Question

The common stock of Leaning Tower of Pita Inc., a restaurant chain, will generate payoffs to investors next year, which depend on the state of the economy, as follows:

		Dividend				Stock Price
Boom		$	8			$	240
Normal economy			4				90
Recession			0				0

The company goes out of business if a recession hits. Assume for simplicity that the three possible states of the economy are equally likely. The stock is selling today for $80.

a-1. Calculate the rate of return to Leaning Tower of Pita shareholders for each economic state. (Negative amounts should be indicated by a minus sign. Enter your answers as a percent rounded to 2 decimal places.)

a-2. Calculate the expected rate of return and standard deviation of return to Leaning Tower of Pita shareholders. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

All the states are equally likely

Hence the probability of each = 1/3

	Probability	Dividends	Stock price	Current price	Returns	Probability*(Expected return-Return)^2
Boom	(1/3)	$8.00	$240.00	$80.00	210.00%	0.935208333
Normal economy	(1/3)	$4.00	$90.00	$80.00	17.50%	0.020833333
Recession	(1/3)	$0.00	$0.00	$80.00	-100.00%	0.676875
Expected return	42.5000%
Standard deviation of returns	127.7856%

a1)

	Returns
Boom	210.00%
Normal economy	17.50%
Recession	-100.00%

a2)

Expected return	42.5000%
Standard deviation of returns	127.7856%