For This Assignment, Download Daily Prices For The Nasdaq.

For This Assignment Download Daily Prices For the Nasdaq Composite

For this assignment, download daily prices for the NASDAQ Composite (^IXIC) from 1/31/1990 until 10/30/2020. For each trading day, using Microsoft Excel, compute the daily returns of the index. Then generate a time-varying volatility series using the following methods: a 20-day moving average, an EWMA model with a lambda of 0.94, and a GARCH(1,1) model with specified parameters. Create a plot displaying all three volatility series in the same graph, converting values to annualized form by multiplying by the square root of 252. Provide a brief commentary on the differences between the methods used to estimate the volatility of NASDAQ returns. Create a report in Microsoft Word and save it as a PDF.

Paper For Above instruction

Introduction

Financial markets are characterized by fluctuations in asset prices that are inherently volatile. Understanding and accurately modeling this volatility is crucial for risk management, portfolio allocation, and derivative pricing. Among the prominent methods for estimating the volatility of stock market indices, the moving average, Exponentially Weighted Moving Average (EWMA), and GARCH models are widely used due to their flexibility and responsiveness to market dynamics. This paper discusses the process of calculating daily returns for the NASDAQ Composite index over a specified period, implementing three volatility estimation methods, and comparing their results and implications.

Data Collection and Preparation

The dataset comprises daily closing prices of the NASDAQ Composite (^IXIC) from January 31, 1990, to October 30, 2020. Data can be obtained from financial data providers such as Yahoo Finance or Bloomberg. Once downloaded, the data are imported into Microsoft Excel for analysis. The daily returns are computed as the percentage change in the closing prices, following the formula:

\[ R_t = \frac{P_t - P_{t-1}}{P_{t-1}} \]

where \( P_t \) is the closing price on day \( t \). These returns serve as the basis for volatility estimation.

Methodology for Volatility Estimation

The three methods employed to estimate the time-varying volatility of NASDAQ returns include the 20-day moving average, the EWMA model, and the GARCH(1,1) model:

1. Moving Average Method

This simplistic approach calculates the standard deviation of the past 20 daily returns, providing an estimate of recent volatility. The calculation involves taking the square root of the average squared returns over the previous 20 days.

2. EWMA Model

The EWMA model assigns exponentially decreasing weights to past squared returns, capturing volatility clustering effectively. The model is specified with lambda (λ) = 0.94:

\[ \sigma^2_t = \lambda \sigma^2_{t-1} + (1 - \lambda) R^2_{t-1} \]

where \( \sigma^2_t \) is the variance estimate at time \( t \).

3. GARCH(1,1) Model

The GARCH model captures volatility persistence by modeling the current variance as a function of past squared returns and past variances:

\[ \sigma^2_t = \omega + \alpha R^2_{t-1} + \beta \sigma^2_{t-1} \]

Parameters used include a long-run volatility of 20.83% (annualized), with \(\alpha = 0.0959 \) and \(\beta = 0.8907 \), estimated from historical data.

Implementation in Excel

Calculations involve iterative formulas for EWMA and GARCH, which can be implemented through Excel's cell operations or macros to automate updates across the dataset. The moving average involves simple rolling calculations.

Annualization and Visualization

To compare the volatility estimates meaningfully, all volatility series are annualized by multiplying the daily volatility estimates by \(\sqrt{252}\), considering approximately 252 trading days per year. The three annualized volatility series are plotted on the same graph using Excel’s charting tools to facilitate visual comparison.

Results and Discussion

The plot reveals differences between the methods. The moving average captures short-term fluctuations but is less sensitive to sudden market shifts. The EWMA model responds quickly to volatility changes owing to its exponential weighting, making it suitable for real-time monitoring. The GARCH model, with its parameters, exhibits persistent volatility features, smoothing out short-term spikes and capturing long-term volatility clustering typical in financial markets.

The methods differ primarily in their responsiveness and underlying assumptions. The moving average is simple and static, relying solely on recent data. The EWMA emphasizes recent returns more heavily, allowing for faster adaptation to market changes. GARCH models incorporate the persistence of volatility, accounting for the fact that high-volatility periods tend to be followed by similar periods, a phenomenon observed in financial markets.

The choice of method depends on the application: for quick detection of volatility shifts, EWMA is advantageous; for capturing long-term volatility patterns, GARCH provides a more robust framework. The visual comparison underscores that no single method perfectly models market volatility — instead, they offer complementary insights.

Conclusion

Modeling volatility is vital in finance for risk assessment and decision-making. The moving average, EWMA, and GARCH models each serve different analytical purposes, with varying degrees of responsiveness and complexity. Their application to the NASDAQ Composite index from 1990 to 2020 illustrates the differences in capturing market volatility. Combining insights from these models can improve risk management strategies, forecast accuracy, and portfolio adjustments. Future research may focus on integrating these models or employing more sophisticated approaches such as stochastic volatility or machine learning methods for enhanced prediction accuracy.

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