¶ … Utility and Benefits of Derivative Instruments A European asset manager believes there is an elevated risk of extreme volatility in the markets during the next 3 months and wish to fully hedge their portfolio against all risks. However, they are mandated to remain fully invested at all times so selling securities is not an option. Their portfolio currently comprises the following positions.

Notional/Amount Security Term

€1,000,000 Schatz 2-year on-the-run [Futures contract 2-year German debt as underlying]

€10,000,000 Euro Interest Rate swap 5-year Fixed Receiver [As fixed rate receiver, the buyer of an Euro-Swap Futures contract is obliged to accept the delivery}

$50,000,000 USD LIBOR Interest Rate deposit 1 year

Current data for pricing and obtaining rates can be found at www.ft.com under data archive.

The asset manager wants to fully hedge the interest rate risk on the bond by using bond futures. Calculate the appropriate number of bond futures that should be sold. (bond future data can be found at www.eurexchange.com ) (20 marks)

The principle undergirding hedging with bonds it the long position in the bonds needs to be offset with a short position ("WPS Pearson," n.d.). Note that forward contracts terminology refers to parties who buy a futures contract and will receive (buy) the bonds as taking a long position, while parties who sold a futures contract and will deliver (sell) the bonds are said to have taken a short position ("WPS Pearson," n.d.). This means that the bond futures contract will need to be sold. A cross hedge will be employed because the underlying asset in the futures contract differs from the asset that is being hedged ("WPS Pearson," n.d.). Hedging the interest-rate risk on the bond can be accomplished by taking a short position; this is because a drop in bond prices could cause losses on bonds held and an offsetting gain in futures contracts is needed ("WPS Pearson," n.d.). By taking a short position, if the bond price drops, the bonds can be purchased in the market at a price that is lower than the price that was agreed upon for delivery of the securities, which will result in an offsetting profit for bonds being held ("WPS Pearson," n.d.).

The number of contracts that would be needed to hedge the interest-rate risk can be determined by dividing the amount of the asset to be hedged by the dollar value of each contract ("WPS Pearson," n.d.). First, calculating the hedge ratio tells how many points the price moves on the hedged asset for a 1-point change in the futures contract that is being used for the hedge. The hedge ratio shows the par dollar amount of the futures contract that is needed per par dollar of the asset being hedged.

NC = HR x PVa / PVf

Where:

HR = hedge ratio [assume 1.10]

PVa = par (face) value of the asset hedged [€10,000,000 Euro Interest Rate swap 5-year]

PVf = par (face) value of the futures contract [€1,000,000 Schatz 2-year on-the-run]

Contracts = 1.10 x €10,000,000 / €1,000,000 = 1.10 x 10 = 11

2. Explain the risks of the interest rate swap position and how could it be could be hedged? (20 marks)

Hedging swaps is useful for managing risk in derivatives portfolios and can also be an effective tool to keep changes in the conditions of one particular asset from affecting the conditions of another asset in the same portfolio (Sooran, 2015). The risks of a swap position are managed by utilizing portfolio techniques such as those that might be used for a fixed income cash position or equities, but naturally are more sophisticated (Sooran, 2015). The constructed portfolio consists of hedges that employ bonds, forward rate agreements (FRAs), futures, and swaps (Sooran, 2015). As the interest rates, currency rates, or the basis between the bonds and the futures fluctuate, changes in the value of assets are used to offset the changes in the value of swap portfolio that undergirds the arrangement (Sooran, 2015).

A structure based on buckets arranged according to the intervals of consecutive maturity is used to group cash flows. The cash flows are valued at market rates in order to give the dealer an accurate idea of the sensitivity of the cash flows to market rates. When categorizing swaps portfolio risk, different types of yield curve risk matters, including changes in the swap spreads and parallel and non-parallel shifts in the yield curve (Sooran, 2015).

