Hedging an Equity Portfolio - Assignment Example

Portfolio setup

1. a). I Choose June as a delivery month because it is close to the month containing the expiration of the hedge.

b). The size of the portfolio has been constructed and date of birth chosen as indicated in question 1(a), above. Therefore, my equity position would be 28×1000=28000. On the other hand, the value of my position will be determine by multiplying my equity position with the FTSE 100 index which is 6104.19 as follows

= 28000*6104.19= 170917320

Hedging

Question (a)

The fund manager may face numerous some of the most common risk faced by fund manager include; currency risk, cost transaction risk, liquidity risk and bottom line risk. Currency risk is attributed to the fluctuation of exchange rates between the foreign and domestic currency. Fund managers may face currency risk through exchange rate parity. Assuming a fund manager who has invested a portfolio in an international market, and want to sell part of the portfolio in order make some returns. The value of the returns realized from the sale of a portfolio may be adversely affected by the fluctuation of currency. For instance, if the fund manager wants to convert the returns realized into local currency, the manager may realize that a significant proportion of the investment returns will be lost due to the lower value of the local currency against foreign currency. Therefore, a fund manager should be aware on how currency risk can be hedged and ensure that the portfolio returns are not adversely affected by the lower currency value. The fund manager may put the portfolio returns in derivatives such as futures, options, and swaps (Agarwal, Fos, & Jiang, pp.1271-1280).

Transaction cost risk is also a major challenge facing fund manager. The risk tends to reduce the number of returns realized because fund manager must eliminate all the cost be four counting that they have realized returns from their investment. Some of the transaction cost include; brokerage fee, commission, government taxes, and clearance fee. Transaction cost risk can be hedged through measures such as American and London Depository Receipts (Spiegel, & Zhang, pp.506-516).

Liquidity risk involves lack of ability to sell stocks quickly and get liquid cash. The risk also faces fund manager because some of the securities in the portfolio may not be sellable immediately because some retail investors may perceive that they are risky and less profitable. Fund managers hedge liquidity risk through spreads. The other risk faced by fund managers is bottom line risk; it is the risk attributed to obtaining loss or very lower net profit after all deductions have been made. Such risk can be diversified by diversifying portfolio accordingly to obtain higher net profit after all expenses have been removed. The fund manager should be able to understand the various risk and losses that are likely to be experience and how such risk can be hedged or avoided if possible. The climatic risk is also another contemporary risk that most fund manager’s experience in the current market. Climatic risk entails the risk of global warming. Those managers who fail to take care of the environment and expose it to the global warming tend to face the risk of lawsuits and litigations. The global warming fall under systematic risk, the risk may make significantly reduce the value of the portfolio and exposes fund managers who ignore this risk under the risk of facing legal actions and fines. Fund managers have a fiduciary responsibility to take care of the environment because such environment may cause significant loss not only to the company but also to the society at large. Climatic risk can be hedged only by taking care of the environment and participating in environment conservation as part of corporate social responsibility (Spiegel, & Zhang, p.224).

Question (b)

Futures are the tools used to hedge risk; it is an agreement between two parties to buy or sell an underlying asset a given price at specified future date. Most investors prefer using future contracts. To protect themselves against exposure to investment risk and ensure that they are protected against fluctuation in securities prices. Therefore, when trading options, June and September will be most appropriate because it is the time when the most quarterly contract is excised. During the two periods, the buyer or the seller may exercise his or her position depending on whether it was a short or a long position. A short position in an option is to sell while a long position is the option to buy underlying assets at a given price. Hence, June and September are the most appropriate months for exercise one position given that it is the expiry date for the most future contracts (Spiegel, & Zhang, p.527).

Question (c)

The tool/formulae for computing future price are as follows;

Futures Price = Spot Price × (1 + Risk-Free Interest Rate – Income Yield) (Agarwal, V., Jiang, Tang, & Yang, 2013).

Assuming that the spot price is $1000, risk free rate is 10% and dividend is 5%

Spot Price=$1000

Risk free Interest Rate=10%

Dividend= 5%

Futures Price =$1000*(1+10%-5%)

=$1000*(1.05)

=$1050

• To hedge the risk in a portfolio the number of contracts may be given by the fomula

Where:

VA = the value of the portfolio=170917320

β= is beta

VF =is the value of one futures contract =6079.5

Therefore, based on the value computed in 1(a). and using the above formula

However, since the portfolio, the value is 1 so the equation will look like this

170917320=28113.7

6079.5

Number of futures that should be bought are 28113.7

Question (d)

The Option Scenario Analysis function confirms that the number of futures that will be required to hedge the 28000 units of the FTSE 100 will be 28113.7. This the optimal point at which the position will not have any risk. The product of the Option Scenario Analysis is illustrated in the figure 1.0 below.

Figure 1.0 Option Scenario Analysis

The equivalent to the hedge ratio in the Option Scenario Analysis is 0.85. This indicates that 85% of the securities in the investment portfolio will be covered by the hedge. The remaining 15% will remain uncovered.

