RM and Derivatives

Question 1

Risk Management

Answer 1

understand risks; determine when it’s appropriate to take risk

1. identify risks
2. set risk tolerances
3. report risk to stakeholders
4. monitor

Question 2

Risk Governance

Answer 2

policies and procedures establishing risk management

• structure - centralized (best), decentralized
• reporting
• methologies
• infrastructure needs

Question 3

Enterprise Risk Management

Answer 3

centralized risk management

1. identify risk factors
2. quantify risk
3. aggregate to measure firm wide risk
4. report/ allocate risk
5. monitor

Question 4

Financial Risk

Answer 4

due to events external to firm, in financial markets

1. market risk
2. credit risk
3. liquidity risk

mitigate with derivatives (options, swaps)

Question 5

Market Risk

Answer 5

1. interest rate risk
2. exchange rate risk
3. equity price risk
4. commodity price risk

Question 6

Nonfinancial Risk

Answer 6

1. operational risk
2. settlement/ perf netting risk - one party pays, other defaults
3. model risk - GIGO
4. sovereign risk
5. regulatory risk
6. tax, accounting, political risk

mitigate with insurance

Question 7

VaR

Answer 7

probability of expected loss over a specified time; comparable across asset classes, not managers

1. analytical: VaR = [R - z * σ] V
2. historical
3. monte carlo simulation

Question 8

One Tail SD

Answer 8

• 5% = 1.65 SD
• 1% = 2.33 SD

Question 9

VaR Complements

Answer 9

• incremental VaR: risk from additional factor
• cash flow/ earnings at risk: min CF loss for given prob over time
• tail value at risk (TVaR): avg outcomes in tail

Question 10

Credit Risk

Answer 10

possibility counterparty defaults; current and potential credit risk

prob default * PV losses

PV rec - PV paid

Question 11

Credit Risk of Currency Forwards

Answer 11

long base currency

S₀ / ( 1 + b )^t - F_t / ( 1 + p )^t

highest credit risk in middle of forward’s life

Question 12

Credit Risk of Currency Swaps

Answer 12

highest credit risk btwn middle/end of swap’s life

PV rec - PV pay

Question 13

Credit Risk of Options

Answer 13

long position = credit risk

current credit risk when option is exercised

Question 14

Managing Credit Risk

Answer 14

1. limiting exposure
2. marking to market
3. collateral
4. netting payments
5. closeout netting
6. credit derivatives

Question 15

Risk Budgeting Factors

Answer 15

must consider correlation of risk in diff units

1. VaR limits
2. position limits
3. liquidity limits
4. performance stopout
5. risk factor limits

Question 16

Sortino Ratio

Answer 16

ratio of excess return to risk; doesn’t penalize manager for good performance

( R_p - MAR ) / downside deviation

Question 17

Forward vs Future

Answer 17

Forward: custom, high default risk, less liquidity; currency, int payments

Futures: standardized, trade on exchange, low default risk; bond, equity

Question 18

Modifying Equity Beta

Answer 18

contracts = ( Δβ / β_f ) * ( V_p / Vf )

Question 19

β

Answer 19

cov_i,m / σ_m²

Question 20

Effective Beta

Answer 20

%Δ value of portfolio / %Δ value of index

Question 21

Why Effective Beta Deviates

Answer 21

basis risk = imperfect hedge

• num/ demon based on diff items
• evaluating before expiration
• # contracts rounded
• F and S not priced correctly

Question 22

Modifying Bond Duration

Answer 22

contracts = β_yield * ( ΔMD / MD_f ) * ( V_p / Vf )

Question 23

Synthetic Stock

Answer 23

beta = 1

repliate buying contracts; buy futures contract, long T-bills

• N_f = FV_Vp / V_f
• terminal shares replicated = N_f * mult (beg = discount by div yield)
• initial eqty eq = PV( N_f * mult * price ) [terminal = FV]

Question 24

Synthetic Cash

Answer 24

beta = -1

replicate selling contracts; long equity, short futures contract

• N_f = - FV_Vp / V_f
• initial cash eq = PV( N_f * mult * price ) [terminal = FV]
• terminal shares = N_f * mult

Question 25

Exchange Rate Risks

Answer 25

1. transaction risk
2. economic risk
3. translation risk (translating financial statements)

Question 26

Hedging Currency Positions

Answer 26

• receiving foreign curr = sell forward
• paying foreign curr = buy forward

Question 27

Covered Call

Answer 27

long stock, short call; exp lower volatility

• payoff: S_t - max( 0, S_t - X ) - S₀ + C
• max gain: (ex opt) X - S₀ + C
• max loss: (don’t ex opt, S_t = 0) S₀ - C
• breakeven: (initial cost) S₀ - C

