Fixed Derivatives Flashcards

Question

Gamma is Greatest for...

Answer 1

At the money options

Answer 2

Po = Co - So + x/e^(r)(t) * - t should be in decimal form (90 days = .25)* * - this formula assumes continuous compounding*

Answer 3

P0 = Co + [(X - F(0,T) / 1+r^t] ## Footnote * 1. F(0,T) = value of future now that expires in time T* * 2. The numerator could be negative*

Answer 4

Step 1: Calculate max gain for up and down move Step 2: prob = (1 + Rf% - d) / u - d Step 3: Co = [prob(call+) + 1-prob(call-)] / (1 + Rf%) * - d = 1 - the likely decline in value in percentage terms* * - u = 1+ the likely rise in value in percentage terms* * - call+ = The maximum value of the call assuming the positive forecast comes true at expiration*

Answer 5

Step 1: Calculate max gain for up, down, and up/down-down/up moves - up and down move must be squared Step 2: prob = (1 + Rf% - d⁻) / u⁺ - d⁻ Step 3a: C⁺⁺ = [prob(call⁺⁺) + 1-prob(call⁺⁻)] / (1 + Rf%) Step 3b: C⁻⁻ = [prob(call⁺⁻) + 1-prob(call⁻⁻)] / (1 + Rf%) Step 4: C = [prob(C⁺⁺) + 1-prob(C⁻⁻)] / (1 + Rf%) - d = 1 - the down move (or 1/1+upmove if no down move given) - u = 1+ the up move - call+ = The maximum value of the call assuming the positive forecast comes true at expiration

Answer 6

1. Volatility of the return on the underlying stock is known and constant 2. Stock prices are lognormally distributed 3. Continuous Rf% is known and constant

Answer 7

Fixed Rate = DFn / (DF1 + DF2 + DF3... + DFn) * - DF: Discount Factor* * - If annualized then Fixed rate must multiplied by the appropriate factor - semi-annual x2. *

Answer 8

Step one: NPV of next coupon payment PMT/1+r^t Step two: (Vo - NPVcoupon) X 1+r^t' * t = time to next coupon/365* * t' = forward length/365* * Vo = price of bond now* * r = effective rf%*

Answer 9

Step one: Current NPV of next coupon payment PMT/1+r^t\* Step two: V1 - NPVcoupon - (Original forward value) / 1+r^t\*' t\* = Current time to coupon payment / 365 t\*' = Current time to expiration / 365 * Original calculation to determin forward's first price...* * Step one: NPV of next coupon payment PMT/1+r^t* * Step two: (Vo - NPVcoupon) X 1+r^t'* * t = time to next coupon/365* * t' = forward length/365* * Vo = price of bond now* * r = effective rf%*

Answer 10

= ({[(1+150d%)^150/360] / [(1+60d%)^60/360]} - 1) / 360/90 *- curve moves in 30 day increments*

Answer 11

Step one expected Payoff = (FRAo - FRA1)(notional value)(90/360) Step two PV of expected Payoff = payoff/1+120day%^(120/360) *- note: the PV is probably not going to be much less than step 1.*

Answer 12

Floor Payoff = Principle X (Floor rate - Market rate)

Answer 13

The option to enter into an interest rate swap

Answer 14

Allows buyer to enter into a swap as the fixed rate payer/ variable rate reciever

Answer 15

Allows buyer to enter into swap as fixed rate receiver and floating rate payer

Answer 16

1. Collect only interest payments from mortgage pool 2. If rates rise, prepayments drop and interest payments stay high for a longer period 3. Worried about contraction risk

Answer 17

1. Collect only principle payments from mortgage pool 2. Discount security so falling interest rates = quicker return of capital 3. Worried about extention risk

Answer 18

1. SMM = 1 - (1 - CPR)^1/12 2. CPR = 1 - (1 - SMM)^12 3. EMP = SMM X (MBSo - Principle)

Answer 19

PSA benchmark for conditional prepayment rate (CPR) 1. Assumed to be .02% in month one and increases .02% per month until month 30. 2. Remains at 6% after month 30 until 100% PSA

Answer 20

Planned Amortization Class - They have priority on principle payments over other classes - The non PAC classes are "support" tranches with uncertain paybacks

Answer 21

The PSA speeds within which the PAC tranche has protection from the support tranches.

