DJIA) is one of the oldest stock market indexes. It was created in 1986 by Charles Dow and Edward Jones. The index presents how the top 30 large, publicly owned, U.S.-based companies have traded during a trading session. The index is price-weighted, which means that each company’s contribution to the index depends on the share price. The market capitalization covered by DJIA reached USD 4.67 trillion of USD. The stated objective of DJIA is “To represent large and well-known U.S. companies. Covers all industries with the exception of Transportation and Utilities” (DJIA Index Fact Sheet, n.d.).

To analyse the volatility of the NASDAQ Composite Index, a time series figure was prepared for 2009 (see Figure 1).

Figure 1. 2009 NASDAQ Composite Index (Daily Closing). Source: Yahoo Finance

Figure 1 presents the daily change of the NASDAQ Composite Index (value at the close of the trading day) for 2009. The first quarter of the year shows a declining trend, in which the value of the index dropped from approximately 1700 to below 1300. The trend was broken in the first week of March and the NASDAQ Composite Index kept gaining until the end of the year, reaching a maximum of 2291.28 points in December.

To better examine the volatility of the index, the following key statistical measures were used:

· AVG (Average) – The average value of the index in the given time period, calculated as the sum of the individual values divided by the total number of values.

· Min (Minimum) – The minimum value of the index in the given time period.

· Max (Maximum) – The maximum value of the index in the given time period.

· Median – The numerical value separating the higher half of the data from the lower half of the data, sorted in ascending or descending order.

· StdDev (Standard Deviation) – The amount of dispersion from the average that exists, calculated as the square root of the average of the squared differences of the values from their average value.

· Range – The difference between the Max and Min.

· Var (Variance) - How far the numbers spread out in the data set, calculated as the square of the standard deviation.

Table 1. Key Measures of NASDAQ Composite Index in 2009. Source: Yahoo Finance

In 2009, the NASDAQ Composite Index had an average value of 1845 points. The lowest value reached during that year was 1268 points; the highest value reached was 2291 points. This indicates a spread range of 1022 points, which is considered very high. The standard deviation was 270, with a variance of 73024. The median value of the index in 2009 was 1844 points.

The volatility of the index can be calculated using the statistical measures above.

Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility is measured by using either the standard deviation or the variance between returns from that same security or market index. The higher the volatility, the higher the risk.

In order to compare the volatility of indexes with very different values, which result in difficult-to-compare standard deviations, the average value of the index is applied as the denominator:

Volatility = StdDev/AVG = 270.23 / 1845.38 = 0.146

Thus, the NASDAQ Composite Index had a volatility index of 0.146 in 2009. This means that, for that year, the index had a low risk of changing its value over time.

To determine whether this index is low or high, a reference point is needed. Figure 2 presents a comparison of the NASDAQ Composite Index between 1999 and 2009. Unlike Figure 1, which presented daily data, Figure 2 illustrates monthly data.

Figure 2. NASDAQ Composite Index (monthly) for 1999 and 2009. Source: Yahoo Finance

Figure 2 Shows that the NASDAQ Composite Index in 1999 and 2009 had a steady increasing trend over time. In addition, in 1999, the index experienced dynamic growth at the end of the year (starting in September).

Table 2. Key Measures of NASDAQ Composite Index in 1999 and 2009. Source: Yahoo Finance

As indicated by the key measures in Table 2, the NASDAQ Composite Index had a much higher standard deviation in 1999 than in 2009: the standard deviation was 70% higher, while the variance was nearly three times larger. This might suggest that the volatility of the index in 1999 was much greater. However, Figure 2 calls this assumption into question.

In order to better compare volatility for both years, we normalize it as follows:

1999 volatility = 486.92 / 2787.56 = 0.175

2009 volatility = 286.90 / 1856.53 = 0.154

Now the years 1999 and 2009 can be compared. Dividing the volatility of indexes (1999 volatility / 2009 volatility - 1 = 0.175 / 0.154 - 1 = 13.6%) yields the conclusion that the NASDAQ Composite Index in 1999 was characterized by 13.6% more volatility than the NASDAQ Composite Index in 2009. This means that the value of the index changed 13.6% more in 1999 than in 2009.

The previous section identified the volatility of the NASDAQ Composite Index in 2009 and 1999. This section compares the volatility of the NASDAQ Composite Index with that of the S&P 500 and DJIA Indexes.

