Assume you have $1 million Cash and are trying to choose among three securities to invest. a
Question:
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)?