PROBABILITY MODELS, EXPECTED VALUES, AND BAYES’ FORMULA:
- Expected Value: The expected value of a random variable is the weighted average of possible outcomes, calculated using probabilities. For example, the expected earnings per share (EPS) can be calculated as a weighted average of each EPS outcome.
- Variance and Standard Deviation: Variance measures the dispersion of a random variable, and standard deviation is the square root of variance. These values are essential in assessing the volatility of investments, calculated using a probability model.
- Investment Problem as a Probability Tree: A probability tree helps visualize the probabilities of various outcomes based on different scenarios. Expected EPS can be calculated using conditional probabilities, adjusting for new information (like tariffs).
- Bayes’ Formula: Bayes’ formula updates prior probabilities in light of new data. It helps revise the probability of an event given updated information, such as the probability of a strong economy after a stock’s positive performance.
KEY CONCEPTS :
- Expected Value: The expected value of a random variable is the weighted average of its possible outcomes.
- Variance: Variance is the probability-weighted sum of squared deviations from the expected value.
- Standard Deviation: The standard deviation is the square root of the variance.
- Probability Tree: A probability tree shows the probabilities of two events and their subsequent conditional probabilities.
- Conditional Expected Value: Conditional expected values depend on the outcome of prior events and can refine forecasts when new information is available.
- Bayes’ Formula: Bayes’ formula updates probabilities based on the occurrence of an event, often represented by a tree diagram.