Figure 3. NASDAQ Composite and S&P 500 Indexes (monthly) in 2009. Source: Yahoo Finance

Figure 3 presents a comparison of value of the NASDAQ Composite and S&P 500 Indexes in 2009. As the figure illustrates, both indexes steadily gained in value, but the NASDAQ Composite Index grew more dynamically and had higher value.

Table 3. Key Measures of NASDAQ Composite and S&P 500 Indexes in 2009. Source: Yahoo Finance

As Table 3 indicates, the average value of the NASDAQ Composite Index was twice the average value of the S&P 500 Index. The same ratio can be seen in the minimum, maximum and median values. At the same time, the range of the NASDAQ Composite Index was nearly 2.5 times higher than that of the S&P. The standard deviation of the NASDAQ Composite Index was also 2.25 times larger than that of the S&P, while the variance was over 5 times larger.

To better evaluate the volatility the measures are normalized as follows:

NASDAQ volatility = 286.90 / 1856.53 = 0.154

S&P 500 volatility = 122.96 / 948.52 = 0.130

NASDAQ volatility / S&P 500 volatility = 0.154 / 0.130 -1 = 18.4%

The volatility of the NASDAQ Composite Index is 18.4% higher, which means that the NASDAQ Composite Index carries 18.4% higher risk to investors than the S&P 500 Index. It also means that the NASDAQ Composite Index changed over time 18.4% more than the S&P 500 Index. Figure 3 confirms this finding.

Figure 4 presents the time series (monthly) for the NASDAQ Composite and DJIA Indexes for 2009. It is difficult to draw conclusions from the figure, as the values are much different and hard to compare. The key statistical measures must be calculated in order to proceed with the analysis (Table 4).

Figure 4. NASDAQ Composite and DJIA Indexes (monthly) in 2009. Sources: Yahoo Finance, St. Louis Federal Bank

Table 4. Key Measures of NASDAQ Composite and DJIA Indexes in 2009. Source: Yahoo Finance

Comparison of the key measures for the NASDAQ Composite and DJIA Indexes suggests that the DJIA Index is much more volatile and likely to change than the NASDAQ Composite Index. The standard deviation is over 3 times higher, while the variance is 14 times larger. All the measures of the DJIA Index are much higher in comparison to the NASDAQ Composite Index, as Table 4 demonstrates.

In order to compare the volatilities of both measures, normalization is applied as follows:

NASDAQ volatility = 286.90 / 1856.53 = 0.154

DJIA volatility = 1083.81 / 8887.83 = 0.122

DJIA volatility / NASDAQ volatility = 0.122 / 0.154 *100 = 79.2%

This analysis reveals that, in fact, the DJIA Index carries less risk to investors than the NASDAQ Composite Index. The DJIA Index has 21% (calculated as 100%-79%) lower volatility than the NASDAQ Composite Index, or that the DJIA Index has had 21% less change over time than the NASDAQ Composite Index.

Figure 5. Box Plot of NASDAQ Composite and DJIA Indexes (monthly) in 2009. Sources: Yahoo Finance and St. Louis Federal Bank

The box plot presents a visualization of the outliers in the data. Figure 5 reveals that there are no outliers in the indexes. The box plot does not confirm the findings regarding the volatility; it merely displays the spread of values for each index.

The previous sections analysed the volatility of a single index in two separate years, and compared the volatility of different indexes within the same time period. This section investigates the volatility of the DJIA Index over 1989, 2009 and 2012.

Figure 6. DJIA Index (monthly) in 1989, 2009 and 2012. Source: St. Louis Federal Bank

It is difficult to draw conclusions from the time series in Figure 6 due to differences in scale. The index had a much lower value in 1989 than in 2009. While the flattened line might indicate low volatility, the statistical measures should be evaluated before reaching this conclusion.

Table 5. Key Measures of DJIA Index in 1989, 2009 and 2012. Source: St. Louis Federal Bank

Table 5 presents an overview of key statistical measures for the selected years. The year 2009 is characterized by much higher standard deviation and range than the other two selected years. This suggests that the volatility of this year might be higher. In order to compare the three years, the volatility was normalized as follows:

1989 DJIA Volatility = 182.93 / 2535.72 = 0.072

2009 DJIA Volatility = 1083.81 / 8887.83 = 0.122

DJIA 2012 Volatility = 274.68 / 13003.92 = 0.021

The normalized volatility measure confirms the initial observation that conclusions should not be drawn based on Figure 6. It is not 1989 that had the lowest volatility, but 2012: only 2.1%. The DJIA Index had 7.2% volatility in 1999, while it reached 12.2% in 2009. In addition, 2012 had the fewest changes to the value of the index, while 2009 had the highest probability of change.

