Risk Management

Question 1

•••••••Risk Mgt•••••••

Annualized VaR

Answer 1

Annualized VaR = VaR_n-day × √(250/n)

Question 2

•••••••Risk Mgt•••••••

Analytical VaR

Answer 2

Analytical VaR = [ER_{p (daily return)} – (z_{(1.65 @ 5% sign.)}) * (σ_daily)] * MV_{p (total portfolio amount)}

Question 3

•••••••Risk Mgt•••••••

Risk-adjusted return on invested capital

Return over maximum drawdown

Sortino ratio

Answer 3

Risk-adjusted return on invested capital: RAROC =Er / Capital @ risk

Return over maximum drawdown: RoMAD = R_p / maximum drawdown

Sortino ratio: = (R_p – M_inimumA_cceptableR_eturn) / downside deviation

Question 4

•••••••Risk Mgt•••••••

of Futures for Equity

Answer 4

of contracts = [(β_Target – β_current) / β_futures] * [V_stocks / V_futures]

REMEMBER:

If a fund needs to change % allocation (e.g. 10% increase), β_Target is the current, β_Target is 0, V_stocks is the $$$ change

Question 5

•••••••Risk Mgt•••••••

of futures for debt

Answer 5

of contracts = [(MD_Target – MD_Current) / MD_Futures] * (V_bonds / V_futures) * (yield beta)

REMEMBER:

If a fund needs to change % allocation (e.g. 10% increase), MD_Target is the current Duration, MD_Current is equal to cash Duration (close to 0), V_bonds is the $$$ change

Question 6

•••••••Risk Mgt•••••••

Ex post beta

Answer 6

Ex post beta = portfolio return / index return

Question 7

•••••••Risk Mgt•••••••

Covered Call

Answer 7

Covered Call = Long Stock + Short Call

(Limits upside but retains most downside)

Question 8

•••••••Risk Mgt•••••••

Protective Put (Portfolio Insurance)

Answer 8

Protective Put (Portfolio Insurance) = Long Stock + Long Put (Limits downside risk and retains upside)

Question 9

•••••••Risk Mgt•••••••

Bull Spread (used for profit)

Answer 9

Bull Spread (used for profit)

Call = Long Call ITM + Short Call OTM

Put = Long Put OTM + Short Put ITM (rarely used)

Question 10

•••••••Risk Mgt•••••••

Bear Spread

Answer 10

Bear Spread

Call = Long Call OTM + Short Call ITM

Put = Long Put ITM + Short Put OTM

Question 11

•••••••Risk Mgt•••••••

Butterfly Spread

Answer 11

Butterfly Spread

L_Call = LC ITM + 2 SC ATM + LC OTM (high vol)

L_Put = LP ITM + 2 SP ATM + LP OTM (high vol)

S_Call = SC ITM + 2 LC ATM + SC OTM (inverse, low vol)

Question 12

•••••••Risk Mgt•••••••

Straddle

Strangle

Short Straddle

Answer 12

Straddle = LC + LP (high vol)

Strangle = LC OTM + LP OTM (cheaper high vol)

Short Straddle = SC + SP (low vol)

Question 13

•••••••Risk Mgt•••••••

Collar

Answer 13

Collar = LP + L Stock + SC (used as hedge)

Question 14

•••••••Risk Mgt•••••••

Box Spread

Answer 14

Box Spread = LC + SC + LP + SP or bull + bear spread

Question 15

•••••••Risk Mgt•••••••

SWAP - Floating / Fixed leg rate duration

Answer 15

Floating leg rate duration ≈ ½ the payment frequency period

Fixed rate leg duration (zero coupon) = term to maturity.

Fixed rate leg duration (with coupon) ≈ ¾ of swap’s maturity

§ D_{pay floating} = D_fixed − D_floating = +D | ↑ mkt value risk / ↓ cash flow risk

§ D_{pay fixed} = D_floating − D_fixed = –D | ↓ mkt value risk / ↑ cash flow risk

Question 16

•••••••Risk Mgt•••••••

of Swaps needed for Bond

Answer 16

N_{otional Principal} = (V_{Bond portfolio}) * [(MD_Target − MD_Current) / MD_swap]

Question 17

•••••••Risk Mgt•••••••

Swaption (pay or receive floating/fixed?)

Answer 17

Receiver swaption = the right to enter a pay-floating (receive-fixed) in a swap

Payer swaption = the right to enter the swap in a pay-fixed position