Risk Management and Derivatives Flashcards Preview

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Flashcards in Risk Management and Derivatives Deck (53):
1

Risk Goverance

Two Types:

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

 

2

Enterprise Risk Management (ERM) Evaluation

Goal: Identify and take profitable risks

  • Aggregates risks
  • Considers correlation
  • Serious commitment and expense

3

Market and Financial Risk Factors

Market Risks (manage by derivatives)

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

Financial Risk

  • Credit risk
  • Liquidity risk

 

4

Nonfinancial Risk Factors

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

5

Value at Risk (VaR)

Analytical Method

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

6

Value at Risk (VaR)

Analytical Method - Monthly/Weekly

Formula: [Rp - (z)(std)] * Vp

To compute weekly:
Rp = R/ 52

std = std / √52

To compute monthly:
Rp = R/ 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

7

Value at Risk (VaR)

Analytical Method - Disadvantages

 

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

8

Value at Risk (VaR)

Historical Method

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%.

9

Value at Risk (VaR)

Monte Carlo

Similar to Historical, ranks outcomes.

Advantages

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

10

VaR Extentions

  • 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)

11

Credit Risk and Credit Risk VaR (CVaR)

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

CVaR estimates loss due to credit events

12

Types of Stress Testing

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

13

Forward Contract

Value of Credit Risk (Currency)

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

14

Forward/Swaps/Options/Futures Credit Risk

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

15

Option Credit Risk

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

16

Managing Market Risk

VaR manager example


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

17

Risk Budgeting

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

18

How to Manage Credit Risk

  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)

19

Sharpe Ratio vs Sortino

Sharpe

Rp - Rf / stdp

Assumes normal distribution (no skew)

Sortino (use if std is inflated)

Rp - MAR / stddownside

Only downside being considered

20

Risk-Adjusted ROC

RAROC = Rp / capital at risk

 

capital at risk = VaR, etc.

21

Return over Maximum Drawdown (RoMAD)

RoMAD =  Rp / maximum drawdown

 

maximum drawdown = largest historical % decline from high to low

22

Beta Formula

Bi = Cov(i,m) / stdm2

23

Beta Contracts

(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

Target Duration with Futures

# 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

Ex Post Results (Effective Beta)

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

What is Basis Risk?

Describe each cause/type

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

Synthetics

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

Synthetic Equity/Cash Position Formula

# of contracts

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

but the FV for VP = VP(1 + Rf)t

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

Synthetic Equitized/Initial Cash Position

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

Adjusting Asset Allocation with Futures (Example)

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

Types of Foreign Exchange Risk

  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

How to Hedge a Currency Position

Receiving Foreign

Paying Foreign

                                           Position              Action

Receiving Foreign             Long                  Sell forward

Paying Foreign                  Short                 Buy forward

33

Call Options

Right to buy underlying

Make money when goes up

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34

Put Options

Right to sell

Make money when goes down

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35

Relation to Calls/Puts

Rf, Volatility, and Asset Price

Input                    Calls                         Puts

Asset Price ↑       Positive                    Negative

Rf  ↑                      Positive                    Negative

Volatility ↑            Positive                    Positive

36

Covered Call

Buy underlying and selling call option

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

 

Example:

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

37

Protective Put

AKA portfolio insurance/hedged portfolio

Definition: Hold underlying buy a put option

  • profit = (X - ST) - P+ 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

Bull Spread

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

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39

Bear Spread

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

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40

Box Spread

Bull and Bear Spread combined

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

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41

Straddle and Reverse Straddle

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

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42

Straddle

Profit

Max Profit

Max Loss

Breakeven

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

Butterfly Spread

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

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44

Collar

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.

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45

Hedging with Interest Rate Options

Borrowing/Lending

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

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

46

Caps and Floors

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

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47

Delta

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

Swap Risks

Floating and Fixed Rate

  • 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

 

 

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49

Interest Rate Swap Duration

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

Swap Cash Flow and Market Risk Strategies

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

Modified Duration Swap

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

Swaption

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

EAR

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