Question

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. What is its average expected rate of return?
At what price would the asset have a zero rate of return?

Answer 1

Answer:

1. the average expected rate of return = 3.13%
2. the current price at which the asset would have a zero rate of return is $123.75

Explanation:

To determine the expected rate of return we must first calculate the expected future value of the asset:

$100 x 25% = $25.00

$115 x 25% = $28.75

$140 x 50% = $70.00

the expected future value = $25.00 + $28.75 + $70.00 = $123.75

the average expected return = $123.75 - $120 = $3.75

the average expected rate of return = ($3.75 / $120) x 100 = 3.13%

the current price at which the asset would have a zero rate of return is $123.75, since the average expected return = $123.75 - $123.75 = 0

Answer 2

Answer:

Average expected rate of return is 3.13%

The asset have a zero rate of return if at price of $120

Explanation:

Rate of return RR = $\frac{Future\:Value - Initial\:Value}{Initial\:Value} \times 100$

Rate of return of the first possibility:  (100-120)/120 * 100 = -16.67%

Rate of return of the second possibility:  (115-120)/120 * 100 = -4.16%

Rate of return of the third possibility:  (140-120)/120 * 100 = 16.67%

Average expected rate of return = $\sum{weight_{i}RR_{i}}$

= 0.25*(-16.67%) + 0.25*(-4.16%) + 0.5*16.67% = 3.13%

RR = 0 => Future Value - Initial Value = 0

The asset have a zero rate of return when future price is the same as current price ($120)