S&P 500 and Apple Stock Analysis

S&P 500 as a Benchmark

• The S&P 500 stock price index is used as a benchmark for investment returns.

• Investing in the S&P 500 from 2000 to 2016 resulted in a volatile ride.

• Experienced a significant drop, losing about half its value and then a long increase starting in 2003.

• Great Financial Crisis from 2007 to 2009.

• Tripled in value from 02/2009 to the present, showing market instability.

Dependence Across Stocks

• The Law of Large Numbers doesn't apply because of the dependence across stocks.

• If stocks were independent, the market would be more constant.

• The stock market is hard to forecast.

• Risk quantification is done through the standard deviation of past risks.

Apple's Performance vs. S&P 500

• Apple's performance was superimposed on the S&P 500 chart (rescaled to start at 100) reflecting a 40-fold increase in value in about 15 years (from Feb).

• Investing $400,000 in Apple stock in February could have resulted in over $15,000,000 now.

• Significant drop after February, losing about three-quarters of its value, followed by years of slow recovery.

Steve Jobs and Apple's Culture

• Steve Jobs was fired from Apple and later brought back.

• The Economist magazine example shows lasting success due to company culture.

• The Economist doesn't use bylines, creating a unique culture.

• Every company possesses their own unique culture that produces outlier effects.

Apple's Volatility and Correlation with S&P 500

• Apple's returns are more variable than the S&P 500.

• Apple lost almost 60% in one month.

• Investing is challenging due to the noise and variability and difficulty in maintaining conviction.

• Correlation with S&P 500: Apple tends to move with the S&P 500.

Variance and Returns

• Scatter plot of Apple's variance (horizontal axis) vs. returns (vertical axis) shows an upward slope, indicating correlation.

• Apple is more variable than the S&P 500.

Regression Line and Beta

• A regression line fitted through the scatter has a slope of 1.45, meaning Apple overreacts to the market.

• (Beta) of a stock measures its relation to the market.

  • (Beta = 1): Asset moves one-to-one with the market.

  • (Beta = 2): Rare.

  • (Beta = 1.45): Apple's beta shows overreaction to the market.

Market Risk vs. Idiosyncratic Risk

• Market risk: Risk of the entire stock market.

• Idiosyncratic risk: Apple-specific risk (e.g., Steve Jobs' death, product failures).

• Apple takes risks that don't always work out.

Variance of Return on a Stock

• The variance of the return on a stock is:

  • \text{Variance of Return} = \beta^2 \times \text{Variance of Market Return} + \text{Variance of Residual}

  • Systematic Risk: \beta^2 \times \text{Variance of Market Return}

Regression Line Explained

• Regression line: A single line that best fits the data in a scatter plot.

• Residual: Vertical distance between a data point and the regression line; indicates the error of the line for that point.

• Least Squares Method: Used to minimize the combination of residuals.

• Equation for a line: Y = mX + b

  • (Y): Return on Apple stock.

  • (X): Return on the market.

  • (m): Beta.

  • (b): Alpha.

• (Beta) measures how much a stock co-moves with the market, indicating systematic risk.

• Idiosyncratic risk is how far the point will lie above or below the regression line.

S&P 500 as a Benchmark

• The S&P 500 stock price index serves as a benchmark for investment returns.

• Investing in the S&P 500 from 2000 to 2016 was a volatile experience, with significant drops and subsequent increases.

• The market experienced a major decline during the Great Financial Crisis from 2007 to 2009.

• From 02/2009 to the present, the market has tripled in value, highlighting ongoing instability.

Dependence Across Stocks

• The Law of Large Numbers is not applicable due to the dependence across stocks.

• If stocks were independent, the market would exhibit greater stability.

• Forecasting the stock market is challenging.

• Risk quantification is performed using the standard deviation of past risks.

Apple's Performance vs. S&P 500

• Apple's performance, when superimposed on the S&P 500 chart (rescaled to start at 100), showed a 40-fold increase in value in approximately 15 years (from Feb).

• An investment of $400,000 in Apple stock in February could have grown to over $15,000,000.

• Apple experienced a significant drop after February, losing about three-quarters of its value, followed by a period of slow recovery.