The volatility of indexes varies over time. It is important to perform a proper investigation of key statistical measures and to normalize the volatility in order to compare the volatility correctly across time and indexes. While the time series or a box plot can support this analysis, each method often can lead to incorrect observations and therefore should be approached with caution.

Based on the findings, it is recommended that stock market analysts take great precaution when comparing different indexes, or even when comparing the same index in different time periods. The data set should be carefully analysed and all the key statistical measures carefully calculated before drawing any conclusions. While visualizing data on the time series proved helpful, that method also should be treated with caution, especially when the values of indexes significantly differ from each other, thus flattening the visualization. The key factor to correct analysis of the volatility is the normalization of the volatility figures, which allows for a truer analysis.

References

1. S&P 500 – Year 2009, Monthly Close

2. DJIA – 1989, 2009, 2012, Monthly Close

3. NASDAQ Composite – 1999, 2009, Monthly Close

4. NASDAQ Composite – 2009, Daily Close

5. Table 1. Calculations:

AVG = 2269.15 + 2291.28 + 2288.4 + 2291.08 + 2285.69 + 2269.64 + 2252.67 + 2237.66 + 2211.69 + 2180.05 + 2206.91 + 2201.05 + 2212.1 + 2190.31 + 2190.86 + 2183.73 + 2172.99 + 2189.61 + 2194.35 + 2173.14 + 2185.03 + 2175.81 + 2144.6 + 2138.44 + 2176.05 + 2169.18 + 2176.01 + 2146.04 + 2156.82 + 2193.14 + 2203.78 + 2197.85 + 2167.88 + 2149.02 + 2166.9 + 2151.08 + 2154.06 + 2112.44 + 2105.32 + 2055.52 + 2057.32 + 2049.2 + 2045.11 + 2097.55 + 2059.61 + 2116.09 + 2141.85 + 2154.47 + 2165.29 + 2150.73 + 2163.47 + 2176.32 + 2156.8 + 2173.29 + 2172.23 + 2139.89 + 2139.14 + 2139.28 + 2123.93 + 2110.33 + 2103.57 + 2068.15 + 2048.11 + 2057.48 + 2122.42 + 2124.04 + 2130.74 + 2090.92 + 2107.61 + 2131.42 + 2146.3 + 2138.04 + 2132.86 + 2126.75 + 2133.15 + 2102.64 + 2091.78 + 2080.9 + 2084.02 + 2060.39 + 2037.77 + 2018.78 + 1983.2 + 1967.07 + 1968.89 + 2009.06 + 2028.77 + 2027.73 + 2024.43 + 2024.23 + 2017.98 + 2020.9 + 1989.22 + 1969.24 + 1955.92 + 1930.84 + 1985.52 + 2009.35 + 1998.72 + 1969.73 + 1992.24 + 2000.25 + 1973.16 + 1993.05 + 2011.31 + 2008.61 + 1978.5 + 1984.3 + 1967.76 + 1975.51 + 1967.89 + 1965.96 + 1973.6 + 1926.38 + 1916.2 + 1909.29 + 1886.61 + 1885.03 + 1862.9 + 1799.73 + 1793.21 + 1756.03 + 1752.55 + 1747.17 + 1746.17 + 1787.4 + 1796.52 + 1845.72 + 1835.04 + 1844.06 + 1838.22 + 1829.54 + 1792.34 + 1764.92 + 1766.19 + 1827.47 + 1807.72 + 1808.06 + 1796.18 + 1816.38 + 1858.8 + 1862.37 + 1853.08 + 1860.13 + 1842.4 + 1849.42 + 1850.02 + 1825.92 + 1836.8 + 1828.68 + 1774.33 + 1751.79 + 1731.08 + 1750.43 + 1692.01 + 1695.25 + 1727.84 + 1734.54 + 1732.36 + 1680.14 + 1689.21 + 1664.19 + 1715.92 + 1731.24 + 1739 + 1716.24 + 1759.1 + 1754.12 + 1763.56 + 1719.2 + 1717.3 + 1711.94 + 1673.81 + 1679.41 + 1694.29 + 1652.21 + 1646.12 + 1643.85 + 1608.21 + 1673.07 + 1670.44 + 1626.8 + 1625.72 + 1653.31 + 1652.54 + 1590.66 + 1561.61 + 1606.71 + 1621.87 + 1602.63 + 1551.6 + 1528.59 + 1501.8 + 1545.2 + 1587 + 1528.95 + 1516.52 + 1555.77 + 1457.27 + 1483.48 + 1491.22 + 1462.11 + 1404.02 + 1431.5 + 1426.1 + 1371.64 + 1358.28 + 1268.64 + 1293.85 + 1299.59 + 1353.74 + 1321.01 + 1322.85 + 1377.84 + 1391.47 + 1425.43 + 1441.83 + 1387.72 + 1441.23 + 1442.82 + 1467.97 + 1470.66 + 1534.36 + 1541.71 + 1530.5 + 1524.73 + 1591.56 + 1591.71 + 1546.24 + 1515.05 + 1516.3 + 1494.43 + 1476.42 + 1507.84 + 1558.34 + 1504.9 + 1489.46 + 1477.29 + 1465.49 + 1507.07 + 1440.86 + 1529.33 + 1511.84 + 1489.64 + 1546.46 + 1538.79 + 1571.59 + 1617.01 + 1599.06 + 1652.38 + 1628.03 + 1632.21 / 252 [252 is the count of the summed values] = 1845.38

