ERM Chapter 27

Question 1

What are the three strategies used to manage market risk?

Answer 1

1. Diversification - holding a range of assets so as to limit losses within a portfolio
2. Investment strategy - ensuring it is appropriate for the liabilities of the organisation
3. Hedging - using derivatives to manage risk

Question 2

What are the key activities of market risk management?

Answer 2

1. setting and monitoring policies
2. setting and monitoring limits
3. reporting
4. capital management
5. implementing risk-portfolio strategies e.g. hedging, matching

Question 3

What should market risk policies cover?

Answer 3

• roles and responsibilities: who is responsible within the company for developing, implementing, monitoring and reviewing policies
• delegation of authority and limits: who is permitted to execute market risk positions and to what extent
• risk measurement and reporting: how risks are measured and reported, particularly critical issues such as limit violation
• valuation and back-testing: how positions are valued
• hedging policy: what risks are to be hedged, the products, limits and strategies for hedging and how the effectiveness is measured
• liquidity policy: how liquidity is to be measured and what the contingency plans are in times of distress
• exception management: how exceptions are to be handled and reported

Question 4

What is a derivative?

Answer 4

An investment product whose values depends on changes in the market price of an underlying asset or index. The underlying may be:

• an interest rate
• a foreign exchange rate
• a commodity e.g. oil, gas, gold
• an equity

Question 5

What are the four main types of derivates?

Answer 5

1. Options - the right but not the obligation for one party to exercise the contract in return for payment of a premium to the counterparty.
2. Forwards - the obligation of both counterparties to complete a transaction on a future date at a known price.
3. Futures - like a forward, but a standardised contract traded on an exchange.
4. Swaps - the obligation for both counterparties to exchange a series of cashflows.

Question 6

Describe the characteristics of exchange-traded contracts.

Answer 6

• they are standardised - available only on certain assets and indices and only for specified delivery dates, as determined by the exchange
• trading is done through the exchange based on market prices
• deals are settled through a clearing house
• the clearing house acts as a counterparty to both the buyer and the seller of the contract and therefore takes on the counterparty risk
• counterparty risk is reduced, for the clearing house, by the pooling of many contracts. It is managed by forcing the trading parties to provide the clearing house with collateral
• the above features result in a highly liquid market with comparatively low transaction prices

Question 7

Describe the characteristics of over-the-counter markets.

Answer 7

• forwards and swaps are traded OTC, as well as some options
• trading is done at the convenience of the parties and no money changes hands until the delivery date
• pricing is by negotiation between the parties who take on the risk of the counterparty defaulting on the arrangement
• OTC contracts are very flexible in terms of choice of the underlying and the delivery date. They are generally provided by the banks to address specific needs of a company, or other institution, usually for an option or a swap.
• documentation is usually based on standard terms and conditions, such as those published by the International Swaps and Derivatives Association (ISDA).

Question 8

What are the main factors that influence the price of an OTC contract?

Answer 8

• the current (spot) price of the underlying
• the time to delivery
• expectations of interest rates over this period
• expected income yield of the underlying over this period
• residual counterparty risk (allowing for the effect of any collateral)
• the cost of carry (opportunity cost of providing collateral, cost of storage of the underlying if a commodity)

Question 9

What is marking-to-market?

Answer 9

The process of adding or removing amounts from the margin account to reflect the movements in the price of the underlying.

Question 10

What are the advantages and disadvantages of using derivatives?

Answer 10

A:

• it may be cheaper and easier to deal in a derivative than the underlying asset
• derivatives can be very flexible and exposure can be changed quickly without the need to deal in the underlying asset

D:

• while hedging is designed to reduce market risk, strategies can be ineffective and may even result in losses. Hedging a risk means that gains as well as losses may be eliminated
• hedging is a costly process, involving transaction costs, spreads, premiums and management time and effort. Hedging requires experienced staff.

Question 11

List all of the risk types associated with dealing in derivatives.

Answer 11

• credit (counterparty) risk
• settlement risk (the risk that one counterparty doesn’t deliver a security as agreed when the security was traded, after the other counterparty has already delivered the security)
• aggregation risk
• operational risk
• liquidity risk
• legal risk
• reputation risk
• concentration risk
• basis risk

Question 12

What is basis risk w.r.t. derivatives and how may it arise?

Answer 12

The risk that the basis changes over time, where basis is the difference between the spot price of an asset and the price of a future.

Basis risk may arise if:

• hedger is uncertain as to the exact date when the asset will be bought or sold
• hedger requires the futures contract to be closed out well before its expiration
• hedger requires the futures position to be rolled over at, or prior to, expiration (as the contract is shorter than the desired period of the hedge)
• differences in income, benefits and/or costs between the futures contract and the underlying asset are not known precisely in advance

Question 13

What are the equations for pricing futures contracts?