Answer 22

1. Calculate average cap rates from recent sales (Price/NOI) 2. Apply average cap rate to expected NOI

Answer 23

Step 1: Calculate Price per SqFoot for each comparable Step 2: Multiply step 1 by 1+(age of building (depreciation), location, condition, age of transaction (appreciation)) Step 3: Apply average of step 2 to investment

Answer 24

1. Equity (use LTV to calculate) 2. Annual debt service costs (12 X Monthly service costs) 3. Net operating income 4. EDR = (NOI - ADSC) / Equity

Answer 25

PMT = NOI - Debt Service PV = - Equity (use LTV to calculate) FV = Expected Sale price - Loan payoff N = Expected holding period CPT I/Y = Levered IRR

Answer 26

Replacement cost (include builder profit) - Curable deterioration - Incurable deterioration (Vo X (age/total age)) _- Total Obsolescence_ Building value _+ Land value_ Total cost estimate

Answer 27

- Curable: Deferred maintenance that is curable - Incurable: Depreciation of the building.

Answer 28

Appraisal values lag changing transaction values. If prices are rising, they rise first and then appraisals come up. Combat appraisal lag by unsmoothing the index or relying on transaction indexes.

Answer 29

1. HY Corp bonds 2. Structured products (MBS, ABS) 3. Emerging Market bonds 4. Bank loans 5. Special situation and distressed debt

Answer 30

OAS spread with monte carlo simulation

Answer 31

On the BS in other comprehensive income. Versus held for trading where gains/losses are shown on income statement. Or held to maturity where amortized cost and interest income is only thing reported on BS and IS respectively.

Answer 32

1. Industrial - Retail Sales 2. Apartments - Population and job growth 3. Office - job growth

Answer 33

NOI - Non-cash Rents _+ Acquisition Adjustment_ Proforma NOI PFNOI (1+g) = Projectied NOI PrNOI / cap rate = estimated value of assets + other assets _- Liabilities_ NAV

Answer 34

Avoid structural conflicts of interest that may exist in REOC and REIT

Answer 35

1. Determine present value of dividends over forecasting period. 2. Determine terminal value (look at instructions) 3. Discount rate = Cap rate + Expected growth rate

Answer 36

1. It would experience price compression 2. Short term rates are likely falling more than intermediate or long term rates 3. However, prices of callable bonds are capped. - limiting the upside.

Answer 37

1. Durations of different maturities are negative - multiply them by the interest rate increase (+) or decrease (-). 2. Add the changes determined in step 1 to find change in portfolio duration.

Answer 38

1. Calculate discount factors for each semi-annual period ie 1 / 1 + (.0245 x 180/360) = .9879 for the first 6 months or 180 days. 2. Determine fixed rate using annualized interest rates (assume this is a 2-year swap) [(1 - 720discount) / (180discount + 360discount + 540discount + 720discount)] X 2 = fixed rate

Answer 39

1. Doesn't matter how long cap has been in place. 2. (Current R% - Cap R%) X 90/360 X Notional = Payoff

Answer 40

FP = So X [e^(r-d)(t)] 1. e = ln or 2.71818 2. the exponent is the Rf% - Dividend rate times time 3. t = days to expiration / 360

Answer 41

Is the non-monetary benefits of holding an asset that is in short supply. if there is a shortage of a commodity, your storage costs as the holder may be less than the costs of the future's price.

Answer 42

If the interest rate is constant then there will be no difference between futures and forward price.

Answer 43

1. the liquidity risk of the bond with options when compared to similar bonds with options. 2. Different volatility assumptions will affect OAS

Answer 44

= Expected future value / 1+r^n - Don't worry about initial investment since this is post money.

Answer 45

1. called down capital - management fees + performance for each year = end of year NAV 2. Difference between total NAV

Answer 46

They tend to be non-recourse and are only supported by the value of the property and its cash flows. The lender cannot generally go after the company's other assets like you can with a residential MBS.

