BFF9515 Options, Futures and Risk management
Semester 1, 2014
Due date: 16.05.2014
BFF5915 Group Assignment
1. Compute Beta
First, compute the returns of each stocks and the return of the index. They can be calculated using excel with the formula: (current price / the previous price) – 1,
Second, use covariance and variance function in excel to calculate the beta of each stock.
Third, multiply each beta with the corresponding weight to calculate the portfolio beta.
* The beta for each stocks and the beta for portfolio (see table 1.1)
Details can be seen in sheet “EquityReturnData” in the data file “Data.xlsx”.
Table 1.1 The ...view middle of the document...
63% (calculated by 5% / 0.6552). The bottom line of the index points in 20 March is 5,367.91*(1 - 7.63%) = 4958.27.
The corresponding option we choose is AXJO5000O4.AX.
* Calculate the number of contracts
The option value per contract is $10*5,000 = $50,000, where $10 is the index multiplier and 5,000 is the exercise price of the option.
So, the number of contacts we should buy is $150,000,000 / 50,000 = 3,000.
3. The cost of buying options
* The total costs of buying options are 3,000 * $29.1 = 87,300
* Estimate historical volatility
First, use standard deviation function in excel to calculate σ, which is the standard deviation of daily returns of ASX200.
Second, multiply σ by√252. The estimate historical volatility is 14.49%. Details can be obtained in sheet “Portfolio” in the data file “Data.xlsx”.
* Compute the implied volatility
The implied volatility can be calculated by using excel. Through computing, the implied volatility is 14.34%. Details can be observed in sheet “Volatility” in the data file “Data.xlsx”.
* Compare the two volatilities
It is obvious that the two volatilities are very close to each other, which means they are both acceptable. Respond to that, the cost of the put option contracts we bought is reasonable.
4. The new composition of the portfolio
Since we have bought the option contracts, the composition of the portfolio can be seen from table 4.1
Table 4.1 New Composition of the Portfolio (Date: 2/1/2014)
Market value of shares | 145,947,650 |
Cash | 3,965,050 |
Options | 87,300 |
Total | 150,000,000 |
The market value remains constant, and the option value was is from the original cash value.
5. Evaluate the effectiveness of the hedging
* The current value of the portfolio
Today is 20/3/2014, the ASX200 index point is 5294, which is greater than the strike price 5000. So, the put option will not be exercised. The current value of the portfolio can be seen from table 5.1
Table 5.1 Current Value of the Portfolio (Date: 20/3/2014)
Market value of shares | 144,631,004* |
Cash | 3,979,362* |
Options | 0 |
Total | 148,610,366 |
*144,631,004 = 145,947,650* [1 – (5367.91-5294)/5367.91*0.6552]. 145,947,650 is from table 4.1, 5367.91 is the index points in 2/1/2014 which is observed in sheet “Portfolio” in the data file “Data.xlsx”,5294 is the index points in 20/3/2014 which also retrieved from sheet “Portfolio” in the data file “Data.xlsx”. 0.6552 is the portfolio beta we have calculated at the beginning.
*3,979,362 = 3,965,050*(1+2.42%) ^ (55/365)
3,965,050 is from table 4.1 and 2.42% is the risk-free rate p.a. 55, is the trading days between 2/1/2014 and 20/3/2014.
* Compare the current value against the value on 2/1/2014.
The future value on 2/1/2014 can be seen from table 5.2
Table 5.2 Comparable Value on 2/1/2014 before Buying Options
Market value of shares | 144.631,004 |
Cash | 4,066,978* |
Total | 148,697,982 |