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CFA Level III > Risk Management and Derivatives > Flashcards

Risk Management and Derivatives Flashcards

1
Q

Risk Goverance

A

Two Types:

Decentralized - each unit is responsible
Centralized (aka ERM) - one central unit is responsible
Allows overview
Economies of scale

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2
Q

Enterprise Risk Management (ERM) Evaluation

A

Goal: Identify and take profitable risks

  • Aggregates risks
  • Considers correlation
  • Serious commitment and expense
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3
Q

Market and Financial Risk Factors

A

Market Risks (manage by derivatives)

  • Interest rates
  • Exchange rates
  • Equity prices
  • Commodity prices

Financial Risk

  • Credit risk
  • Liquidity risk
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4
Q

Nonfinancial Risk Factors

A

Non-Financial Risks (manage by insurance)

  1. Operational - computer, human, or weather events
  2. Settlement (Hersatt)- other party fails to pay
  3. Model
  4. Sovereign
  5. Regulatory
  6. Tax, accounting and legal
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5
Q

Value at Risk (VaR)

Analytical Method

A

Also called variance-covariance method

Formula: [Rp - (z)(std)] * Vp

Know the following for z:

5% = 1.65 2.5% = 1.96
1% = 2.33 0.5% = 2.58

Example: Calculate 5% annual VaR for 150M
R = 9.55, std =14.87

9.55 - 1.65(14.87) = -14.99%
.1499 * 150M = 22.49M loss

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6
Q

Value at Risk (VaR)

Analytical Method - Monthly/Weekly

A

Formula: [Rp - (z)(std)] * Vp

To compute weekly:
Rp = Rp / 52

std = std / √52

To compute monthly:
Rp = Rp / 12

std = std / √12

Example: Calculate 5% weekly VaR for 150M
R = 9.55, std =14.87

(9.55 / 52) - 1.65(14.87 / √52) = -3.22%
.0322 * 150M = 4.83M weekly loss

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7
Q

Value at Risk (VaR)

Analytical Method - Disadvantages

A
  • Some returns, like options, are skewed (assumes normal)
  • Market distributions have fat tails (leptokurtosis)
  • Std hard to estimate for large portfolios
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8
Q

Value at Risk (VaR)

Historical Method

A

Rank all returns from lowest to highest and identify the % you need

Advantages: reflects past distributions
nonparametric
Disadvantage: assumes historical returns will will repeat

Example: 100 daily returns, the 5 lowest are:
-.0019, -.0025, -.0034, -.0096, -.0101
Calculate daily VaR at 5%

5th lowest -.0019. Means a 5% chance of daily loss exceeding 0.19%.

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9
Q

Value at Risk (VaR)

Monte Carlo

A

Similar to Historical, ranks outcomes.

Advantages

  • Can customize (normal distribution for some assets, skewed for others, etc.)
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10
Q

VaR Extentions

A
  • Incremental VaR
  • Tail Value at Risk (TVaR) - average value in the 5% tail
    • Looks at whole tail (even past VaR)
  • Cash Flow at Risk (CFAR)
  • Earnings at Risk (EAR)
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11
Q

Credit Risk and Credit Risk VaR (CVaR)

A

Credit Risk Loss depends on:
Probability of default
Amount that can be recovered

CVaR estimates loss due to credit events

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12
Q

Types of Stress Testing

A

Complement to VaR

  1. Factor Push: puts factors at worst combination
  2. Maximum loss optimization: models the worst combination of factors
  3. Worst-case scenario
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13
Q

Forward Contract

Value of Credit Risk (Currency)

A

value to long = St / (1 + Rforeign)t - F0 / (1 + Rdomestic)t

Positive = long credit risk Negative = seller credit risk

F = foreign (must be BASE)

Example: US enters 2-yr forward, purchase = 10,000 EUR at USD 0.90
6 months later: Spot = .862/EUR. 1.5 yr rates: US 6%, EUR 5%
Calculate potential credit risk