Question 28

Protective Put

Answer 28

long stock, long put; exp higher volatility

• payoff: S_t + max( 0, X - S_t ) - S₀ - P
• max gain: unlimited
• max loss: (ex opt) S₀ + P - X
• breakeven: (initial cost) S₀ + P

Question 29

Bull Call Spread

Answer 29

long CL, short CH; long P_L; short P_H; exp inc S

• profit: C_H - C_L + max( 0, S - X_L ) - max( 0, S - X_H )
• max profit: (both ex) X_H - X_L + C_H - C_L
• max loss: (neither ex) C_L - C_H
• breakeven: (ex C_L) X_L + C_L - C_H

Question 30

Bear Put Spread

Answer 30

long P_H, short P_L; long C_H, short C_L; exp dec S

• profit: max( 0, X_H - S ) - max ( 0, X_L - S ) + P_L - P_H
• max profit: (both ex) X_H - X_L + P_L - P_H
• max loss: (no ex) P_H - P_L
• breakeven: (ex P_H) X_H + P_L - P_H

Question 31

Butterfly Spread with Calls

Answer 31

long C_L and C_H; short 2 C_M; exp dec volatility

• profit: max( 0, S - X_L ) + max( 0, S - X_H ) - 2max( 0, S - X_M ) + 2C_M - C_L - C_H
• max profit: (ex C_L, C_M) X_M - X_L + 2C_M - C_L - C_H
• max loss: (no ex) C_L + C_H - 2C_M
• breakeven: 2C_M - C_L - C_H + 2X_M - X
  
  • C_L + C_H - 2C_M + X_L

Question 32

Butterfly Spread with Puts

Answer 32

long P_L and P_H; short 2 P_M; exp dec volatility

• profit: max( 0, X_H - S ) + max( 0, X_L - S ) - 2max( 0, X_M - S ) + 2P_M - P_L - P_H
• max profit: (ex P_H, P_M) X_H - X_M + 2P_M - P_L - P_H
• max loss: (no ex) P_L + P_H - 2P_M
• breakeven: P_L + P_H - 2P_M +
  
  • 2P_M - P_L - P_H +

Question 33

Straddle

Answer 33

long call and put OR short call and put; exp inc price volatility

• profit: max ( 0, S - X ) + max ( 0, X - S ) - C - P
• max gain: unlimited
• max loss: (inv) C + P
• breakeven: X - C - P or X + C + P

Question 34

Collar

Answer 34

stock, long P_L, short C_H; exp low price volatility

• profit: max ( 0, X_L - S ) + max ( 0, S - X_H ) + S - S₀
• max profit: X_H - S₀
• max loss: S₀ - X_L
• breakeven: S₀

Question 35

Box Spread

Answer 35

combo of bull and bear spreads; arbitrage opp

• profit: X_H - X_L + P_L - P_H + C_H - C_L
• compare annualized HPR to r_f

Question 36

Interest Rate Call Payoffs

Answer 36

• net loan: loan - FV(premium)
• call payoff: NP [max[ 0, LIBOR - X] * D/ 360 ]
• eff $ int cost = loan int - call payoff
• EAR: [(loan + eff $ int cost) / net loan]^365/D - 1

Question 37

Interest Rate Put Payoffs

Answer 37

• net loan: loan + FV(premium)
• put payoff: NP [max[ 0, X - LIBOR] * D/ 360 ]
• eff $ int cost = loan int + put payoff
• EAR: [(loan + eff $ int cost) / net loan]^365/D - 1

Question 38

Interest Rate Cap

Answer 38

payment when rate > X

series of int rate calls; caplets

good for floating rate payer

Question 39

Interest Rate Put

Answer 39

payment when X < rate

series of int rate puts; floorlets

good for floating rate receiver

Question 40

Delta

Answer 40

change in option price/ change in underlying

Question 41

Delta Hedging

Answer 41

hedge downside risk of short options (dealers); earn r_f

stock required = - delta * # options

Question 42

Gamma

Answer 42

change in delta/ change in underlying

Question 43

Vega

Answer 43

change in underlying/ change in volatility

Question 44

Swap Duration

Answer 44

• fixed duration = 0.75 maturity
• floating duration = 0.5 reset period
• D_{pay floating} = D_fixed - D_floating = +D
• D_{pay fixed} = D_floating - D_fixed = -D

Question 45

Modifying Swap Duration

Answer 45

NP = [( MD - MD₀ )/ MD_swap] V_p

rec floating = neg swap duration

Question 46

Payer Swaption

Answer 46

buyer = right to be fixed-rate payer, receive floating

exp rates to go up

Question 47

Receiver Swaption

Answer 47

buyer = right to be fixed-rate receiver, pay floating

exp rates to go down