Min = 1268.4 [I sort the values in data set descending and pick the lowest value]

Max = 2291.28 [I sort the values in data set descending and pick the highest value]

Median = (1844.06 + 1845.72) / 2 = 1844.89 [I sort the values descending, take since we have even amount of numbers I take 126th and 127th and take their average]

StdDev = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

Range = Max – Min = 2291.28 – 1268.4 = 1022.64

Var = 270.23^2 = 73024.49

6. Table 2. Calculations:

AVG 1999 = (4069.31 + 3336.16 + 2966.43 + 2746.16 + 2739.35 + 2638.49 + 2686.12 + 2470.52 + 2542.86 + 2461.4 + 2288.03 + 2505.89) / 12 = 2787.56

AVG 2009 = (2269.15 + 2144.6 + 2045.11 + 2122.42 + 2009.06 + 1978.5 + 1835.04 + 1774.33 + 1717.3 + 1528.59 + 1377.84 + 1476.42) / 12 = 1856.53

Min 1999 = 2288.03 [I sort the values in data set descending and pick the lowest value]

Min 2009 = 1377.84 [I sort the values in data set descending and pick the lowest value]

Max 1999 = 4069.31 [I sort the values in data set descending and pick the highest value]

Max 2009 = 2269.15 [I sort the values in data set descending and pick the highest value]

Median 1999 = (2638.49 + 2686.12)/2 = 2662.31

Median 2009 = (1835.04 + 1978.5)/2 = 1906.77

StdDev 1999 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

StdDev 2009 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

Range 1999 = 4069.31 – 2288.03 = 1781.28

Range 2009 = 2269.15 – 1377.84 = 891.31

Var 1999 = (486.92)^2 = 237093.69

Var 2009 = (286.90)^2 = 82310.69

7. Table 3 Calculations

AVG S&P 2009 = (825.88 + 735.09 + 797.87 + 872.81 + 919.14 + 919.32 + 987.48 + 1020.62 + 1057.08 + 1036.19 + 1095.63 + 1115.1) / 12 = 948.52

AVG NASDAQ 2009 = (2269.15 + 2144.6 + 2045.11 + 2122.42 + 2009.06 + 1978.5 + 1835.04 + 1774.33 + 1717.3 + 1528.59 + 1377.84 + 1476.42) / 12 = 1856.53

Min S&P 2009 = 735.09 [I sort the values in data set descending and pick the lowest value]

Min NASDAQ 2009 = 1377.84 [I sort the values in data set descending and pick the lowest value]

Max S&P 2009 = 1115.10 [I sort the values in data set descending and pick the highest value]

Max NASDAQ 2009 = 2269.15 [I sort the values in data set descending and pick the highest value]

