Question

Suppose the economy can only be in one of the following two states: (i) Boom or “good” state and (ii) Recession or “bad” state. Each of the states can occur with an equal probability. At the beginning of a month, you can purchase the following two securities in the market: • Security 1: It is currently trading at $4. At the end of the month, the stock price is expected to increase by $10 in the good state and expected to remain unchanged in the bad state. • Security 2: It is also currently trading at $5. This asset has payoffs that are like an insurance contract. It yields a positive return when the economic conditions are poor. At the end of the month, the price of security 2 is expected to remain unchanged in the good state and expected to increase by $10 in the bad state. a) Compute the expected returns (not prices) of securities 1 and 2. b) Compute the standard deviations of returns for securities 1 and 2. c) Compute the covariance and the correlation between the returns of two securities. d) Why does the second security have a higher price? Please explain briefly.

Answer 1

			Security 1	Security 2
	Current price		4	5
	State	Probability
	Boom	0.50	14	5
	Bad	0.50	4	15
	Return
State	Probability	Security 1	Security 2
Boom	0.50	250%	0%
Bad	0.50	0%	200%
a)	Expected return	125%	100%
b)		Security 1	Security 2
	Std Dev	125%	100%
c)	Covar	-125%
	Correlation	-1.00
d)	Security 2 has a higher price as it has lower volatility expressed by the lower standard deviation