EMV

Expected Monetary Value


Goklas Tunggul Partoho
07/05/2007


This paper describes about Expected Monetary Value as a concept and how to use in real activities



Background

In our life, we have to make decision. When growing up, we make lot of mistakes or wrong decisions maybe until now. Just a few of us make a good decision. Then we come to the question, how to make a good decision? Because we know every decision has a risk, which is the chance that some unfavorable hence we have to learn make a good decision to minimize the risk. A good decision is based on logic. Logic means everyone in general can understand the decision we make rationally.

There are some types of decision, as:
a. Under Certainty
Under Certainty means the decision makers know with certainty the consequences of every alternative or decision choice. Generally, people will choose the alternatives that maximize the best outcome/profit. For example, a person has Rp. 100.000.000,00. S/he can save in bank with interest 8.5% a year and to invest in ORI with bonds’ interest 12% a year. Rationally if both options are secure and guaranteed, s/he must choose to invest in ORI.

b. Under Uncertainty
Under Uncertainty means the decision makers know the several possible outcomes for each alternatives, what the decision makers don’t know is the probabilities of the various outcomes. For example, rationally we believe if we invest money in telecommunication companies stocks, we will have profit, because we believe the user of telecommunication tools increasing every year. What we don’t know is the probabilities of interest we will get in the future.

c. Under Risk
Under Risk means the decision makers know there are several possible outcomes for each alternative, also know the probability of occurrence of each outcome.
For example on a die, the probability of occurrence each number is 1/6.

At beginning, scientist studying about math, then math applied in gambling. Gamblers learned about the probabilities each outcome. The probability is studying by economics to be useful in economics decision making.


Concept

The most popular methods of making decision under risk are Expected Monetary Value (EMV) which is selecting the alternative with the highest expected monetary value. EMV also can determinate the expected opportunity loss.

EMV will be useful when an investor has interest to invest in a project. For example when an oil company wants to explore a location, that company need a big capital to invest hence must calculate all the options to minimize the risk. When someone retires from a company and s/he got retirement money, s/he has options to invest the money or do nothing with the money. All the possibilities must be calculated.
EMV is the weighted sum of possible payoffs for each alternative. In statistic science EMV = Mean. In simple words, EMV is the money that accepted by investor in average IF the decision is made in a conditional situation constantly.

Example 1:
Mrs. Fitry while studying in Jogja, wants to open a barber shop near of her house. She has 2 probabilities of Favorable Market (50%) or Unfavorable Market (50%). In diagram
Alternative Favorable Market Unfav Market
Large Barbershop 2.000.000 1.800.000
Small Barbershop 1.000.000 200.000
Do Nothing 0 0
P’ 50% 50%

EMV (Large B) = (50% x 2.000.000) + (50% x -1.800.000) = 100.000
EMV (Small B) = (50% x 3.000.000) + (50% x -500.000) = 400.000
EMV (DN) = (50% x 0) + (50% x 0) = 0

From this example, clearly state that EMV is a Mean between Favorable Market + Unfavorable Market as each probability.

The conclusion can get from this simple EMV model is Mrs. Fitry should make a small barbershop rather than a large barbershop or do nothing because small barbershop gives more money than other alternatives.

At present, the finance activities more complex than years ago hence investors need some surveys or consultants before making decision. On that reason, EMV is modified in order to give more useful information. The modification of EMV called EVPI (Expected Value of Perfect Information) and EVwPI (Expected Value with Perfect Information). EVPI uses by investor to determine the maximize money should be spent on information by consultants or surveys. EVwPI is the expected or average return in the long run.

EVwPI = The Biggest Profit – The Lowest Profit
EVPI = EVwPI – Maximum EMV

Example 2:
If Mrs Fitry wants to pay a consultants, how much money should be spent maximize?
EVwPI = (50% x 2.000.000) - (50% x 0) = 1.000.000
EVPI = 1.000.000 – 400.000 = 600.000

Thus, the most Mrs Fitry would be willing to pay for perfect information is 600.000
Why 600.00 ? As stated in example above, from calculation the biggest EMV is for small barbershop. The favorable market for small barbershop is 1.000.000. So the sum of EVPI+EMV maximize equal to favorable market once at start. More than that means Mrs. Fitry made an irrational decision.

An alternative approach to maximizing EMV is to minimize Expected Oppurtunity Loss (EOL).
Minimum EOL = Maximum EMV, hence
EVPI = Minimum EOL
From diagram above, we can make another diagram portraying loss logically.



Alternative Favorable Market Unfav Market
Large Barbershop 0 1.800.000
Small Barbershop 1.000.000 200.000
Do Nothing 2.000.000 0
P’ 50% 50%

EOL (Large B) = (50% x 0) + (50% x 1.800.000) = 900.000
EOL (Small B) = (50% x 1.000.000) + (50% x 200.000) = 600.000
EOL (DN) = ( 50% x 2.000.000) + (50% x 0) = 1.000.000
The minimum value of EOL is 600.000 same as EVPI.
IF we don’t know the PROBABILITY of each option, can we know find it??
How to solve this question called as Sensitivity Analysis. We learn about Sensitivity Analysis because sometimes we got imperfect information, If we know each alternative probability, we can minimize risk and maximize profit.

First, define variable : P = probability of a favorable market, thus
1-P = probability of unfavorable market

So :
EMV (Large) = 2.000.000P – 1.800.000 (1-P)
= 3.800.000P – 1.800.000 ======== P = < 0.615
EMV (Small) = 1.000.000P – 200.000 (1-P)
= 1.200.000P – 200.000 ======== P = 0.167 – 0.615
EMV (DN) = 0 ======== P = > 0.167


From diagram, we have clear information about the probabilities and the outcomes. The probability of Do Nothing just only less than .167. So we should avoid this option. The best option is to make large barbershop because the large barbershop probability is greater than .615.

Understanding EMV, will make us understand decision tree easier because the basic of Decision Tree Model based on EMV Model.


“A man is nothing but his mind; if that be out of order, all’s amiss, and if that be well, the rest is at ease”
Girolamo Cardanao “De Vita Propria Liber”