.862 / (1.05)1.5 - 0.90 / (1.06)1.5 = -0.0235
Long is losing. NO credit risk
Seller is winning, has credit risk of 10,000 EUR * 0.235 = $235

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14
Q

Forward/Swaps/Options/Futures Credit Risk

A

Forward: only change hands at end. Party winning has risk. Highest risk near the end

Swaps: credit risk at each swap date. Highest risk in the middle

Options: only long positions faces credit risk

Futures: No credit risk

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15
Q

Option Credit Risk

A

Currrent credit risk: only at exercise

Potential credit risk: positive market value of the option

Example:

Dealer sold a call option, X = $35, value = $46

Current credit risk: none

Potential credit risk: None for dealer, $46 per share for buyer

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16
Q

Managing Market Risk

VaR manager example

A

VaR is not additive because it considers correlation

Example A B
Capital $100,000,000 $500,00,000
VaR $5,000,000 $10,000,000
Profit $1,000,000 $3,000,000
Return on Capital 1% 0.6%
Return on VaR 20% 30%

RoC has A winning, but RoVaR has B winning

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17
Q

Risk Budgeting

A

Determining where and how much risk to take through ERM

Types: (not important)

  1. VaR limits
  2. Liquidity limits
  3. Performance stop loss
  4. Risk factor limits
  5. Scenario analysis limits
  6. Leverage limits
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18
Q

How to Manage Credit Risk

A
  1. Collateral
  2. Credit default swap/forward
  3. Mark to market - settle contract now to reprice
  4. Minimum credit standards
  5. Limit exposure (position, loss, factors, VaR, leverage, liquidity)
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19
Q

Sharpe Ratio vs Sortino

A

Sharpe

Rp - Rf / stdp

Assumes normal distribution (no skew)

Sortino (use if std is inflated)

Rp - MAR / stddownside

Only downside being considered

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20
Q

Risk-Adjusted ROC

A

RAROC = Rp / capital at risk

capital at risk = VaR, etc.

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21
Q

Return over Maximum Drawdown (RoMAD)

A

RoMAD = Rp / maximum drawdown

maximum drawdown = largest historical % decline from high to low

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22
Q

Beta Formula

A

Bi = Cov(i,m) / stdm2

23
Q

Beta Contracts

A

(BT - BP) / Bf * Vp / Pf (multiplier)

Example: 5M portfolio w/ beta of 0.8.
Futures contract beta = 1.05 and price = 240,000
Calculate # of contracts to get beta of 1.1 and 0.0

of contracts = (1.1 - 0.8 / 1.05) * (5M / 240,000) = 5.95
Means buy 6 contracts at 240K
# of contracts = (0 - 0.8 / 1.05) * (5M / 240,000) = -15.87
Means sell 16 contracts at 240K

24
Q

Target Duration with Futures

A

of contracts = ((DT - Dp) / DF) * [Vp / PF (multiplier)] * Yield Beta

Use yield beta if not parallel shift

Example: bond portfolio 103,630, 1 year period. Futures = 102,510
duration p = 1.793, duration f = 1.62, yield beta = 1.2
Calculate # of contracts to get duration to 0 and 3

(0 - 1.793) / 1.62 * (103,630/102,510) * 1.2 = -1.34
(3 - 1.793) / 1.62 * *103,630/102,510) * 1.2 = 0.9

25
Q

Ex Post Results (Effective Beta)

A

effective beta = % change in Vp / % change in the index

Example:5M portfolio increased to 5.255M and futures increased 240K to 252,240. Market return was 5.2%.
Bought 6 contracts

contracts went up 12,240 * 6 = 73,440
hedged portfolio value = 5,255,000 + 73,440 = 5,328,440
Hedged return = (5,328,440/5,000,000) - 1 = 6.57%
effective beta = 6.57 / 5.2 = 1.26

26
Q

What is Basis Risk?

