Expected Monetary Value
Expected Monetary Value
In a business environment, we frequently use probabilities to assess alternative financial decisions
Example 1: A coin is tossed ten times.
When a head is obtained, €4 is won.
When a tail is obtained, €2 is lost
Calculate the expected winnings. Outcome
HEAD TAIL
Winnings
€4 -€2
Probability
0.5 0.5
Expected winnings in one toss:
Expected Monetary Value (or just Expected Value (EV) = €1
Note: You never actually receive €1; you either receive €4 or lose €2. Play this game many times, sometimes you receive €4, sometimes lose €2, but it ‘averages out’ at €1 per game.
This is your Expected Value.
Expected winnings in ten plays: Decision Making using Expectation
Example 2:
A potential customer for a €50,000 fire insurance policy has a home in an area that, according to experience, may sustain a total loss in a given year with a probability of 0.001 and a 50% loss with a probability of 0.01. There is a 98.9% chance that no claim will be made.
Ignoring partial losses, what premium should the insurance company charge to break even?
Solution:
Expected Claim = 50000*0.001 (Full claim)
+ 25000*0.01 (Partial Claim) + 0*0.989 (No Claim) = €300
A premium of €300 would break even in the long run
Decision Making using Expectation
Example 3:
An investor has a certain amount of money to invest. Three alternative portfolio selections are available. The estimated profits depend on the economic conditions as follows:
Profit (€’000) Portfolio Selection A B C
Economy declines
No change
Economy expands €.5 -€2 -€7 €1.0 €2 -€1 €2.5 €5 €22
The probabilities of the occurrence of the economic conditions are: P(economy declines) = 0.3 P(no change) = 0.5 P(economy expands) = 0.2
Determine the best portfolio for the investor.
Weight each
In a business environment, we frequently use probabilities to assess alternative financial decisions
Example 1: A coin is tossed ten times.
When a head is obtained, €4 is won.
When a tail is obtained, €2 is lost
Calculate the expected winnings. Outcome
HEAD TAIL
Winnings
€4 -€2
Probability
0.5 0.5
Expected winnings in one toss:
Expected Monetary Value (or just Expected Value (EV) = €1
Note: You never actually receive €1; you either receive €4 or lose €2. Play this game many times, sometimes you receive €4, sometimes lose €2, but it ‘averages out’ at €1 per game.
This is your Expected Value.
Expected winnings in ten plays: Decision Making using Expectation
Example 2:
A potential customer for a €50,000 fire insurance policy has a home in an area that, according to experience, may sustain a total loss in a given year with a probability of 0.001 and a 50% loss with a probability of 0.01. There is a 98.9% chance that no claim will be made.
Ignoring partial losses, what premium should the insurance company charge to break even?
Solution:
Expected Claim = 50000*0.001 (Full claim)
+ 25000*0.01 (Partial Claim) + 0*0.989 (No Claim) = €300
A premium of €300 would break even in the long run
Decision Making using Expectation
Example 3:
An investor has a certain amount of money to invest. Three alternative portfolio selections are available. The estimated profits depend on the economic conditions as follows:
Profit (€’000) Portfolio Selection A B C
Economy declines
No change
Economy expands €.5 -€2 -€7 €1.0 €2 -€1 €2.5 €5 €22
The probabilities of the occurrence of the economic conditions are: P(economy declines) = 0.3 P(no change) = 0.5 P(economy expands) = 0.2
Determine the best portfolio for the investor.
Weight each