Expectation in Finance (AQA Level 3 Mathematical Studies (Core Maths))

Revision Note

Author

Naomi C

Expertise

Maths

Expectation in Finance

What is the expected value?

The expected value is the average (mean) value of a particular experiment
- For example, the expected number of times a coin will land on tails when flipped 5 times is 2.5
Probability theory has applications in many industries, including business, manufacturing, and finance, where there is uncertainty
- For example, expected value can be used to find the average cost of manufacturing errors
- The expected value can be anything with a perceived value, e.g. profit, time, cost etc.
You can calculate the expected value of an experiment with n events by multiplying the value of each event, v, by its probability, p, of occurring
- Expected value = $p_{1} v_{1} + p_{2} v_{2} + . . . + p_{n} v_{n}$
- E.g. Consider a fairground game where there is a 5% chance of winning a prize of £3, a 10% chance of winning a prize of £0.50 and an 85% chance of winning nothing
  - The expected value, the amount a person would win on average each go, would be:
  - 0.05 x 3 + 0.10 x 0.50 + 0.85 x 0 = £0.20

Exam Tip

You may have to calculate the value associated with an event before finding the expected value.

E.g. Given the cost price and the selling price of an individual item, you may need to calculate the profit for each event before being able to calculate the expected profit

Worked Example

A company manufactures vases. Each vase costs £1.40 to be manufactured but can be sold for £3.75.

In the manufacturing process, there is a 13% chance that a vase will have a defect. It costs £0.90 to fix each defect.

What is the company's expected profit?

First find the profit for a vase that does not develop a defect

Profit (no defect) = 3.75 - 1.40 = 2.35

Then find the profit for a vase that has a defect that requires fixing

Profit (defect) = 3.75 - 1.40 - 0.90 = 1.45

Calculate the expected profit for the company by multiplying the value of each event by the probability that it will occur and adding them together

Remember that the P(Vase no defect) = 1 - P(vase defect)

2.35 x (1 - 0.13) + 1.45 x 0.13 = 2.233

Round to 2 decimal places as we are dealing with money

Expected profit = £2.23

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