Describe each cause/type

A

When hedging is not perfect

  • *Type:** Cross hedge (hedging an index with few stocks)
  • *Type:** Contract expiration differs from hedge time frame
  • *Type:** Portfolio and contracts perform differently
  • *Type:** Rounding contracts
27
Q

Synthetics

A

More precisely replicates outright ownership. Must calculate FV

Synthetic Stock: buy contracts and hold enough cash earning Rf to pay for shares

Synthetic Cash: sell contracts and hold enough shares of stock w/ dividends reinvested to deliver shares at expiration

28
Q

Synthetic Equity/Cash Position Formula

of contracts

A

Remember its the same: (BT - BP) / BF * VP / PF (multiplier)

but the FV for VP = VP(1 + Rf)t

So: (BT - BP) / BF * VP(1 + Rf)t / PF (multiplier)

Example: Convert 100M to cash for 3 months
Rf = 3.5%, Equity price = $325,000, Index dividend yield = 2%

No beta given so (1 - 1) / 1 * 100M(1.035).25 / 325,000 = -310.35

29
Q

Synthetic Equitized/Initial Cash Position

A

Amount required today:

(# of contracts)(multiplier)(price) / (1 + Rf)t

For EV do it again: (1 + Rf)t

Example: 300M synthetic in R2000, 3mo futures price = 498.30
Multiplier: 500, Rf: 2.35%, Dividend yield: 0.75%

of contracts: (300M)(1.0235)3/12 = 1211.11
Amount equitized: (1211)(500)(498.30) / (1.0235)3/12 = 299,973,626
EV at contract expiration: 299,973,626(1.0235)3/12 = 301,720,650

30
Q

Adjusting Asset Allocation with Futures (Example)

A

Current Portfolio: 80/20 stocks/bonds
Size: 300M, Beta: 1.1, Duration: 6.5
Desired Temporary Allocation: 50/50
Stock futures price: 200,000, Beta: 0.96
Bond futures price: 105,250, Duration: 7.2

Need to sell stock contracts, buy bond contracts for 30%

300M * .3 = 90,000,000

Sell stock contracts: ((0 - 1.1) / 0.96) * (90,000,00 / 200,000) = -515.63
Buy bond contracts: ((6.5 - 0) / 7.2) * (90,000,000 / 105,250) = 717.97

Sell 516 stock contracts at 200,000
Buy 772 bond contracts at 105,250

31
Q

Types of Foreign Exchange Risk

A
  1. Transaction - cash flow at later date, can be hedged
    1. most common
  2. Economic - ▲ in currency affect competitiveness
    1. Example; dollar ^, less competitive in foreign markets
    2. Can be difficult to hedge
  3. Translation - risk of reporting in another currency
32
Q

How to Hedge a Currency Position

Receiving Foreign

Paying Foreign

A

Position Action

Receiving Foreign Long Sell forward

Paying Foreign Short Buy forward

33
Q

Call Options

A

Right to buy underlying

Make money when goes up

34
Q

Put Options

A

Right to sell

Make money when goes down

35
Q

Relation to Calls/Puts

Rf, Volatility, and Asset Price

A

Input Calls Puts

Asset Price ↑ Positive Negative

Rf ↑ Positive Negative

Volatility ↑ Positive Positive

36
Q

Covered Call

A

Buy underlying and selling call option

  • profit = (ST - X) + C0 + ST - S0
  • max profit = X + C0 - S0
  • max loss = S0 - C0
  • Breakeven = S0 - C0

Example:

(35 - 45) + 35 - 43 + 2.10 = 5.90

37
Q

Protective Put

A

AKA portfolio insurance/hedged portfolio

Definition: Hold underlying buy a put option

  • profit = (X - ST) - P0 + ST - S0
  • max profit = ST - P0 - S0
  • max loss = S0 + P0 - X
  • breakeven = S0 + P0

Example:

