Saturday Brain Storming Thought (186) 26/08/2023


Expected Value (EV)

Expected value is a predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence

In quantum mechanics, the expected value is the probabilistic expected value of the result (measurement) of an experiment

Key Takeaways of Expected Value

1) expected value describes the long-term average level of a random variable based on its probability distribution

2) in investing, the expected value of a stock or other investment is an important consideration and is used in scenario analyses

3) Modern portfolio theory uses expected value in conjunction with an investment’s risk (standard deviation) to come up with optimized portfolios

4) expected value can help investors size up whether an investment’s risk is worth the potential reward

Expected Value in Machine Learning

Expected value is the average value of a random variable over a large number of experiments

A random variable maps numeric values to each possible outcome in an experiment

Expected Value in Investments

Expected value is often used by trading firms to determine the expected profit or loss from some investment

5% annual return with a probability of 95%

20% annual loss with a probability of 5%

Expected Value = (5 X 0.95) + (-20 X 0.05) = 3.75%

Expected Value in Weather

Expected value is often used by agricultural companies to determine the expected amount of rain that will fall during a given season

20% chance of 1″ rain
70% chance of 2″ rain
10% chance of 3″ rain

Expected Value = (0.20 X 1) + (0.70 X 2) + (0.10 X 3) = 1.9 inches

Expected Value in Gambling

Expected value is often used by gamblers to determine how much they could potentially win at a certain game

5% chance of winning 100
50% chance of winning 0
45% chance of loosing 20

Expected Value = (0.05 X 100) + (0.50 X 0) + (0.45 X -20) = -4

Expected Value in Business

Expected value is often used by businessman to calculate the expected return on advertising spending

10% chance of return 5
30% chance of return 2
60% chance of return -8

Expected Value = (0.10 X 5) + (0.30 X 2) + (0.60 X -8) = -3.70

Expected Value in Entrepreneurship

Expected value is often used by individuals when deciding whether or not they should pursue entrepreneurship

60% chance to earn 20000 per year
30% chance to earn 60000 per year
10% chance to earn 0 per year

Expected Value = (0.60 X 20000) + (0.30 X 60000) + (0.10 X 0) = 30000 per year

Depending on whether or not this amount of money sufficient, the individual could then choose to remain in their current job or quit

Random Variable

A random variable is a variable that takes on numerical values determined by the outcome of a random experiment

Expected Value and Variance

All probability distributions are characterized by an expected value (mean) and a variance (standard deviation squared)

Expected Value for Binomial Probability

When an experiment meets the four conditions of a binomial experiment with n fixed trials and constant probability of success p

Expected value = E(x) = np

Expected Value criteria

Expected value is a criterion for making a decision that takes into account both the possible outcomes for each decision alternative and the probability that each outcome will occur

Possibility of expected value to be zero

Expected Value of any experiment can be zero, but it does not mean that it’s real outcome will be zero

Risky Investment

Won get 10000
Lose give 10000

Probability of winning or loosing is equal

Can be expected value be negative

Probabilities can never be negative, but the expected value of a random variable can be negative

Expected Value criterion is also called the Bayesian Principle

Advantages of Expected Value

1) helps investors and managers in deciding on projects on expected ROI

2) highlights red flags in case an investment is going to underperform

3) various outcomes are combined to arrive at a single outcome, which eases decision making

4) the easy calculation makes it accessible for anyone with basic mathematical skills to calculate the expected value

5) consider every possibility of outcome to calculate the expected value

Disadvantages of Expected Value

1) it is based on mathematical calculations and is a numerical representation of the Future value of any investment

2) the EV depends on probability, which is highly subjective

3) it is an average of all possible outcomes, hence it doesn’t give the actual result or outcome

4) one cannot use it for a one time activity but scenarios with repeated outcomes

5) it does not give a view of the Risk involved

6) it may not correspond to any of the possible outcomes

Limitations of Expected Value

Probabilities used in expected value calculations are usually based on past data and are therefore likely to be estimates

There is a danger, therefore, that these estimates are likely to be unreliable because they are not accurate

Compiled by:

Er. Avinash Kulkarni

Chartered Engineer, Govt Regd Valuer, IBBI Regd Valuer

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