Value-at-Risk of JCP Stock and Analysis of Calendar Effects
Abstract
This paper presents the value-at-risk (VaR) analysis of J.C. Penney Company Inc. (JCP) stock daily negative log returns between 1993 and 2018. The statistical properties of JCP are thoroughly examined and a series of diagnostic tests are conducted to check the conditions of the time series data over the two decades. The GARCH and EGARCH models with normal distribution and Student’s t-distribution are used to estimate the volatility and VaR of the stock. By analyzing VaR, we show that there is currently a high risk of investing in JCP stock. In addition, this paper examines the calendar effects and seasonality of JCP stock through the fundamental properties of the data as well as the VaR. We compare the performance of the stock in four quarters which further confirms our result that JCP stock is at immense risk at this point in time. These results are valuable for anyone interested in evaluating and forecasting JCP stock. The methodology we use is applicable to any other stock that meets our test conditions and is more accurate and realistic in predicting volatility and VaR than the commonly used standard normal distribution based VaR model.
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Introduction
Over the past two decades, the proliferation of the Internet has contributed to the development of e-commerce and has affected the market share of traditional retailers. Purchasing goods online as a convenient alternative to in-store shopping largely saves people’s time and is increasingly popular among customers. J.C. Penney Company Inc. is a US department store chain that operates more than 1000 stores across the United States. It was founded by James Cash Penney and William Henry McManus [1] in 1902. Most J.C. Penney stores are located in shopping centers, and their business mainly includes sales of clothing, cosmetics, household items, jewelry and cookware. As J.C. Penney is one of the largest apparel and home retailers in the United States, investors are deeply concerned about the performance of J.C. Penney Company Inc. stock (NYSE: JCP). In this paper, we will investigate the risk of buying JCP stock as well as the calendar effects of the JCP stock returns. We want to provide investors with useful investment advice.
In 2017, Caroline, Emma, Madelon, Mikkel and Marc from Columbia Business School conducted a research project on J.C. Penney named “Competing for Survival: A Turnaround of Department Store J.C. Penney” [2]. They analyzed the company’s performance from an operational perspective and provided a variety of strategies to help the company better organized. So far, we have found a lack of statistical analysis of J.C. Penney's paper. In this paper, we conducted a complete time series analysis of the JCP stock returns. We focus on the statistical characteristics of JCP stock and draw conclusions only from the statistics.
Risk management is a key process for making investment decisions. In order to control risk in an investment, we need to first determine the amount of risk involved in the investment, and then decide to either accept or alleviate the risk. Standard deviation, beta, value at risk (VaR) and expected shortfall are common measures to quantify the risk. In this paper, we use VaR as the primary tool for measuring the risk of buying stocks. Value-at-risk is a statistical indicator of the riskiness of financial entities or portfolios. It is defined as the maximum dollar amount that is expected to be lost at a predetermined confidence level for a given time frame. The stock market crash in 1987 triggered the innovation of VaR. It was developed as a systematic approach to separating extreme events from daily price changes. In 1994, it was extended by J.P. Morgan who launched the Risk Metrics and published the methodology [3]. Nowadays, VaR has become one of the most commonly used measures of market risk in the financial industry.
In order to calculate the VaR of the stock, we need to accurately predict the price of the stock. The main characteristic of a stock is its return. We model the negative log return series to derive estimates of volatility and VaR. It is well known that financial markets are highly volatile and the periods of high volatility tend to persist for some time before the market returns to a more stable environment (Tsay,2005)[4]. The autoregressive method helps to build a more accurate and reliable volatility model.
Conclusion
In this paper, we analyze the fundamental statistics and the VaR of the daily negative log returns of JCP stock. We use GARCH and EGARCH models to fit the data with normal distribution and Student’s t-distribution assumptions of white noise respectively. Based on the models, we estimate VaR of the stock at quantiles 95%, 99% and 99.9% to measure the riskiness of the stock. Comparing the VaR of JCP and SPY, we find that the VaR of JCP stock is much higher than SPY, and the price of JCP is significantly lower than SPY, especially in the past ten years. The summary statistics also indicates that the daily negative log returns of JCP averaged over ten-year period increased over time and reached the highest during the past ten years. These results help us conclude that the risk of investing in JCP stock is very high.
By analyzing the calendar effect of JCP, we find that although the returns in the four quarters are different, the performance of the stock is not good for either of the four quarters. It is surprising that Q4 has positive average daily negative log return and the highest one-day-ahead VaR among the four quarters. In general, for traditional retailers, the fourth quarter should be the most profitable, because Thanksgiving and Christmas are at the end of the year, and all goods have great discounts during the festivals. The fourth quarter is usually the quarter that Americans spend the most. However, even in the fourth quarter, J.C. Penney cannot make a profit either. It even suffered losses during Q4 and had the highest VaR in a year. It reinforces our previous conclusion that JCP is at immense risk for investment.