RISK: EXPONENTIAL SMOOTHING FORECASTING AND VALUE OF INFORMATION Risk: The Value of Information Scenario: Using the same situation from the Module 3 SLP, recall that you are deciding among three investments. You have heard of an expert who has a highly re

Wouldn’t it be nice if you could find an expert that could predict the future with 100% accuracy? (Imagine how rich this expert would be.) All you would have to do is pay this expert and he would tell you whether the future will go one way or the other, and then you would know what to do. Your decision would be easy. But that is a fantasy. Some experts are good at predicting the future and we can find out what their track record is.

For example, suppose you are in the last stages of product development of two similar product designs, a new smart phone. One smart phone has many new advanced features but will be very costly to produce and sell with a high price. The other smart phone has only a few new features and would be considered to be only average in its value and have only an average price on the market. We need to decide which one of these two smart phone options we are going to finish and take to market, but only one. We estimate the two possible future states of the market demand: the market will generally want a High Value, High Price smart phone (Pr = 0.4), or an Average Value, Average Price smart phone (Pr = 0.6). This is the decision tree for this decision including the payoffs.

You know an Expert that you can consult who has a good track record of predicting the future in these situations. This is the track record:

When the Market actually is demanding High Value, the expert is correct (predicts “High value”) 85% of the time, and is wrong (predicts “Avg. value) 15% of the time. When the Market is actually demanding Avg. value, the expert is correct (predicts “Avg. value) 92% of the time, and is wrong (predicts “High value”) 15% of the time. We can also state these using conditional probability statements:

Pr( Expert Says "wants high value" | Market demand is High value) = 85%

Pr( Expert Says "wants avg value" | Market demand is High value) = 15%

Pr( Expert Says "wants high value" | Market demand is Avg value) = 8%

Pr( Expert Says "wants avg value" | Market demand is Avg value) = 92%

We are showing these probability statements because in a moment you will be asked to read an article that explains Bayes’ Theorem, which uses this kind of probability statements.

Here is the modified decision tree if you were to consider consulting an Expert. Note that you have not yet consulted the expert, but are only considering it.

In this scenario, with the consideration of consulting an expert, you do not know what he/she will say, and therefore these are unknown future states. He could say the market “wants High V” or “wants Avg V”. We need to determine these probabilities. And note that the probabilities of which actual future market will occur will be different depending on the expert’s prediction.

We need to use Bayes’ theorem to help us determine these new probabilities. Go to this website page which provides an easy to understand explanation of Bayes’ theorem using a medical example, testing for cancer.