In conclusion, by using STIR futures, the company can hedge the interest rate reset risk in the FRN effectively.
Question 2: Explain how to use interest rate swaps to hedge the reset risk in the FRNs.
As scenario, the company has issued £250,000,000 of Floating Rate Notes (FRNs) paying LIBOR plus 40 basis points. This FRN has three years to maturity and pays semi-annual coupons. However, the company expect LIBOR to go up steadily over the next three years. Thus, it will suffer from interest rate reset risk.
The company can eliminate the reset risk by converting floating rate portfolio into a fixed rate portfolio, using Swaps with bank as model below.
The specification of Swaps with bank:
- Six-month payment
- Three years to maturity
- Fixed rate which is fixed in the contract based on LIBOR at the specific time = r + 0.2
- Notional principal = £250,000,000
In this case, the company will receive from the bank a floating rate of LIBOR and pay for the bank the fixed rate r + 0.2 that fixed on the contract at signature date. Therefore, the company will pay the rate = rLIBOR + 0.4 + r + 0.2 – rLIBOR = (r +0.6) % . Thus, in spite of the rise of the interest rate (LIBOR), the company still pays a fixed rate of (r+0.6)%
By using Swaps with bank, the fixed payments to the bank under the swap become the fixed coupons on the FRNs portfolio. Pay-off in every payment is completely not affected by the LIBOR interest rate but only depends on the fixed rate which is defined on the contract at signature date.
In conclusion, by using interest rate Swaps, the company can hedge the reset risk in the FRNs effectively.
Question 3: Calculate the price of a three-year swap that will hedge reset risk for the company.
There are five step to determine the swap price
Step 1: Work out the Forward Rate derived the spot rate
According to Watsham, T. J., (1998), the general formula of the forward rate T year is:
In particular, the six month forward rate 1 year and 1.5 year out would be:
Step 2: Calculate the Forward LIBOR
The formula:
Where:
D = the number of days in the forward period
C = the number of days in a year according to the appropriate convention.
For example, the Forward Rate LIBOR 1 year and 1.5 year are:
Step 3: Calculate the Floating Cash Flow.
Where:
P = notional principle
D = number of days and
C is the assumed number of days in a year according to the appropriate day count convention.
250* * = 5.485
250* * = 6.192
Step 4: Calculate the present value of the floating leg using the spot rates.
The present value of the floating leg of the swap is calculated as:
Step 5: Calculate the fixed payment
The semi-annual fixed payment is 6.69 million £, so the swap price of a three-year swap that will hedge reset risk for the company is 13.38 million £.
Question 4: Explain the difference between Hedging and Insurance, and how using a Futures contract or an Option will enable you to manage the equity market risk in the pension fund portfolio.
4.1. Explain the difference between Hedging and Insurance.
Hedging and Insurance are the effective strategies for the companies facing cash-flow risks. They have similar aims. However they are not interchangeable.
Firstly, the differences between Hedging and Insurance are about definition and mechanism. Hedging is a risk management tactic to offset any unfavourable events in the future such as the probability of loss from the variations of securities price or commodity price. For hedging, a party needs at least one person or an entity that calls counter party to enter into the strategy. Although there are many methods to hedge an investment, they all have agreements between this party and the counter parties. About mechanism of hedging, it involves choosing from the currently available financial tools such as forward, futures, options, swaps, money market, and leveraged spot contracts to best manage the currency exposure. For Insurance, generally, it is a strategy implemented to limit the effects of negative events which may occur in the future such as theft, fire, accidents, sickness, injury, disaster, vandalism, market movement. Different from hedging, the company buy insurance from a company licensed by the state which regulates term of insurance. About mechanism, in essence, simply risks are shared with other participants through the tools such as put options on stocks or financial guarantees.
