BFF9515 Options, Futures and Risk management
Group assignment
Semester 1, 2014

Due date: 16.05.2014

BFF5915 Group Assignment
Part 1 1. Compute Beta * Method:
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 Beta(s) of Stocks and Portfolio Name | Code | Weight | Beta | CROWN RESORTS | 51333T(RI) | 7.25% | 0.8039 | COMMONWEALTH BK.OF AUS. | 314054(RI) | 7.26% | 0.8950 | NATIONAL AUS.BANK | 901842(RI) | 3.74% | 1.1317 | COCHLEAR | 871051(RI) | 3.96% | 0.8402 | WESTFIELD GROUP | 912307(RI) | 2.56% | 0.7096 | TELSTRA | 871685(RI) | 4.60% | 0.5050 | MACQUARIE GROUP | 865438(RI) | 4.36% | 1.4238 | INVOCARE | 28047X(RI) | 3.87% | 0.7210 | FLIGHT CENTRE TRAVEL GP. | 871048(RI) | 4.28% | 1.0063 | CSL | 131775(RI) | 4.89% | 0.6488 | SLATER & GORDON | 50509L(RI) | 4.79% | 0.3001 | JB HI-FI | 27736M(RI) | 4.50% | 0.8261 | CARSALES.COM | 67967W(RI) | 4.54% | 0.8459 | WOOLWORTHS | 322714(RI) | 4.86% | 0.5500 | FORTESCUE METALS GP. | 314160(RI) | 7.15% | 1.8687 | The Portfolio Beta | 0.6552 | * The beta of the portfolio is 0.6552, which is less than 1. It means the risk of the portfolio is less than market risk. 2. Compute the number of contracts * Choose the maximum portfolio loss:
Considering the beta of the portfolio as well as the expectation of drop in the market in March, we decide that the maximum portfolio loss level is 5%. * Identify the relevant put option
If the maximum loss of the portfolio is 5%, then our tolerance of the drop of the index points is 7.63% (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
(Date: 20/3/2014) Market value of shares | 144.631,004 | Cash | 4,066,978* | Total | 148,697,982 |
*4,066,978 = 4,052,350*(1+2.42%) ^ (55/365). 4,052,350 is the original cash before buying options, which can be seen in sheet “Portfolio” in the data file “Data.xlsx”.
Comparing table 5.1 with table 5.2, it can be observed that the value with option involved is less than the one without option. The reason is that the option contacts we choose are not be exercised. Although, it seems that the put option contracts we bought are useless, the reality is that the losses that caused by buying options are acceptable. Since losses are not beyond our bottom line, the put option contracts do protect the portfolio against suffering big losses potentially. * All in all, we are happy with the hedge.

Part II
1.
Shortly after sub-primes made headlines in July/August, as defaults shot upwards, another group of hedge funds made the news. This time, it was the quant funds. From July through August, some of these quant funds lost billions.

Authors also indicated that the Unwind Hypothesis actually cannot explain the empirical facts fully due to its underestimated the importance of liquidity in determining market dynamics.

This paper measured price impact and market liquidity at the time of Quant Meltdown period by using the transaction data of August 2007 and the simulation of the performance of typical mean-reversion and valuation-factor-based long/short equity portfolios. The finding of the simulation suggested that there was a relatively stable unwinding of factor-driven portfolio that caused significant dislocation in August. Furthermore, this is because of the increasing of pace of liquidation and the decline of the risk capital by liquidity provider during August.

Quants use advanced statistical methods and high frequency data to create complex financial models. Consistent profits can hide inherent risks, however. Most complex quant strategies have proven to be unstable. The reasons behind the quant meltdown are hard to explain unless there is a common risk factor. In this case, authors limited their attention to five factors.

The evidences that authors used are indirect, because Quant Meltdown involve hedge funds, proprietary trading desks, and their prime brokers and credit counterparties, primary sources are impossible to access. They have no confidential information about the Quant Meltdown, or the possible to access the historical data or private records in industry. In this case, all of their conclusions are indirect, tentative, and speculative.

