- 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 and Conditional Probabilities
Let’s say you are asked the following question:
What is the probability of your portfolio earning a return greater than 10%?
This kind of probability is an unconditional probability as the probability is not dependent on the occurrence of any other event. The event, A, is that the portfolio will earn a return greater than 10%. The probability of such an event will be specified as P(A). The calculation is quite simple. The numerator is the sum of probabilities of all returns being above 10%. Assume this is 0.60. The denominator is 1, the sum of probabilities of all possible returns. The probability P(A) = 0.60/1 = 0.60.
Now, let’s ask another related question:
What is the probability of your portfolio earning a return greater than 10% given that the returns are never below 5%?
Notice that we have added a new condition - given that the returns are never below 5%. Now the probability of portfolio earning returns greater than 10% is not unconditional. It is conditional on another event, B, that is, the returns are never below 5%. Such a probability is called conditional probability, and is expresses as P(A|B), the probability of A given B.
Our calculation will now change.
The numerator will still be the same: the sum of probabilities of all returns being above 10%. We assumed this to be 0.60.
The denominator will now consider Event B as well - the sum of probabilities of all returns being 5% or more. Assume this is 0.80.
The conditional probability will be calculated as P(A|B) = 0.60/0/80 = 0.75.
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