S&P 500 PRICE FORECAST FOR THE NEXT TWO YEARS

Since mid-March, markets have continued to recover. Following the CARES act passed on March 27, 2020 by the US Federal Government, investments in stocks increased rapidly. Now, before the controversial second stimulus plan hits, index prices seem to remain dormant. Owing to the course of the oncoming elections, market pricing behavior could change, and investors may want to consider proceeding with caution once they decide to invest in the stock market.

The usual perception of market pricing on stocks suggests that if the current president is elected, prices will spike, but if the opposing candidate is elected, prices will sharply decline with only a slight increase overtime. For the purpose of this article, however, the methods used have not been predicated on the outcome of the November 3^rd election, rather, I have attempted to conduct a general analysis to forecast the results of the S&P 500 price index by applying the Box-Jenkins method.

An answer to the question “how long will we wait for the market to reach the 4000s?” can be shown by the forecasted price index demonstrated in this article. ARMA(11,23) and EGARCH(11,23) models both predict that there will be new record highs in prices by April 2021, similarly, both models reflect potential record high prices in the 4000s by February 2022 on average. These forecasts are independent of election results and different presidential scenarios. Let us dive into forecasting along with the Box-Jenkins methodology by starting with a unit root test to determine the level of integration for the S&P 500 price index series.

For this analysis, I use the ADF unit root test, which is one of the most reliable tests to define unit root with a time series, for the index; it shows that if a time series has a unit root, it is not stationary or vice versa. Since the S&P 500 price index series has a unit root, it can be inferred that the market is not stationary at level. Hence, the first difference of the price index series should be examined to understand whether it is stationary. If so, we may continue practicing fairly well technical forecasts using a stationary time series.

According to the results of the ADF unit root test, the price index series does not have a unit root at the first difference, so the S&P 500 price index becomes a stationary time series after this formulation. Stationary time series are used in econometrics for making reasonable forecasts. This rule is particularly important for ARMA and ARCH models.

The Box-Jenkins method assumes that if a time series is stationary, we may continue building proper models to make convenient forecasts. The S&P 500 price index series for the period 2008M1-2020M10 is stationary at first difference. Therefore, forecasts are made of this stationary series which means that the difference of the natural logarithm of the original price index series is run for the entire analysis.

The second step of the method is to define which ARMA terms should be selected for a solid model so that we could be able to make coherent forecasts. Taking a look at the correlogram of the series helps us to find out which ARMA terms should be used for generating an outstanding model.

  TABLE 1

CORRELOGRAM OF S&P PRICE INDEX SERIES

The correlogram found in table 1 indicates significant spikes for some lags such as 6th lag, 15th lag, and 22nd lag. These lagged values are preferred to be in autoregressive moving average models and autoregressive conditional variance models. I tried various combinations to find the most appropriate model based on the smallest Akaike information criteria. Hence, I ended up making a forecast with ARMA(11,23) for the index.

The third step of the Box-Jenkins method is to check the diagnosis of residuals to see if the residuals of the models are normally distributed and homoscedastic and whether they have no serial correlation. Since financial time series practice leptokurtic distribution in which kurtosis is larger than that of a normal distribution, it is not deemed as a matter for the models. Yet, forecasts made with ARMA and ARCH models are perceived as arts more than science. Both models do not practice autocorrelation and heteroscedasticity, and they are stable. The last step of the method requires forecast analysis.

                                          

Graph 1: S&P 500 Forecasted Returns with ARMA(11,23) Model

Graph 1 shows the forecasted returns of the S&P 500 index for the period 2020M11-2022M10. As you can see in Graph 1, the time series indicating returns of the S&P 500 index has almost zero mean, therefore it is stationary and can be technically analyzed. The ARMA(11,23) model expects negative returns at the end of  November, December 2020, and January 2021, and then the index will see positive returns again way through 2021 with some fluctuations in May and July.

 

 Graph 2: S&P 500 Adjusted Price Index

Graph 2 shows the prices of the S&P 500 index created by forecasted returns for the period 2020M11-2022M10. The price will not hit the last peak of the index until April 2021 in terms of the ARMA(11,23) model’s forecast. However, recovery resumes as of March 2021 and the index sees its record high of 3923 by the end of January 2022. Prices move steadily during 2022 with some fluctuations in March and April. 4053 is tested by October 2022.

LONG TERM VOLATILITY ON S&P 500 INDEX AND ITS RELATION TO POLITICAL PARTIES

Financial markets have been badly affected by COVID-19. Especially market indexes plunged dramatically in a short while. S&P 500 dropped by 22.8% between February and April but it quickly started to recover through April and May. However, the index tumbled to its trough by approximately 85% in June 1932 from its peak in September 1929. Of course, this comparison does not seem so coherent before seeing index prices during the next two years but it can be easily said that the index has begun to rise shortly after its dip occurred because of COVID-19. As of June first, two months after its dip, the index rebounded more than two-thirds of its losses. Nevertheless, it could not rebound even half of its losses until March 1937 from its June 1932 dip and it took almost a quarter of a century to reach the same price it had in 1929. Some forecasts which I am planning to discuss in my next article show that the index will have recovered all its losses by March 2022.