Answer 47

1. Derive PV Factors (example of a 2-year swap) * a. Z360 = 1/[1+360Rf%(360/360)] = 360PV Factor b. Z720 = 1/[1+720Rf%(720/360)] = 720PV Factor* * 2*. Fixed payment in "pesos" * a. (1-720PV)/(720PV + 360PV) = Fixed payment per peso* 3. Annual fixed payment * Fixed payment per peso X $Notional / Current exchange rate*

Answer 48

- Global credit risk not the credit risk of the counterparties

Answer 49

1. Currency swaps: peaks at the end because notional amounts must be exchanged. 2. Interest rate swaps: peaks at the middle and then declines as swap payments are made and fewer are due.

Answer 50

1. Calculate the Annual Fixed Payment from original rate structure 2. Use the new rate structure to find PV factors (adjust for time passing) 3. Present Value * Annual fixed payment X (new360PVF + new 720PVF) + Notional X new 720PVF = PV *

Answer 51

1. Amortizing ABS collateral is not changed after creation (home loans, auto loans, etc) 2. Non amortizing (revolving) collateral may change during lockup period. Principle payments are used to buy more collateral

Answer 52

Triggers a provision where cash flows are used to pay down principle if the value of the ABS has been impaired. This applies to credit card ABS in the lockup period.

Answer 53

Issuer pays a lower coupon than the coupon on underlying collateral. The excess cash is used to pay for losses on the colateral. **Internal credit enhancement.**

Answer 54

An agreement from a bank to cover losses on an ABS up **to a certain amount**. This can be affected by the credit of the bank and is an **external credit enhancement**. This is an example of the **weak link philosophy.**

Answer 55

1. Internal credit enhancement 2. Principle of collateral is greater than principle of tranches 3. Absorbes losses before junior traunches

Answer 56

1. OAS value per Option cost a. 36 bp OAS for 15bp option cost b. 36 bp OAC for 19bp option cost A is the better choice in terms of OAS value.

Answer 57

For triangular arbitrage or covered interest rate parity or whatever, just convert at the bid or ask for the worst deal.

Answer 58

= Required Return - Growth Rate

Answer 59

Investment(1+r^n) / Expected Vo in future

Answer 60

Vt = St - F(0,T)/(1+r)^T-t * Vt = value now* * St = Spot price now* * F(0,T) = Forward value at expiration* * T-t = Time to expiration at the beginning and t is time to expire now. ie 90/360*

Answer 61

F(0,T) = [Soe^-(δc)T] X [e^(rc)T] δc = Continuously compounded dividend rate rc = Continuously compounded interest rate

Answer 62

= So X (1+rD)^T / (1+rF)^T - **MAKE SURE YOU CHECK FOR 360 vs 365 YEAR**

Answer 63

= So(1+r)T - (div/1+r^t + div/1+r^t... - *The t in the dividends needs to be time to dividend divided by the time to expiration. *

Answer 64

So = C - P + Long bond/(1+r^t)

Answer 65

receives principle and interest after PAC and sequential pay tranches have been paid. Interest owed to accrual tranche will be added to principle.

Answer 66

Each SPT recieves principle payments after the tranches in front of it have been paid off.

Answer 67

Reduction of debt by the time the company is sold.

Answer 68

1. Total value = NAV after distributions (last year) + total distributions 2. TVPiC = TV/Paid in capital in last year (the sum)

Answer 69

Step one=1+gain on equity - 360df - (.XX)(Df+Df+df+df) Step two = Notional x Step one = value

Answer 70

= Max (0), (fR% - Market rate)X(Dfn+Dfn+Dfn...)XNotional ## Footnote **- Remember to use 360 not 720 in your Df calculations** **- the market rate needs to be calculated from the rate structure**

Answer 71

**EXPECTED** Spot price = Futures price + Risk premium

Answer 72

Max of: Sharp of potential asset \> Sharpe port X correlation between port and new

Answer 73

= √(w1² X σ1²) + (w1² X σ1²) + 2(w1,w2r1) X σ1σ2

Answer 74

Max (0, (r-M%) X (DF1 + DF2...)xNP