Imagine there are two free agent outfielders available. They both cost the same

Question

Imagine there are two free agent outfielders available. They both cost the same price, but you only have the money to sign one. Assume home runs alone are a proxy for performance. Suppose Player 1 has a 20% chance of hitting 20 home runs and a 20% chance of hitting 25 home runs, a 25% chance of hitting 30 home runs, a 20% chance of hitting 35 home runs, and a 15% chance of hitting 40 home runs. Player 2 has a 10% chance of hitting 10 home runs and a 10% chance of hitting 15 home runs, a 10% chance of hitting 25 home runs, a 30% chance of hitting 30 home runs, a 30% chance of hitting 35 home runs, and a 10% chance of hitting 50 home runs.

Which player has the highest expected return?

Which player would represent the riskier investment?

Which player would you choose?

What does this say about your risk preferences?

Explanation / Answer

Imagine there are two free agent outfielders available. They both cost the same price, but you only have the money to sign one. Assume home runs alone are a proxy for performance. Suppose Player 1 has a 20% chance of hitting 20 home runs and a 20% chance of hitting 25 home runs, a 25% chance of hitting 30 home runs, a 20% chance of hitting 35 home runs, and a 15% chance of hitting 40 home runs. Player 2 has a 10% chance of hitting 10 home runs and a 10% chance of hitting 15 home runs, a 10% chance of hitting 25 home runs, a 30% chance of hitting 30 home runs, a 30% chance of hitting 35 home runs, and a 10% chance of hitting 50 home runs.

Prob. x (Return - Expected Return)^2

Standard Deviation

Prob. x (Return - Expected Return)^2

Standard Deviation

Player 2 is riskier because its standard deviation is higher.

Player 1 would be selected because high returns and low risk.

Imagine there are two free agent outfielders available. They both cost the same price, but you only have the money to sign one. Assume home runs alone are a proxy for performance. Suppose Player 1 has a 20% chance of hitting 20 home runs and a 20% chance of hitting 25 home runs, a 25% chance of hitting 30 home runs, a 20% chance of hitting 35 home runs, and a 15% chance of hitting 40 home runs. Player 2 has a 10% chance of hitting 10 home runs and a 10% chance of hitting 15 home runs, a 10% chance of hitting 25 home runs, a 30% chance of hitting 30 home runs, a 30% chance of hitting 35 home runs, and a 10% chance of hitting 50 home runs.

Which player has the highest expected return? Which player would represent the riskier investment? Which player would you choose? What does this say about your risk preferences? Player 1 Probability Home Runs Expected Return 20% 20 4 20% 25 5 25% 30 7.5 20% 35 7 15% 40 6 100.00% 150 29.5 Player 2 Probability Home Runs Expected Return 10% 10 1 10% 15 1.5 10% 25 2.5 30% 30 9 30% 35 10.5 10% 50 5 1 165 24.5 Player 1 has highest expected Return. b) Player 1 Probability Home Runs (Return) Return - Ex(Return)

Prob. x (Return - Expected Return)^2

20% 20 -9.5 18.05 20% 25 -4.5 4.05 25% 30 0.5 0.0625 20% 35 5.5 6.05 15% 40 10.5 16.538 100.00% 150 Variance 44.75 Sqrt(Variance) 6.690

Standard Deviation

Player 2 Probability Home Runs Return - Ex(Return)

Prob. x (Return - Expected Return)^2

10% 10 -14.5 21.025 10% 15 -9.5 9.025 10% 25 0.5 0.025 30% 30 5.5 9.075 30% 35 10.5 33.075 10% 50 25.5 65.025 1 165 137.25 Sqrt(Variance) 11.715

Standard Deviation

Player 2 is riskier because its standard deviation is higher.

c.

Player 1 would be selected because high returns and low risk.

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