Answer 13

If the asset provides no income:
F0 = S0 x exp(rT)

If the asset has an associated income stream:
F0 = (S0 - I) x exp(rT), where I is the PV of the future income stream

If the income stream is continuous throughout the life of the futures contract:
F0 = S0 x exp[(r-q)T],
the cost of carry is considered a negative income

Question 14

Define the optimal hedge ratio.

Answer 14

The optimal hedge ratio is expressed as the ratio of the size of the position taken in futures contracts to the size of the exposure.

h = p x os / oF,

os = standard deviation of the change in spot prices over the life of the hedge
oF = standard deviation of the change in futures prices over the life of the hedge

This is a method to allow for any basis risk

Question 15

What methods are used to hedge foreign exchange or currency risk?

Answer 15

Derivatives:

• currency forward
• currency swap
• currency future
• currency option

Alternatives:

• netting
• leading and lagging - attempt to bring forward or delay foreign currency cashflows in order to exploit expected movements in exchange rates

Question 16

What are the delta, gamma and vega of a portfolio?

Answer 16

DThe first, second, and third partial derivative of price w.r.t. x respectively.

The portfolio will be considered to be delta, gamma and vega hedged if the manager buys u1, …, un units of D1, …, Dn such that:
Deltap + u1 x Delta1 + … + un x Deltan = 0
Gammap + u1 x Gamma1 + … + un x Gamman = 0
Vegap + u1 x Vega1 + … + un x Vegan = 0

• Delta is the rate of change of a portfolio’s value relative to changes in the price of the underlying
• Gamma is the rate of change of delta with the price of the underlying. It measures the curvature or convexity of the relationship between derivative price and underlying asset price
• Vega is the rate of change of the price of the derivative with respect to a change in the assumed level of volatility of the underlying i.e. Vega = dV/do

D:

• the number of derivatives required to maintain gamma and vega neutrality might be quite large
• individual traders tend to have responsibility for trading in all derivatives linked to a single underlying quantity only. They will be given limits as to how far they can deviate from neutrality. The overall portfolio manager is responsible for managing the total neutrality.

Question 17

Outline dynamic hedging.

Answer 17

• Difficult to find offsetting transactions for options. Few are prepared to write such options given the substantial downside risk inherent in a short call or put option.
• Dynamic hedging is used to manage the risk from writing options, with traders rebalancing option portfolios using forwards, futures and asset holding in order to remain delta neutral.
• Because it is impractical to rebalance continuously, the trader remains exposed to risk it can make losses between rebalancing points. The trader also incurs dealing costs at each rebalance.
• A large value of gamma will mean substantial rebalancing will be required to maintain delta neutrality,. This reflects the risks associated with jumps in prices as well as the risks of hedging at discrete points in time and not continuously.
• Vega tells us how sensitive the portfolio is to changes in the volatility of the underlying index or asset price. The higher the portfolio vega, the higher the risk associated with an incorrectly specified volatility.
• Where there are a number of liquid traded derivatives on a given underlying index or asset price, it may be possible to maintain delta, gamma and vega neutrality. However, a lack of traded derivatives or poor liquidity may make this difficult to achieve in practice, and as such there will be limits imposed on the acceptable gamma and vega of a portfolio.

Question 18

Describe the two types of interest rate risks.

Answer 18

1. Direct exposure - changes in interest rates have a direct effect on the size of the company’s cashflows e.g. holding a floating rate loan
2. Indirect exposure - changes in interest rates affect the value of future cashflows e.g. the PV of future cashflows of an annuity

Question 19

How is direct interest rate exposure hedged?

Answer 19

1. Forward Rate Agreements (FRAs) - commits two parties to exchange some interest-rate-dependent payments at a future date. Payments are calculated by applying two different pre-agreed forms of interest rates (e.g. one fixed and one floating) to the same specified monetary amount.
2. Caps and floors - interest rate caps provide insurance against the rate of interest on an underlying floating rate note rising above a certain level, known as the cap e.g. mortgage. An interest rate floor provides a payoff when the interest rate of an underlying floating rate note falls below a certain rate e.g. savings.

Question 20

How is indirect interest rate exposure hedged?

Answer 20

1. Cashflow matching - investing in assets with cashflows exactly matching known cashflow liabilities, both in size and timing.

D:

• suitable assets may not be available
• future cashflows may not be known
• expected future cashflows may change frequently making it costly to alter the portfolio

2. Immunisation - reducing the risk of failing to meet liabilities as they fall due, arising from a change in investment conditions, particularly a change in interest rates. Used in situations where pure matching is not possible.
   Immunisation requires:
   - PV of liability and asset cashflows to be equal
   - the discounted mean term of asset cashflow and liability cashflows to be equal
   - convexity of asset cashflows exceeds that of liability cashflows

D:

• relates to ensuring the PV of assets and liabilities match, rather than matching the timing and amounts of individual cashflows themselves
• only protects the PV against changes in interest rates
• only works for small changes in interest rates
• only works where interest rates change equally at all terms
• requires regular rebalancing of assets

3. Hedging using model points - rather than full immunisation, it may be acceptable to hedge cashflows at key reference points in the future.