Consider an asset that costs 120dollars today. You are going...

Consider an asset that costs $120$dollars today. You are going to hold it for 1 year and then sell it. Suppose that there is a 25 percent chance that it will be worth $100$dollars in a year, a 25 percent chance that it will be worth $115$dollars in a year, and a 50 percent chance that it will be worth $140$ dollars in a year. What is its average expected rate of return? Next, figure out what the investment's average expected rate of return would be if its current price were $130$ dollars today. Does the increase in the current price increase or decrease the asset's average expected rate of return? At what price would the asset have a zero rate of return?

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Key Concepts

Expected Value

The expected value is a fundamental concept in probability and finance where outcomes are weighted by their corresponding probabilities to determine an average result. It is used to summarize the anticipated outcome of a random event by multiplying each possible result by its probability and summing these products.

Rate of Return

The rate of return measures the gain or loss generated on an investment relative to the amount of money invested. It is calculated by comparing the final value of an asset to its initial cost, typically expressed as a percentage, providing insight into the efficiency and profitability of an investment.

Probability Weights

Probability weights are used in calculating the expected value by assigning the relative likelihood of each possible outcome. These weights ensure that outcomes are scaled according to how probable they are, allowing for a more accurate reflection of risk and return in decision making.

Break-even Analysis

Break-even analysis determines the specific conditions, such as the asset price, at which the investment's net return is zero. This involves finding the price point where the expected gains perfectly offset the cost of the asset, indicating the threshold at which an investor neither profits nor loses.

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