Chapter 5: Market Risk Flashcards
1
Q
What is market risk?
A
- Market risk is the risk of achieving a loss on an investment product due to a change in its market risk drivers.
- Currency investments: exchange rate risk
- Fixed income instruments: interest rate risk
- Stock investments: equity risk
- Commodities: commodity risk
- Managing risk is all about analyzing the impact of a change in the market risk factor on the value of your investment.
2
Q
What is exchange rate risk?
A
- Originates from changes in the value of currencies. Such changes can arise in 3 different settings:
- Floating FX regime: due to depreciation or appreciation of a currency relative to another.
- Fixed FX: risk of devaluation or revaluation which is an adjustment to parity value to recover from trade imabalnces: monetary policy tool.
- Eg. EMS crisis in 1992
- Any change in regime from floating to fixed or vice versa exposes us to risk
3
Q
What is interest rate risk?
A
- Originates from changes in the value of fixed income products due to changes in the general level of interest rates.
- Important: the term structure of interest rates (yield curve) which summarizes the level of interest rates in function of its maturity.
- The shape of TS determines profitability of the financial sector.
4
Q
How to analyze interest rate risk?
A
- Analyze the volatility of bond returns (not usually done).
- Analyze the volatility of changes in the yield = yield volatility: more intuitive as it remains more constant over time. Return volatility goes to zero as we approach maturity.
5
Q
What is commodity risk?
A
- Commodity risk originates from changes in the value of commodity prices.
- Contrary to the others market risk, commodity risk is influenced by its capacity to store: the harder to store the commodity, the larger the imbalances between supply and demand and thus the more volatile prices.
6
Q
What is a fixed income instrument?
A
- Security that obliges the borrower to make specific payments at specific times.
- Key properties of a bond:
- Interest rate sensitive
- Type of issuer determines the creditworthiness
- Term to maturity is most often fixed, but can also be variable (callable, puttable, convertible).
- Most pay intermediate income (fixed or variable coupons), some do not (zero coupon).
7
Q
What are the risks with a bond?
A
- Bond investing entails different market risks.
- Interest rate risk: inverse relation with bond price
- Exchange rate risk (foreign bond): depreciation / devaluation of foreign currency
- Reinvestment risk: coupons need to be reinvested for the future
- Call risk: risk of early repayment gives the risk of looking for new investment opportunities.
- All of these risks are reflected in the value of the bond.
- Credit risk also influences the bond price
8
Q
What is the time value of money?
A
- Price of a bond equals its discounted future cashflow. The discount rate is a maturity specific discount factor.
- Market value V is determined by supply and demand which also allows us to compute the yield to maturity (YTM)
- YTM is the time-independent discount factor y such that discounted cash flows correspond to market price: this YTM is an internal rate of return (assuming thus that coupons are reinvested at this YTM).
- The concept of YTM allows for comparison across bonds (expressed on annual basis we have effective annual rates).
9
Q
What is the price-yield relation of a bond?
A
- Price-yield relation is a nonlinear function.
- A bond with higher coupon rate sells at a higher price
- A longer maturity bond is more steep and more curved.
- Yield < coupon rate: longer maturity bond sells at a higher price
- Yield > coupon rate: longer maturity bond sells at al lower price
10
Q
How do we analyze the impact of changes in the yield on the value of the bond?
A
- Central task of risk management = model the P&L of a particular change in the yield.
- To analyze effect of change in the yield on the value of the bond:
- Revalue the bond at its new yield and analyse how the bond price has changed
- Derive a Taylor approximation to analyze a change in the yield on the price of a bond
11
Q
What is the Macaulay duration?
A
- Weighted average of time, where the weights w reflect the overall importance of the present value of cashflows.
- Can be interpreted as the average time over which income is received:
- Longer maturity bonds increase Macaulay duration:
- Higher coupon rate decreases Macaulay duration
12
Q
What is convexity?
A
- Convexity is, roughly speaking, a weighted average of square of time with wt the ratio t cashflow to total cashflow.
- It reflects the degree of curvature of the bond-yield relation (a property that is liked):
- Higher coupon rate decreases convexity
- Longer maturities increase convexity
13
Q
What is modified duration?
A
- Modified duration is intuitively, the percentage change in price for a unit change in the yield.
14
Q
What is equity?
A
- A stock is an asset that represents equity ownership, entitling the holder to a share of the corporation’s success.
- Different classes of stocks can be distinguished such as common stock (junior stock) or preferred stock.
- Key properties:
- Residual claim: payments only occur after all contractuel obligations have been paid
- Remuneration is uncertain: entitled to a dividend if its paid, capital appreciation if you sell at a higher price.
- Limited liability: equity stake can become worthless, but not liable with your own wealth.
- Voting rights and preemptive rights (right to purchase additional shares in the event of a seasoned offering).
15
Q
What are the risks of equity?
A
- Different market risks:
- Equity or stock market risk
- Exchange rate risk (foreign stock)
- Reinvestment risk of the dividend
- All of these risks are reflected in the value of the stock.
16
Q
How do stocks get valued?
A
- When pricing equity, the principle of discounted future cashflows is more challenging as the future cashflows are much more uncertain.