Question (e)

Function 33

The following graphs indicates the profit and loss of the hedged position and un-hedged position

• Scenario matrix hedge

• Scenario matrix un-hedged)

The evaluation indicates that in un-hedged position the return returns as given by profit and loss are very volatile. For example at a rate of –8% the investment generate an income of =$13.6 million but at the rate of 8% the investment generated $13.6 million profit. This creates a probability of a very high loss (13.6 M). On the other hand, the hedged position generates relatively constant returns from -27.67k to -28.55k. The beta (volatility) for the hedged position is relatively low and as such, hedge mitigated the loss where I would have incurred a loss of $13.6million but I only incurred a los s of 28.55 K.

Function 35

The following graphs indicate the evaluation of the hedged and un-hedged positions using the multi-asset scenario analysis.

• Multi-asset scenario hedged

• Multi-asset scenario unheged

The figures indicate that hedge helped to cushion against the loss. For example, on a black Monday (as given above) before the hedge I was supposed to lose 21.67 million but because I was hedged I only lost 51.95 thousand. This means that the hedge cushioned the position against a high risk of loss.

Question (f)

By definition, a hedge ratio can be looked on as a value of the proportion of a hedged position to the entire position value (Carpantier and Samkharadze, pp.150-160). This means that the ratio compares the value of the protected position through the hedge with the entire position size. Bodie (p.158) stipulated that hedge ratio is imperative in comparing the value of the sold or purchased future contracts to the value of the cash commodity that is being hedged. Hedge ratio is mainly used to show the way in which or the extent to which a given investment is exposed to risks. For example, a hedge ratio of 0.55, indicates that 55% of the total investment is protected from the risk of the remaining 45% remaining exposed. This helps the investor or the investment manager to take the necessary steps to minimize the risks of the exposed investment. For example, an investment with a hedge ratio of 0.35 would be the investment manager to consider taking other risks minimization steps such as stocks diversification, investing in less risky securities (such as government bonds and T-bills) because a big proportion of the investment is exposed to the risk (Bielecki, Cousin, Creepy, & Herbertsson, pp.102-120).

Getting the value of the futures contract to the underlying assets value helps to identify and minimize the risk basis the risk in the contract (Chen, Ho, and Tzeng, pp.154-164). This means that hedge ratio is Imperative in making investment decisions and entering in future contracts. On addition to minimizing the basis of risks, hedge ratio is used to project the expected returns from the investment portfolio. For example, if an investor is holding $5, 000 in foreign equity, that are exposed top currency risks, hedging marinating a 0.5 hedge risk, would mean that $2, 500 is the equity position is shielded from hedge risk and thus the investor can calculate the expected income, with more accuracy, and thus make financial planning. On addition, the ratio is calculated to ensure that there are enough futures contracts that will offer financial protection if the cash commodity price either falls or rises. For the options the hedge ratio is obtained by getting the option delta where for example, a hedge ratio of 4 would be required if a $1 barrel change in the price of the underlying future led to a 25% per every barrel change in the premiums of the options (Carpantier and Samkharadze, pp.868-870).

On the other hand, even though the hedge ratio indicates the proportion of the risk exposure for investment, it cannot be used to evaluate the total value of risk that is facing the investment. For example, a hedge ratio of 0.85 of the investment in foreign equity against the currency risk would indicate that 85% of the stocks is shielded from the risk of currency price fluctuation (Carpantier and Samkharadze, p.874). However, the remaining 25% of the investment can pose a high threat than the 85% that is covered. On addition, the investment is only covered against the currency risk, and it is not covered against other risks such as price fluctuations risks. As such, hedge ratio only indicates the extent to which the investment is exposed and shielded to a certain kind of risk only. This shows that hedge ratio has different limitations and thus cannot be relied only by the investment manager to use it in combination with other investment analysis tools to ensure that the portfolio formulated meets the required level of risk and the various risks are converted adequately. This is because Hedge ratio is used to test the extent to which hedge can help to safeguard the investment of the investor (Bebchuk, Brav, and Jiang p.127).

Question (g)

When using futures to hedge a portfolio it is essential to take into consideration the risks of engaging in a future trade. Some of the risks of future trading include leverage risks, hedging imperfections and risks of disclosure statement (Bebchuk, Brav, and Jiang, p.122). Leverage exposure which is provided by the futures can cause significant losses. At the time when the investor is opening the transactions, the outlay is usually limited to the margin, which means that the percentage of the return, either negative or positive, that is made on the investment can be far greater in comparison to the movement in the underlying index. This means that the market will move against the investor, which might cause substantial losses. Unlike in the cases such as option contracts, whether the financial cost to the option buyer can be only limited to the premium cost, both the seller and the future buyer face a potential unlimited level of risk. This means that the investor has to consider whether the future risk is appropriate to the investors’ situations (Forbes et al p.178).

An investor may use index futures to shield themselves against the risk that underlying index will fall or rise. By selling the index futures, the investor can shield the value of a stock portfolio by locking in the purchase price of the index a given future price (Simsek, p.104). This is based on the principle that profit in one market will offset offsets another share market loss. The hedging strategy success relies on how closely the share value movement closely that is being hedged track the underlying index in the future contract. This creates a basis risk. On addition to this, the investor has to consider the fact that share portfolio value that is to be hedged may not be equal to the exact multiple of the index future contracts. This shows that the investor will have to choose between slightly under hedging and slightly over-hedging of the physical. The investor also has to consider risk disclosure statement which sets out the risks that are associated with trading of the futures (Cassar et al p.389).