Chapter 14: Problem 4

During the financial crisis and recovery, stock market prices first fell by about 55 percent and then rose by about 65 percent. Did investors, therefore, come out ahead? Explain why not.

Short Answer

Expert verified

Answer: No, investors did not come out ahead. The final investment value was approximately 74.25% of the initial investment, which is less than the initial investment.

Step by step solution

Identify the initial investment

Let's assume the initial investment made by an investor is \(I_0\). This will be our starting point for calculations.

Calculate the investment value after the 55% drop

During the financial crisis, the investment loses 55% of its value. So, we will find the value of the investment after the 55% drop. To do this, we'll calculate 45% of the initial investment: \(I_1 = I_0 * (1 - 0.55) = I_0 * 0.45\)

Calculate the investment value after the 65% rise

After the 55% drop, the investment value rose by 65% during the recovery. So, we'll calculate the value of the investment after the 65% rise: \(I_2 = I_1 * (1 + 0.65) = I_0 * 0.45 * 1.65\)

Compare the final investment value with the initial investment

Now, we need to compare the final investment value \(I_2\) with the initial investment \(I_0\) to determine if the investors came out ahead: If \(I_2 > I_0\), the investors came out ahead. If \(I_2 < I_0\), the investors did not come out ahead. \(I_2 = I_0 * 0.45 * 1.65 = 0.7425 * I_0\) Since \(0.7425 * I_0 < I_0\), the investors did not come out ahead.

Conclusion

Based on the calculations, investors did not come out ahead after the stock market prices first fell by 55% and then rose by 65% during the financial crisis and recovery. The final investment value was approximately 74.25% of the initial investment, which is less than the initial investment.