This article intends to understand if political parties play a big role on the volatility of the S&P 500 index returns. As we know, volatility is a variance change on time series. In this article, I picked up the index S&P 500 indicating weighted average monthly stock prices of 500 biggest corporations in the U.S. as a time series from January 1928 to June 2020 in order to make a volatility analysis by using an exponential generalized autoregressive conditional variance model. I also try to explain how political parties have changed the volatility on the index over nearly 92 years. I make a comparison among the terms of democrats and the terms of republicans based on their impacts in the economy by observing the volatility on the returns of the biggest market index of the U.S., S&P 500. My criticism is that if volatility on a market index rapidly increases, it harms the economy. I test in which political party’s term the volatility on the index has increased or decreased more throughout almost a century. 

  

I would like to show two different graphs of the S&P 500 index before jumping to volatility analysis. The first one is the nominal (unadjusted with inflation) prices of the market index. 

This graph represents only pure index prices during the term. It merely helps us to get how prices have changed over the term but it cannot provide a comprehensive and right benchmark among crises. When looking at the graph, it may be said that the market index is practicing a price bubble now. Yet, it is not true because we cannot see the month by month percentage price change on this graph.

On the other hand, price change in the logarithmic base can be seen in the second graph and it gives a better presentation to interpret the duration. Since the logarithmic series has a steady trend, which is called trend stationary process, its trend line can be used basically as an average benchmark to determine whether or not a price bubble is currently being revealed. As long as the prices which are on the trend line does not deviate much from itself, a price bubble does not exist. Seemingly, the index prices have been tracking that trend line for almost the last two decades so the index is not practicing a price bubble at the moment. 

Furthermore, the logarithmic series can be used to compare the impacts of crises. The logarithmic series shows that there is no similarity between the great depression and COVID-19 economic crisis in terms of price changes on the S&P 500 index. As can be seen in the logarithmic series, price decline from September 1929 to June 1932 was immensely large compared to price decline from February 2020 to April 2020. Briefly, COVID-19 economic crisis is temporary and it seems like its harms would not affect the U.S. economy in the long run as it was after the great depression stealing the country’s 25 years.   

After touching on the importance of the logarithmic price series we continue to make volatility analysis on the returns of the S&P 500 index and test if there is a trade-off between high volatility and terms of political parties. As I mention in this article before, my standpoint is that high volatility harms economies and my purpose is to remark that the dimension of volatility has been larger in which political party’s terms.

In order to draw a picture regarding the volatility change, differences of logarithmic prices that indicate the percentage change of S&P 500 index prices are used. We call it returns series along the rest of this article. The returns series created by the difference of the logarithmic price series turns the analysis to a more comprehensive and serious one. First of all, the returns series has no trend since returns turn around zero mean (average) thus the returns series describes a difference stationary process. Hence returns of the index do not follow a specific path, they have been asymmetrically changing during these 92 years. Whenever a return is above 0, it is a positive return (profit); whenever a return is below 0, it is a negative return (loss). Yet it does not say enough to make comparisons among largeness of crises occurred over time therefore dimensions of returns should be measured to demonstrate the harmful impacts of distinct crises. Volatility on the returns series exhibits those impacts and allows us to observe how large they are.   

Depart from that, which political party’s terms have experienced more and larger volatility can be determined. How long political parties have kept the power during the period are seen on the third graph with red timelines for terms of republicans and blue timelines for terms of democrats. Democratic Party has ruled the country for 49 years as Republican Party has been ruling it for 43 years since 1928. The longest uninterrupted term during the period belongs to democrats with 20 years while the longest uninterrupted term of republicans is only 12 years. Apparently, terms of republicans are more volatile than terms of democrats on the returns series shown by the third graph. General volatility on returns during terms of republicans is larger particularly in 1928-1933 term, 1981-1993 term, 2001-2009, and current term. Conversely, returns do not practice large general volatility during terms of democrats except the 1933-1953 term. When watching the largeness of negative devastating volatility causing the crisis, Republican Party faces negative volatility on returns more than Democratic Party did. Throughout the period, republicans have been practicing 4 severe economic crisis including the great depression, oil crisis, mortgage financial crisis and COVID-19 economic crisis as democrats practiced only second world war economic crisis and dotcom bubble whose dimensions of its volatility are much smaller than other crisis occurred in Republican Party’s terms.    

The returns series on the third graph also indicates that COVID-19 economic crisis is as bad as the mortgage crisis but it is not even close to the great depression. Besides, oil crisis and crisis exposed owing to the second world war look similar.

Volatility on financial time series is affected by news and information announced to the public. According to the EGARCH model using the S&P 500 index returns during the period, the effect of incoming information to markets is persistent therefore volatility clusters are being revealed over time and there is leverage effect on returns of the index. The leverage effect states that negative news contributes to negative volatility more than positive news contributes to positive volatility so returns of the S&P 500 are more sensitive to bad news.

Believe or not it is just a prospect but the conspicuous thing in this work is that each time republicans come to power, bad news, and despair start to circulate and a sudden crisis pops up. And also, the power passes to Democratic Party notedly after a volatility fluctuation is practiced in Republican Party's terms during the period. Who knows this routine might perish in the coming election.