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# How do you calculate expected payoffs modeled as discrete distributions?

You can invest in one of 3 projects: (payoffs modeled as discrete distributions)
1. Sell land and you make \$60,000
2. Build an apartment: if things go well (probability = 0.70) and estimated payoff is \$130,000, or \$50,000 otherwise
3. Build a single family house: payoff \$100,000 (probability = .80) and \$75,000 otherwise

Find expected payoffs for each and rank the projects according to expected payoffs. Then find variance for each and rank projects according to risk. Does any project dominate in terms of both the expected payoffs and risk? Can any project be eliminated from consideration? Explain.

#### Solution Preview

you can invest in one of 3 projects:(payoffs modeled as discrete distributions)
1. Sell land and you make \$60,000
2. build an apartment: if things go well (probability = 0.70)and estimated payoff is \$130,000, or \$50,000 otherwise
3.build a single family house: payoff \$100,000 (probability = .80)and \$75000 otherwise

Find expected payoffs for each and rank the projects according to expected payoffs. then find variance for each and rank projects according to risk. Does any project dominate in terms of bothe expected payoffs and risk? Can any project be eliminated from consideration? Explain.

We will calculate expected return and standard deviation for each project

1. Sell land and you make \$60,000

Payoff Probability payoff x Probability Difference from mean, i.e.60000 Difference 2 Prob x Difference 2
\$60,000 ...

#### Solution Summary

This solution shows how to find expected payoffs for each of the three projects and ranks them according to expected payoffs. Each project is neatly presented in an attached Excel file with calculations clearly identified (not just in the cells).

\$2.19