Decision Analysis 3: Decision Trees

Decision Analysis 3: Decision Trees


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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