- 2 different approaches to price stocks:
- Fundamental approach: determining the absolute value of a stock: eg. Gordon growth model
- Factor models: focused on determining the relative value of a stock.
- We rely on such factor pricing in risk management, as it clarifies the risk-return relationship.
17
Q
What are factor models?
A
- Central to the factor models is their focus on both return and risk, plus it allows or a distinction between systematic and unsystemastic risk.
- Models: CAPM, Market, Fama-French, Carhart
18
Q
What is the derivates market?
A
- Derive value from other asset.
- Derivative instruments derive their value from an underlying asset (stock; bond, FX,…)
- Distinguish 2 sub-markets:
- Market for linear derivatives: incldues forwards, futures and swaps.
- Market for nonlinear derivates includes options.
- Derivative instruments are of special interest to a risk manager for its hedging capacities: they can be used to reduce or eliminate risk.
19
Q
What is a forward?
A
- Forward contract is an agreement to buy or sell a specific quantity of a particular asset at an agreed price (forward price) for delivery and settlement at a specified future date.
- If you agree to buy = long the contract
- Agree to sell = short the contract
- Key properties of a forward:
- Private and tailored agreement between two parties
- Traded on the OTC market (exposing you to significant counterparty risk or credit risk).
- Payoff of the forward at maturity is the difference between the maturity value of the underlying asset and the agreed forward price: Vt = St - F
20
Q
What is the payoff structure?
A
- A forward has a symmetric payoff structure around the forward price.
- Long forward: the contract is positive when the asset at maturity is worth more than the forward price
- Short forward: contract is positive when the asset at maturity is less more than the forward price
21
Q
What is a futures contract?
A
- A futures contract is similar to a forward contract from a product design point of view.
- It is a standardized agreement to buy (sell) a specific quantity of a particular asset at an agreed price for delivery and settlement at a specified future date.
- Standardization reduces a number of risks that are present in forward contract:
- Futures are traded on an organized market, which increases the liquidity.
- Standardization makes that the contract modalities are fixed across a large number of assets: this increases the liquidity
- Presence of a clearinghouse reduces counterparty risk
- Clearinghouse applies marking-to-market and asks for margins: also reduces credit risk.
22
Q
What is a swap contract?
A
- Swap is an agreement exchange cashflows in the future according to a pre-defined schedule: from a product-design point of view we can look at a swap as a portfolio of forwards.
- Common swaps are:
- Interest rate swaps: floating interest payments are exchanged for fixed interest payments
- Currency swaps: payments in one currency are exchanged for payments in another currency.
23
Q
What are the risks when investing in linear derivatives?
A
- Market risks:
- Specific market risks of the asset that underlies the derivatives contract
- Interest rate risk to bring your contract forward
- Also counterparty credit risk.
24
Q
How to price a linear derivative?
A
- To price a linear derivative, the principle of no-arbitrage is used = identical payoffs trade at identical prices.
- Value of a contract is thus the difference between the current forward rate the locked-in delivery rate.
- Pricing of a futures and a swap is very similar: for futures, only a small difference exists because of daily marking-to-market (P&L accrue during life of the contract and earn interest, whereas they are only earned at the end of the forward contract.) A swap rate is weighted average of multiple futures rates.
25
Q
What are options?
A
- An option is an instrument that gives the holder a right to buy (call option) or to sell (put opion) a specific quantity of a particular asset at a predetermined future date and price (exercise price)
- When you are long the option (holder of the option), you have a right, when you short the option (writer of the option), you have an obligation to follow the holder’s decision.
- Key features of an option:
- Options can be OTC traded or traded on an organized exchange: chicago Board of Options Exchange).
- European call option can only be exercised at maturity, while an American option can be exercised on any day until maturity.
- Asymmetric payoff: you only exercise when profitable, this makes that you cannot buy an option at zero cost, you need to pay a premium to the writer of the option.
26
Q
What are the option payoffs?
A
- 2 types of elementary options: asset S with exercise price K:
- Binary options: payoff is 1 or 0
- Call payoff is 1 if St - K > 0, 0 otherwise
- Put payoff is 1 if St - K < 0, 0 otherwise
- Plain vanilla options whose payoff is > 0 or 0
- Call option: Max (St - K, 0)
- Put option: Max (K - St, 0)
27
Q
What are the different risks when investing in options?
A
- Market risks:
- Market risks of the asset on which the option is traded, this effect is non-linear.
- Asymmetry in the payoff introduces volatility risk
- Interest rate risk to bring your contract forward
- Time-decay, not a risk, but important to determine the value of the option.
- Also counterparty credit risk
28
Q
What is the option value?
A
- Value of an option : option premium which consists of:
- Intrinsic value: value from immediately exercising the option and is determined as max (St - K, 0) for a call or max (K - St, 0) for a put. This intrinsic value is also labelled moneyness
- Time value: reflects the potential future intrinsic value and is determined as the residual between option premium and intrinsic value = highest if close to exercise price
29
Q
What is the relation between the option value in function of the price of the underlying asset
A
Convex
30
Q
How do we price options?
A
- All through no-arbitrage principle:
- Most common methods are:
- Binomial option pricing model
- Black-Scholes - Merton option pricing model