Secondly, Insurance allows for gain whereas Hedging does not. When hedging, a company gets rid of the risk of loss by giving up the potential for gain. When insuring, a premium has to be paid to eliminate the risk of loss and the gain will be retained potentially. For example, a grove of orange trees is concerned about price risk and the harvest is still two months away. The grove wants to guarantee that it will receive $1.00 per pound in two months regardless of what the spot price is at that time. It is selling 250,000 pounds. Suppose that instead of taking a short position in the futures market, it purchases insurance (in the form of a put option on 250,000 pounds) that guarantees the company a minimum price of $1.00 per pound. Cost of Put option is $25,000. The economics of this transaction if the spot price on the delivery date is $0.75, $1.00, or $1.25 per pound is as the table below:
In insurance transaction, as the price at the delivery date rises, the grove will make more money than $250,000. At a price of $1.25 per pound, It receives $287,500 versus $250,000. The gain will be retained.
In hedging transaction, the grove locks in the $250,000. If prices go above $1.00, it will not benefit.
Although Hedging and Insurance have similar purposes, however in order to eliminate or manage the risk and gain profit as much as possible, investors should consider carefully choosing which one is better.
4.2. How using a Futures contract or an Option will enable you to manage the equity market risk in the pension fund portfolio.
In the reality, the pension fund industry has to suffer from negative equity returns and low interest rates. Futures and Options can be used in efficient equity market risk management in the pension fund portfolio. They are able to or to speculate future interest rates and security prices on the price movement of the underlying asset. Using futures and options through their applications in pension fund management such as cash equitisation, hedging portfolio value, transition management, duration adjustment, sector overlay, bond/stock picking and portfolio yield enhancement, pension fund managers can efficiently invest in the equity markets.
Question 5: Calculate the arbitrage free price of a six-month future on the FTSE 100 index.
The annual dividend yield is 4%pa. and the future value (expressed in index points) of dividends due over the next six months is 30 index points, so the futures price in this case will be:
In particular:
The FD index is:
The future price is:
In conclusion, the arbitrage free price of a six-month future on the FTSE 100 index is 5590.4.
Question 6: Calculate the price of a six month, at-the-money, put on the FTSE 100 index.
The annual dividend yield is 4%pa, therefore q = 0.04.
Moreover, the volatility is 20% so the sigma = 20%, S = X = 5500, r = 0.044.
The price of put on FTSE 100 index would be:
With: N(-d1) = Normsdist(-0.084853) = 0.466189
N(-d2) = Normsdist (0.05657) = 0.522556
In conclusion, the price of a six month, at-the-money, put on the FTSE 100 index is £298.2511 million.
References
Watsham, T. J., (1998). Futures and Options in Risk Management 2nd edition, International Thomson Business Press, London, UK.
Watsham, T. J., (1992). Options and Futures in International Portfolio Management, Chapman & Hall, London, UK.
Franzen, D. (2010). Managing Investment Risk in Defined Benefit Pension Funds.
[electronic book] OECD publishing. Available from:<http://www.oecd.org/dataoecd/49/17/44899253.pdf> [Accessed February 10 2012].
Pensions Week (2004). Derivatives: a tool for efficient fund management. [electronic book]. Available from:<http://www.eurexchange.com/download/documents/publications/pensions_week.pdf> [Accessed February 10 2012].
Rochet, J. C & Villeneuve, S. (2009) . Liquidity Management and Corporate Demand for Hedging and Insurance. [electronic book]. Available from:<http://www.scor.com/images/stories/pdf/library/chairscor/chairscor_liquiditymanagement.pdf> [Accessed February 10 2012].
Chauhan, T. (2011). Insurance For Hedging. [electronic book]. Available from:< http://ezinearticles.com/?Insurance-For-Hedging&id=6673719> [Accessed February 10 2012].
Amencis, N., Goltz, F & Stoyanov, S. (2011). A Post-crisis Perspectiveon Diversification for RiskManagement. [electronic book]. Available from:< http://www.scribd.com/doc/55027716/4/Beyond-Diversification-Hedging-and-Insurance> [Accessed February 10 2012].
