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  • 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!

Welcome to this Decision Analysis tutorial for constructing decision trees.

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