Welcome to this decision tree tutorial for Expected Value of Sample Information.
In this tutorial we’ll be constructing a decision tree with Sample Information.
We will also be calculating the Expected Value of Sample information.
We will be using this Payoff Table where Payoffs are Profits.
This is the decision tree for the payoff table. The expected value for Stocks is calculated
as 20.2, for Mutual Funds, it is 18.2,
and for bonds, it is 20. The best of the expected values is 20.2
Therefore, the decision is to invest in Stocks.
Now suppose there is an economic consultant that can provide additional information about
the states of nature (or outcomes). And this consultant has some success history.
We now have an additional decision situation. Should we hire this consultant or not?
If we don’t hire the consultant, we will stick to our initial decision to invest
in stocks. If we decide to hire the consultant,
then we will consider two factors: 1. How successful has the consultant’s information
been in the past? 2. How much does it cost to hire the consultant.
Here is a reduced version of our decision situation.
Now suppose, if we hire the consultant, he or she could give a positive report
or a negative report about economic conditions. These report from additional information is
often referred to as prediction, forecast, or result.
Suppose the probability of the consultant giving a positive report is 0.44.
This will mean that the probability of a negative report is 0.56.
Since these are probabilities, we represent them with a chance node
with positive and negative branches. Suppose given a positive report,
the probability of a Growing Economy is 0.59. And the probability of growth given a negative
report is 0.25. This means that the probability of decline
given positive report is 1 – 0.59 which is 0.41.
And the probability of decline given a negative report
is 1 – 0.25 which is 0.75. These probabilities are called posterior probabilities,
we will discuss them in detail in the next video.
So if the report is positive, we paste the original tree here
with the posterior probabilities, 0.59 and 0.41.
We do the same for negative report with posterior probabilities 0.25 and 0.75.
The chance nodes have now been labelled 1 to 5 here for reference purposes, as we calculate
the expected values: The Expected Value for node 1 is
0.59(70) + 0.41(-13) which equals 35.97. In similar fashion, we calculate the expected
values for node2, for node 3, and for node 4.
Now if the report is positive, the best expected value is 35.97 (from Stocks).
And if the consultant’s report is negative, the best expected value is 20 (from Bonds).
Next we calculate the expected value for node 5
which is 0.44(35.97) + 0.56(20) which gives 27.0268
The Expected Value of Sample information estimates the value of the information supplied by the
consultant. Sample information is also known as Imperfect
Information. So the Expected Value of Sample information,
EVSI is calculated as EV with SI – EV without SI
EV with SI is the Expected Value with Sample information.
That is, best expected payoff if the consultant is hired (without paying the consultant).
EVwithoutSI is the Expected Value without
Sample information. That is, the best expected payoff if the consultant
is not hired.
In this case, EV with SI is 27.0268 And EV without SI is 20.2
Therefore, EVSI is 27.0268 – 20.2 which gives 6.8268.
Now let’s see how to use the EVSI to determine the best decision strategy.
Suppose the cost to hire the consultant is 7.2
which is higher than EVSI. That is, the fee is higher than the value
added by the consultant. And so, the decision strategy will be not
to hire the consultant As a result, we will stick to our initial
decision and invest in Stocks.
On another note, suppose the consultant’s fee is 3.5.
which is less than EVSI. Then the strategy will be stated as follows:
Hire the consultant If the consultant’s report is positive,
invest in Stocks. If the consultant’s report is negative,
invest in Bonds.
And that’s how to calculate and use the EVSI to determine the best decision strategy.
Please post your comments below. Thanks for watching.
Bye for now.