1 Technical analysis

At first I download 10 years of trading data from getSymbols and calculate daily returns of Amazon (AMZN), and calculate monthly, quarterly, and yearly returns both discrete and continuous way.

Furthermore

1.0.1 Comparing both monthly discrete and continuous returns:

1.0.1.1 Monthly Arithmetic Returns

  • Smoother appearance: The line representing arithmetic returns is less volatile, with more gradual peaks and valleys. This reflects how arithmetic returns average out price fluctuations over the whole month.

  • Focus on overall trend: Arithmetic returns give a better sense of the general direction of the stock (upwards or downwards) over a longer time period.

1.0.1.2 Monthly Continuous Returns

  • More jagged: The line for continuous returns shows more frequent and sharper changes in price, highlighting the day-to-day volatility of the stock market.

  • Emphasis on short-term changes: Continuous returns are better suited to analyzing immediate price movements and identifying specific dates of significant change.

1.0.2 Types of Returns:

Moreover we can say that both types of returns are valuable tools for investors, but they serve different purposes:

  • Arithmetic returns help with understanding long-term trends.

  • Continuous returns are better for analyzing short-term market fluctuations.

2 Daily Of 10-year Returns

As we can see that in the image depicts the historical price performance of the stock Amazon (AMZN) . The timeframe covered is from January 3rd, 2012, to December 31st, 2021. The line graph demonstrates the fluctuations in stock price over those years. The stock’s most recent price, as indicated, is $166.72, with a slight downward trend reflected in the daily return of -0.011.

The vertical axis (y-axis) of the chart shows the stock price in dollars. You’ll see that the price has varied significantly over time, with a general upward trend. This means that overall, the value of the stock has increased.

3 Explanation of The Indicators:

3.1 Moving Average Convergence Divergence (MACD):

MACD is a trend-following momentum indicator that shows the relationship between two moving averages of a security’s price. It consists of the MACD line (the difference between the 12-day and 26-day exponential moving averages) and the signal line (a 9-day exponential moving average of the MACD line). When the MACD line crosses above the signal line, it indicates a bullish signal, and when it crosses below the signal line, it indicates a bearish signal.

3.2 Relative Strength Index (RSI):

RSI is a momentum oscillator that measures the speed and change of price movements. It oscillates between 0 and 100 and is typically used to identify overbought or oversold conditions in a security. When RSI values exceed 70, it suggests that the security is overbought and may be due for a pullback. Conversely, when RSI values fall below 30, it indicates that the security is oversold and may be due for a rebound.

3.3 Bollinger Bands:

Bollinger Bands consist of a middle band (typically a 20-day simple moving average) and two outer bands that are standard deviations away from the middle band. The width of the bands expands and contracts based on the volatility of the security’s price. Traders often use Bollinger Bands to identify overbought or oversold conditions and potential price breakouts. When the price touches or crosses the upper band, it may indicate that the security is overbought, while touching or crossing the lower band may suggest that it’s oversold. Additionally, Bollinger Bands can help identify the potential continuation or reversal of trends.