- Probability - Basic Terminology
- Two Defining Properties of Probability
- Empirical, Subjective and Priori Probability
- State the Probability of an Event as Odds
- Unconditional and Conditional Probabilities
- Multiplication, Addition and Total Probability Rules
- Joint Probability of Two Events
- Probability of Atleast One of the Events Occuring
- Dependent Vs. Independent Events in Probability
- Joint Probability of a Number of Independent Events
- Unconditional Probability Using Total Probability Rule
- Expected Value of Investments
- Calculating Variance and Standard Deviation of Stock Returns
- Conditional Expected Values
- Calculating Covariance and Correlation
- Expected Value of a Portfolio
- Variance and Standard Deviation of a Portfolio
- Bayes’ Theorem
- Multiplication Rule of Counting
- Permutation and Combination Formula
Unconditional Probability Using Total Probability Rule
As we learned earlier, the total probability rule determines the unconditional probability of an event in terms of probabilities conditional on scenarios.
P(A) = P(A | S1)P(S1) + P(A | S2)P(S2) + … + P(A | Sn)P(Sn)
Where the scenarios S1, S2, …Sn are mutually exclusive and exhaustive.
Let’s take one more example of the Total Probability Rule.
An analyst is assessing the performance of a stock under different scenarios. He comes up with the following probabilities.
| State of Economy | Probability of Economic State | Stock Performance | Probability |
| No recession P(RC) | 0.60 | Rise P(SR | RC) | 0.70 |
| Fall P(SRC | RC) | 0.30 | ||
| Recession P(R) | 0.40 | Rise P(SR | R) | 0.20 |
| Fall P(SRC | R) | 0.80 |
Question 1
Based on the above data, what is the total probability of a stock rise? We need to find the unconditional probability of a stock rise under all scenarios.
P(SR) = P(SR | RC) P(RC) + P(SR | R) P(R)
\= 0.70*0.60 + 0.20*0.40 = 0.5
Question 2
What is the joint probability of having a recession and at the same time having a stock price fall?
P(R and SRC) = P(SRC | R)x P(R) = 0.8*0.4 = 0.32
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