Median S&P 2009 = (919.32 + 987.48)/2 = 953.40

Median NASDAQ 2009 = (1835.04 + 1978.5)/2 = 1906.77

StdDev S&P 2009 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

StdDev NASDAQ 2009 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

Range S&P 2009 = 1115.10 – 735.09 = 380.01

Range NASDAQ 2009 = 2269.15 – 1377.84 = 891.31

Var S&P 2009 = (122.96)^2 = 15119.46

Var NASDAQ 2009 = (286.90)^2 = 82310.69

8. Table 4 Calculations:

AVG DJIA 2009 = (7062.93 + 7608.92 + 8000.86 + 8168.12 + 8447.00 + 8500.33 + 9171.61 + 9496.28 + 9712.28 + 9712.73 + 10344.84 + 10428.05) / 12 = 8887.83

AVG NASDAQ 2009 = (2269.15 + 2144.6 + 2045.11 + 2122.42 + 2009.06 + 1978.5 + 1835.04 + 1774.33 + 1717.3 + 1528.59 + 1377.84 + 1476.42) / 12 = 1856.53

Min DJIA 2009 = 7062.93 [I sort the values in data set descending and pick the lowest value]

Min NASDAQ 2009 = 1377.84 [I sort the values in data set descending and pick the lowest value]

Max DJIA 2009 = 10428.05 [I sort the values in data set descending and pick the highest value]

Max NASDAQ 2009 = 2269.15 [I sort the values in data set descending and pick the highest value]

Median DJIA 2009 = (8500.33 + 9171.61)/2 = 8835.97

Median NASDAQ 2009 = (1835.04 + 1978.5)/2 = 1906.77

StdDev DJIA 2009 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

StdDev NASDAQ 2009 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

Range DJIA 2009 = 10428.05 – 7062.93 = 3365.12

Range NASDAQ 2009 = 2269.15 – 1377.84 = 891.31

Var DJIA 2009 = (1083.81)^2 = 1174648.41

Var NASDAQ 2009 = (286.90)^2 = 82310.69

9. Table 5. Calculations:

AVG DJIA 1989 = (2258.39 + 2293.62 + 2342.32 + 2418.80 + 2440.06 + 2480.15 + 2645.08 + 2660.66 + 2692.82 + 2706.27 + 2737.27 + 2753.20) / 12 = 2535.72

AVG DJIA 2009 = (7062.93 + 7608.92 + 8000.86 + 8168.12 + 8447.00 + 8500.33 + 9171.61 + 9496.28 + 9712.28 + 9712.73 + 10344.84 + 10428.05) / 12 = 8887.83

AVG DJIA 2012 = (12393.45 + 12632.91 + 12880.09 + 12952.07 + 13008.68 + 13025.58 + 13090.84 + 13096.46 + 13104.14 + 13212.04 + 13213.63 +13437.13) / 12 = 13003.92

Min DJIA 1989 = 2258.39 [I sort the values in data set descending and pick the lowest value]

Min DJIA 2009 = 7062.93 [I sort the values in data set descending and pick the lowest value]

Min DJIA 2012 = 13003.92 [I sort the values in data set descending and pick the lowest value]

Max DJIA 1989 = 2753.20 [I sort the values in data set descending and pick the highest value]

Max DJIA 2009 = 10428.05 [I sort the values in data set descending and pick the highest value]

Max DJIA 2012 = 13437.13 [I sort the values in data set descending and pick the highest value]

Median DJIA 1989 = (2480.15 + 2645.08)/2 = 2562.62

Median DJIA 2009 = (8500.33 + 9171.61)/2 = 8835.97

Median DJIA 2012 = (13025.58 + 13090.84)/2 = 13058.21

StdDev DJIA 1989 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

StdDev DJIA 2009 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

StdDev DJIA 2012 = To simplify calculations we execute the Excel formula =STDDEV(dataset) formula

Range DJIA 1989 = 2753.20 – 2258.39 = 494.81

Range DJIA 2009 = 10428.05 – 7062.93 = 3365.12

Range DJIA 2012 = 13437.13 – 12393.45 = 1043.68

Var DJIA 1989 = (182.93)^2 = 33463.12

Var DJIA 2009 = (1083.81)^2 = 1174648.41

Var DJIA 2012 = (274.68)^2 = 75451.10