According to Sooran (2015), the portfolio maturity bucket sensitivity may be related to or dependent upon the interest rate level due to fixed income flow convexity, a term that refers to the nonlinearities of...

Technically, the reference to convexity is linked to Gamma, the second derivative of the output price in relation to the input price (Hagan, 2003). Bond convexity, then, is the second derivative of the bond price with respect to the interest rates (Hagan, 2003). Gamma, then, is fundamentally a way to express the changes in delta or position size as they correspond to changes in interest rates. Vega is the expression of the sensitivity of the value of the derivative product to implied changes in volatility, all other factors remaining the same, for at-the-money options, in which the "strike price is equal to the current, prevailing price in the underlying cash spot market" (Sooran, 2015).
Delta hedging is used to minimize volatility and to manage risk. When hedging swaps, delta hedging would entail considering a fixed income instrument that exhibits certain attributes. For example, the term to maturity of the fixed income instrument might need to match the interval being considered. Or, also for instance, the instrument might need to demonstrate profit and loss sensitivity to small shifts in the interest rate for a particular bucket at the same level that the swaps portfolio is sensitive to small changes in the bucket as a whole (Sooran, 2015). Assessing the swaps portfolio risk requires thinking about the potential loses on a mark-to-market basis should all the interest rates increase by the same amount, or if, say, the interest rates fall by 25 basis points or the spread between 2-year and 30-year government bonds increase by 15 basis points (Sooran, 2015).

Given these considerations, a hedging swaps portfolio can be constructed by using financial instruments that offset the most undesirable aspects of the risk. The swaps portfolio will only be partially hedged since hedging is an investment, which means that it entails balancing the cost to the benefit of reduced risk. Consider that it does not make fiscal sense to hedge a risk if the marginal benefit of the reduced risk of an individual transaction is less than its marginal cost (Sooran, 2015). Also, carrying a proprietary position in an aspect of the risk is likely to influence decisions about balancing reduced risk vs. cost (Sooran, 2015).

A substantive challenge in hedging swaps portfolios is addressing the short-term or floating rate cash flows (Sooran, 2015). The timing of short-term cash flows can be mismatched when missing the perfect time to match the dates of transactions, a problem that is often brought about because of the additional cost due to market prices at the time of a transaction (Sooran, 2015). Also, the type of index used to hedge may establish a mismatch (Sooran, 2015). If two indices are used for hedging and the correlation between the indices changes, the swap portfolio can be exposed to a type of risk called refunding risk (Sooran, 2015).

3. The asset manager would like to hedge the receipt of $50,000,000 to be received in one years' time from the maturity of the one year interbank deposit. Using current data from www.ft.com, calculate a one year €/$ forward rate and explain how it could be used the hedge the currency risk. (20 marks)

Forward rates, also called implied forward rates, are a reflection of the market sentiment about the future with regard to interest rate changes. The risk-free theoretical spot rates are the jumping off point for the extrapolation of forward rates. Calculating the forward rate is the first step in figuring out the value of a bond. The forward rate is substituted for the yield or the interest rate in the formula used for bond prices.

For the one year investment of the $50,000,000, the future dollars would be calculated by using this formula: x (1 + z) 2

Where:

Z = the bond equivalent yield on the spot rate f1, 2 = (1+3.09%)2 + (1+4.057%)1 -1 = %

Spot Rate

Tenor (in years)

st = t- period spot rate

3.09%

1

4.05%

2

ft-1,t = forward rate applicable for the period (t-1,t)

Formula ((1+D4)^E4)

1.0309

4. The asset manager thinks that there is some possibly that the currency markets could move in their favour and so ideally would like some degree of participation in any favourable move, whilst being fully protected against adverse moves. Discuss alternative hedging choices by using options. (20 marks)

Currency is traded around the clock through a variety of ways including forwards, option contracts, spot transactions, and swaps -- all of which have currency as the underlying instrument (Harper, 2015). Indeed, the second largest traders in the forex market after banks are portfolio managers of pooled funds and…