(35 - 30) + 30 - 37.5 - 1.4 = -3.90

38
Q

Bull Spread

A

Profit when underlying increases

*Built with all calls or puts

  • Buy call at XL, sell call at XH
  • Buy put at XL, sell put at XH
39
Q

Bear Spread

A

Profit when underlying decreases

*Built with all calls or puts

  • Sell call at XL, buy call at XH
  • Sell put at XL, buy put at XH
40
Q

Box Spread

A

Bull and Bear Spread combined

  • Creates an aribtrage relationship
  • Known initial and ending cash flows
41
Q

Straddle and Reverse Straddle

A

Making money from volatility. THE BIG V

Straddle

Buy call and put at same strike
Profit from high volatility

Reverse Straddle

Sell a call and put at same strike
Profit from low volatility

42
Q

Straddle

Profit

Max Profit

Max Loss

Breakeven

A

Profit = (ST - X) + (X - ST) - C0 - P0

Max Profit = Infinite as stock increases

Max loss = C0 + P0

Breakeven = X - C0 - P0 AND X + C0 + P0

43
Q

Butterfly Spread

A

Requires four options (2 long/2 short) with 3 strikes

Option 1:
Buy call XL, sell 2 calls XM, buy call at XH

Option 2:
Buy put XL, sell 2 puts XM, buy put at XH

Option 3:
Buy put XL, sell put and call XM, buy call XH

44
Q

Collar

A

Same as bull spread but done with owning the underlying

buy put XL, sell a call XH, Own underlying

Commonly used for interest rate options.

45
Q

Hedging with Interest Rate Options

Borrowing/Lending

A

Borrowing
Risk: increasing rates
Hedge: buy an interest rate call

Lending
Risk: decreasing rates
Hedge: buy a interest rate put

46
Q

Caps and Floors

A

Cap: Series of interest rate calls
Protects a floating rate debt payer from increasing rates

Floor: series of interest rate puts
Protects owner of floating rate debt from decreasing rate

47
Q

Delta

A

Definition: change in the price of an option for a 1-unit change in the price of the underlying stock (speed)

Call Range from 0-1

Out-of-the-money is closer to 0

In-the-money is closer to 1

Put Range is from -1 to 0

Out-of-the-money is closer to 0

In-the-money is closer to -1

48
Q

Swap Risks

Floating and Fixed Rate

A
  • Floating rate debt has minimal duration but uncertain cash flow
    • High cash flow risk
    • Low duration
    • Low market value risk
  • Fixed rate debt has higher duration but certain cash flow
    • Low cash flow risk
    • High duration
    • High market value risk

Important to draw out the diagram

49
Q

Interest Rate Swap Duration

A

1

Dpay floating = Dfixed - Dfloating = +D paying floating INCREASES duration

Dpay fixed = Dfloating - Dfixed = -D paying fixed DECREASES duration

2

Floating rate duration resets and assume duration is half. (1 year = 0.5)

Example:

5-year pay fixed swap with quarterly settlement. Comparable bond 4.1 duration

-4.1 + 0.25/2 = -3.975

50
Q

Swap Cash Flow and Market Risk Strategies

A

Rates will increase

Scenario Strategy Result

Assets: Fixed Receive Float ↓ MVR, ↑ CFR

Assets: Float Do nothing Accept low MVR, high CFR

Liability: Fixed Do nothing Accept high MVR, low CFR

Liability: Float Receive Fixed ↑ MVR, ↓ CFR

51
Q

Modified Duration Swap

A

NP = VP [(MDT - MDP) / MDswap]

Formula calculates size of swap. Make sure to state what type:

Pay fixed (decrease) or pay float (increase). Put that in the denominator

Example: 60M portfolio, duration 5.2, target 4, swap duration 3.1

Lower duration so we want to pay fixed
60,000,000 [(4-5.2) / -3.1)] = 23,225,806

52
Q

Swaption

A

Definition: option to enter a pre-negotiated swap

Two Types

  1. Payer: allows swaption buyer to enter a pay fixed
    1. gains value if rates rise
  2. Receiver: allows swaption buyer to enter a received fixed
    1. gains value if rates fall
53
Q

EAR

A

Step 1: Premium from call
Premium * (1 + r)days/360

Step 2: Loan - premium

Step 3: Loan interest

Step 4: Call payoff

Step 5: [(Loan + interest - call payoff) / loan proceeds]annual rate

CFA Level III (13 decks)

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