Steve Jobs and Apple's Culture

• Steve Jobs was initially fired from Apple but later reinstated.

• The Economist magazine, which doesn't use bylines, exemplifies lasting success due to company culture.

• Each company has a unique culture that can produce outlier effects.

Apple's Volatility and Correlation with S&P 500

• Apple's returns are more variable compared to the S&P 500.

• Apple's stock value once dropped nearly 60% in a single month.

• Investing is difficult due to market noise, variability, and maintaining conviction.

• Apple's stock movements tend to correlate with the S&P 500.

Variance and Returns

• A scatter plot of Apple's variance (horizontal axis) versus returns (vertical axis) indicates a positive correlation.

• Apple's stock is more variable compared to the S&P 500.

Regression Line and Beta

• A regression line fitted through the scatter plot has a slope of 1.45, suggesting Apple tends to overreact to market movements.

• (Beta) of a stock quantifies its relation to the market.

  • \text{Beta = 1}: Asset moves one-to-one with the market.

  • \text{Beta = 2}: Rare.

  • \text{Beta = 1.45}: Apple's beta indicates overreaction to the market.

Market Risk vs. Idiosyncratic Risk

• Market risk: Risk affecting the entire stock market.

• Idiosyncratic risk: Risk specific to Apple (e.g., Steve Jobs' death, product failures).

• Apple undertakes risks that don't always yield positive outcomes.

Variance of Return on a Stock

• The variance of the return on a stock is calculated as:

  • \text{Variance of Return} = \beta^2 \times \text{Variance of Market Return} + \text{Variance of Residual}

• Systematic Risk: \beta^2 \times \text{Variance of Market Return}

Regression Line Explained

• Regression line: A line of best fit through data points in a scatter plot.

• Residual: Vertical distance between a data point and the regression line, indicating the line's error for that point.

• Least Squares Method: A method to minimize the combination of residuals.

• Equation for a line: Y = mX + b

  • Y: Return on Apple stock.

  • X: Return on the market.

  • m: Beta.

  • b: Alpha.

• Beta measures how much a stock co-moves with the market, indicating systematic risk.

• Idiosyncratic risk is the extent to which a point lies above or below the regression line.

The S&P 500 stock price index is a benchmark for investment returns. Investing in it from 2000 to 2016 was volatile, with drops and increases, including a major decline during the Great Financial Crisis (2007-2009). From 02/2009 to the present, the market has tripled in value, showing ongoing instability.

The Law of Large Numbers doesn't apply due to stock dependence. Independent stocks would mean a more stable market. Forecasting the stock market is challenging, and risk quantification uses the standard deviation of past risks.

Apple's performance, when compared to the S&P 500 (rescaled), increased 40-fold in about 15 years. A $400,000 investment in Apple in February could have grown to over $15,000,000. Apple had a significant drop after February, losing about three-quarters of its value, followed by slow recovery.

Steve Jobs was fired from Apple and later brought back. The Economist magazine, without bylines, shows lasting success due to company culture. Every company's unique culture can produce outlier effects.

Apple's returns are more variable than the S&P 500, with the stock value dropping nearly 60% in a month. Investing is difficult due to market noise, variability, and maintaining conviction. Apple's stock movements often correlate with the S&P 500.

A scatter plot of Apple's variance versus returns shows a positive correlation. Apple's stock is more variable than the S&P 500.

A regression line fitted through the scatter plot has a slope of 1.45, suggesting Apple overreacts to market movements. Beta quantifies a stock's relation to the market. \text{Beta = 1} means the asset moves one-to-one with the market, and \text{Beta = 2} is rare. Apple's beta of 1.45 indicates overreaction.

Market risk affects the entire stock market. Idiosyncratic risk is specific to Apple (e.g., Steve Jobs' death, product failures). Apple undertakes risks that don't always yield positive outcomes.

The variance of the return on a stock is: \text{Variance of Return} = \beta^2 \times \text{Variance of Market Return} + \text{Variance of Residual}. Systematic risk is: \beta^2 \times \text{Variance of Market Return}.

A regression line is a line of best fit through data points in a scatter plot.