Assume you have $1 million Cash and are trying to choose among three securities to invest. 

a. Security A is a price weighted index of the following three stocks with the corresponding price information in period 0 and period 1 (assume the initial index divisor is 3):

Stock	Initial date (t=0)		Final Date (t=1)
	Price	Shares Outstanding	Expected Price
A1	$20	100	$25
A2	$30	500	$30
A3	$40	600	$44

 

b. Security B is a value weighted index of the following three stocks with the corresponding price information in period 0 and period 1 ((assume the initial index divisor is 100):

Stock	Initial date (t=0)		Final Date (t=1)
	Price	Shares Outstanding	Expected Price
B1	$50	800	$100
B2	$60	500	$80
B3	$70	600	$60

 

c. Security C is a single security with the following expectations:

State of the Market	Probability	Final Date (t=1) Ending Price	Holding Period Return (Including dividends; From t=0 to t=1)
Boom	0.4	$200	25%
Normal	0.4	$180	10%
Recession	0.2	$150	-15%

 

Given the above choices, calculate and answer:

i). What is the single period expected return for Security A & Security B, respectively? 

ii). What is the single period expected return for Security A if stocks A1 and A2 were to split 2 for 1 and 4 for 1, respectively, after period 0?

iii). What is the mean and standard deviation of the holding period return for Security C?

iv). With your $1 million cash, if you decided to invest $300,000 in Security A, $400,000 in Security B, and the remaining amount in Security C, what is your single period expected return for your portfolio, without considering the stock splits in question ii)?