Problem 47 - Applied Calculus

Question

On Black Monday, October 28,1929, the stock market on Wall Street crashed. The Dow Jones average dropped from \(298.94\) to \(260.64\) in one day. What was the relative change in the index?

Step-by-Step Solution

Answer

The relative change in the index was approximately 12.81%.

Step 1: Identify the Initial and Final Values

The initial value of the Dow Jones average is given as 298.94, and the final value after the drop is 260.64.

Step 2: Calculate the Absolute Change

Subtract the final value from the initial value to find the absolute change: \[ \text{Absolute Change} = 298.94 - 260.64 = 38.30 \]

Step 3: Compute the Relative Change

The relative change is calculated by dividing the absolute change by the initial value and then multiplying by 100 to express it as a percentage: \[ \text{Relative Change} = \left( \frac{38.30}{298.94} \right) \times 100 \] Simplifying gives:\[ \text{Relative Change} \approx 12.81\% \]

Key Concepts

Stock Market Crash

A stock market crash refers to a sudden and significant decline in the value of the stock market, often marked by panic selling. These events are usually triggered by economic factors, external economic shocks, or even market speculation leading to a dramatic drop in stock prices. Historically, stock market crashes have had widespread economic repercussions, leading to financial uncertainty.

One of the most infamous examples of a stock market crash is "Black Monday," which occurred on October 28, 1929. On this day, the stock market, represented by the Dow Jones Industrial Average, experienced a sharp decline. This crash marked the onset of the Great Depression, a severe worldwide economic depression that took place during the 1930s.

Key features of a stock market crash include:

• Rapid loss of stock value.
• Widespread financial panic among investors.
• Potential global economic impacts.

Understanding crashes is crucial for investors to maintain market stability and take preventive measures to avoid financial catastrophes.

Dow Jones Average

The Dow Jones Industrial Average (DJIA), often referred to as the Dow, is a stock market index that measures the stock performance of 30 prominent companies listed on stock exchanges in the United States. It is one of the oldest and most widely recognized indices in the world. The DJIA serves as a barometer of the overall health of the U.S. economy.

On Black Monday, October 28, 1929, the Dow Jones dropped significantly, highlighting its role as an indicator of economic confidence. The Dow Jones is calculated using a price-weighted average, which means that stocks with higher prices have a more significant impact on the index's movement.

The components of the Dow are selected to reflect a diverse range of industries, helping provide a comprehensive look at economic trends. Investors and economists often analyze the Dow's movement to get insights into the market's overall direction.

Percentage Change

When assessing changes in financial indices like the Dow Jones, percentage change is a valuable measure. It helps in understanding how significant a change is relative to the original figure. Percentage changes are widely used in finance to quantify fluctuations in asset prices, economic indicators, and market indices.

To calculate the percentage change, follow these steps:

• Determine the initial and final values.
• Calculate the absolute change by subtracting the final value from the initial value.
• Compute the relative change by dividing the absolute change by the initial value.
• Multiply by 100 to convert it to a percentage.

In the example from Black Monday in 1929, the drop in the Dow Jones average was from 298.94 to 260.64. This resulted in an absolute change of 38.30. The percentage change, calculated as \(\left(\frac{38.30}{298.94}\right) \times 100\), amounted to approximately 12.81%.

Using percentage change allows for an easy comparison of variations over time or between different scenarios, making it a key tool in financial analysis.