2.
According to the conjectures that authors used in the paper, the risks specific refer to tail risk, systemic risk and liquidity risk.

According to the paper, during Quant Meltdown period, there is an extra risk that short or long-equity-funds-investors faces, which is tail risk. Tail risk refers to occasional liquidations and deleveraging that may be motivated by events completely unrelated to equity markets. Tail risks imply that long/short equity strategies may contribute to systemic risk due to their universality. In additional, when capital suddenly withdrawn by the market, tail risks will affect market dynamics.

Hedge funds are also involved in systemic risk exposures, and the importance has increased in recent years. As a result, the risk exposures of the hedge-fund industry may have a material impact on the banking sector, resulting in new sources of systemic risks.

The main risk that the article talks about is liquidity risk. In finance, liquidity risk is the risk that a given security or asset cannot be traded quickly enough in the market to prevent a loss (or make the required profit). In August 2007, most financial sectors were badly influenced by the subprime mortgage crisis. At the same year, huge number of hedge funds faced uncountable losses during August. From the study of Khandani and Lo(2007), we can find the origin of this situation. They indicated that because of some market makers reduced their risk capital in the face of mounting losses from the onslaught of portfolio liquidations by long/short equity managers. In the past, the long/short strategies were very successful investing strategies which including buying some long-term equities and selling short-term equities, and set the portfolios based on expected return rate. However, once some hedge funds liquidate them position, the relation in long/short equities will change and will also affect the beta of the market. These changes might fail statistical arbitrage to some extend and financial institutions may also need to pay more margin on their assets. Then, mosts of managers choose to deleverage and unwind their hedge funds. Therefore, lots of hedge funds face a numerous loss.

According to Khandani and Lo(2007) , the different level of liquidity will result in different price-impact coefficients in equities. A sudden lack of liquidity could sharply influence equities’ price, making coefficients quite different when comparing with a normal level of liquidity. When hedge funds managers liquidate their position by using contrarian trading strategy, the statistical arbitrage of other hedge funds would face an incredible loss. In order to cover the loss, managers need to deleverage and unwind which indeed increasing the volatility of the market.

In the equities and funds market, both investment institutions, managers and individual investors are participants. So when liquidity risk happens in the market, all parties will face risk and will try their best to avoid loss.

3. A hedge fund is a pooled investment vehicle administered by a professional management firm, and often structured as a limited partnership, limited liability company, or similar vehicle. In addition, hedge funds need lots of money to operate and often face relatively huge risk. When funds facing cash inflow and outflow, managers must choose to how to change to proportion of cash and equities in account. The first choice is operating transaction right now but could generate huge market impact cost. Second one is to keep the current position and wait while this behavior will reduce market impact cost but yield cost of cash drag. Therefore, how to manage liquidity is an important problem, however, using Cash Equitisation that means use derivative to manage cash flow can help to solve it.

The principles of the Cash Equitisation are:
1. If there is a cash inflow, manager could invest it in market and choose to long a reasonable number of index futures which can reduce the cost of cash drag.
2. When there is a cash outflow, manager can borrow or use cash in hand to short reasonable stock index futures. The unsold assets and short position would make up to a zero-risk portfolio.

According to Frino, Lepone and Wong (2006, 2007), they analyze the situation to use derivative to manage funds in Australia. As their outcome shows that the manager that use cash equitistation to manage funds will yield more profit. A further explanation is that when considering liquidity, those who do not use derivative are not good at choosing time to invest. However, hedging by derivatives is better at profit because it is relatively easy to long or short a position in market.

Reference List:

Frino, A., Lepone, A., & Wong, B. (2006). Do Derivatives Improve Managed Fund Performance? The Effects of Cash Equitising Investor Flows. Working Paper, Discipline of Finance, University of Sydney, NSW, 2006, Australia.

Frino, A., Lepone, A., & Wong, B. (2007). Determinants of credit spread changes: evidence from the Australian bond market. Discipline of Finance, University of Sydney, N.S.W., July 2007 , Australia

Khandani, A., Lo, A., 2007. What happened to the quants in August 2007? Evidence from factors and transactions data. Journal of Investment Management 5, 5–54.