Welcome to this Decision Analysis tutorial for constructing decision trees.
We will be constructing a basic decision tree.
We will also be making decisions using the expected value approach.
We will be constructing a decision tree using this payoff table,
where payoffs are profits and the probabilities of the states of nature
are .4 and .6 respectively.
Decision trees use two types of nodes:
A square or rectangle node called DECISION NODE
from which decision alternative branches will originate,
and a circle node called CHANCE NODE
from which states of nature or outcome branches will emanate.
The CHANCE NODE is also referred to as an OUTCOME NODE or EVENT NODE
Now let's construct a decision tree for this PAYOFF table.
We first draw a decision node
with branches coming out of the decision node representing decision alternatives.
Next we draw the chance node or outcome node
with respective states of nature or outcomes.
As it can be seen here for stocks.
The payoffs are placed at the end of the branches as you can see (70 and -13 for Stocks).
We do the same for Mutual Funds and for Bonds.
Notice that the payoff is 20 for Bonds
irrespective of the state of nature.
Therefore, we really don’t need to repeat 20,
we simply need to draw a single branch
from BONDS with a payoff of 20.
Now let's solve the decision tree.
Solving the decision tree is also known as
folding back the decision tree.
In essence, we are going to calculate the expected
values and then choose the best.
For Stocks, the expected value is calculated as
.4 times 70 + .6 times -13 which is 20.2.
So we just usually write the 20.2 on the chance node for stocks.
We do the same for mutual funds. The expected
value is. 4 times 53 + .6 times -5 which is 18.2.
We also write that on the chance node for mutual funds.
For Bonds, no calculation is required.
We can only expect a payoff of 20 (for Bonds).
Now comparing the three values: 20.2, 18.2, and 20,
the best expected value is 20.2.
We usually just place that value close to the decision node.
Therefore, the decision is to invest in Stocks.
Thanks for watching!
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