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Consider an asset that costs $120 today

Economics Dec 07, 2020

Consider an asset that costs $120 today. You are going to hold it for 1 year and then sell it. Suppose that there is a 25 percent chance that it will be worth $100 in a year, a 25 percent chance that it will be worth $115 in a year, and a 50 percent chance that it will be worth $140 in a year.

 

figure out what the investment's average expected rate of return would be if its current price were $130 today. 

 

At what price would the asset have a zero average expected rate of return?

Expert Solution

Computation of Investment's Average Expected Rate of Return:

Expected Payoff = 25% * 100 + 25% * 115 + 50% * 140

 = 25 + 28.75 + 70

= 123.75

 

Average Expected Rate of Return = (123.75 - 120) / 120 = 3.13%

 

If the price of the asset is $130, the average expected rate of return is:

Average Expected Rate of Return = (123.75 - 130) / 130 = -4.81%

 

Computation of Price of Asset for a zero average expected rate of return,

Price = $123.75

At this price

Average Expected Rate of Return = (123.75 - 123.75)/123.75

At Price = $123.75 , Average expected rate of return = 0

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