Chapter 5: Market Risk

Question 1

What is market risk?

Answer 1

• 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.

Question 2

What is exchange rate risk?

Answer 2

• Originates from changes in the value of currencies. Such changes can arise in 3 different settings:
  
  1. Floating FX regime: due to depreciation or appreciation of a currency relative to another.
  2. 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
  3. Any change in regime from floating to fixed or vice versa exposes us to risk

Question 3

What is interest rate risk?

Answer 3

• 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.

Question 4

How to analyze interest rate risk?

Answer 4

1. Analyze the volatility of bond returns (not usually done).
2. 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.

Question 5

What is commodity risk?

Answer 5

• 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.

Question 6

What is a fixed income instrument?

Answer 6

• 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).

Question 7

What are the risks with a bond?

Answer 7

• 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

Question 8

What is the time value of money?

Answer 8

• 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).

Question 9

What is the price-yield relation of a bond?

Answer 9

• 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

Question 10

How do we analyze the impact of changes in the yield on the value of the bond?

Answer 10

• 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:
  
  1. Revalue the bond at its new yield and analyse how the bond price has changed
  2. Derive a Taylor approximation to analyze a change in the yield on the price of a bond

Question 11

What is the Macaulay duration?

Answer 11

• 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

Question 12

What is convexity?

Answer 12

• 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

Question 13

What is modified duration?

Answer 13

• Modified duration is intuitively, the percentage change in price for a unit change in the yield.

Question 14

What is equity?

Answer 14

• 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).

Question 15

What are the risks of equity?

Answer 15

• 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.

Question 16

How do stocks get valued?

Answer 16

• 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:
  
  1. Fundamental approach: determining the absolute value of a stock: eg. Gordon growth model
  2. 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.

Question 17

What are factor models?

Answer 17

• 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

Question 18

What is the derivates market?

Answer 18

• Derive value from other asset.
• Derivative instruments derive their value from an underlying asset (stock; bond, FX,…)
• Distinguish 2 sub-markets:
  
  1. Market for linear derivatives: incldues forwards, futures and swaps.
  2. 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.

Question 19

What is a forward?

Answer 19

• 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

Question 20

What is the payoff structure?

Answer 20

• 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

Question 21

What is a futures contract?

Answer 21

• 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.

Question 22

What is a swap contract?

Answer 22

• 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:
  
  1. Interest rate swaps: floating interest payments are exchanged for fixed interest payments
  2. Currency swaps: payments in one currency are exchanged for payments in another currency.

Question 23

What are the risks when investing in linear derivatives?

Answer 23

• 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.

Question 24

How to price a linear derivative?

Answer 24

• 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.

Question 25

What are options?

Answer 25

• 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.

Question 26

What are the option payoffs?

Answer 26

• 2 types of elementary options: asset S with exercise price K:

1. 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
2. Plain vanilla options whose payoff is > 0 or 0
   
   • Call option: Max (St - K, 0)
   • Put option: Max (K - St, 0)

Question 27

What are the different risks when investing in options?

Answer 27

• 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

Question 28

What is the option value?

Answer 28

• Value of an option : option premium which consists of:
  
  1. 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
  2. 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

Question 29

What is the relation between the option value in function of the price of the underlying asset

Answer 29

Convex

Question 30

How do we price options?

Answer 30

• All through no-arbitrage principle:
• Most common methods are:
  
  1. Binomial option pricing model
  2. Black-Scholes - Merton option pricing model