Fixed Income Securities, FIS Flashcards
Describe four common types of government debt
- Treasury Bills - short term debt, maturity up to 1 year
- Treasury Notes - medium term debt, maturity up to 10 years (semi annual coupons)
- Treasury Bonds - long term debt, maturity up to 30 years
- TIPS - bonds whose principal is indexed to inflation
Define a repurchase agreement
A contract where you sell a security to a pary with an agreement to buy it back at a future date
- Equivalent to a collaterized loan
- Repo rate - interest behind the loan
- Reverse repo - opposite of repo
State the formula for the repo interest
(n / 360) * Repo Rate * (P_t - Haircut)
- haircut is deducted from the bond market price when selling the instrument
State the formula for the return on capital of a repo trade
(P_T - (P_t - Haircut) - Repo Interest) / (Haircut)
- bond sells for P_T
- pay borrowed money with interest
- initial investment is the haircut
Define the discount factor
The time value of $1 between times t and T
Compare bootstrapping with the Nelson-Siegel model
Bootstrapping:
- yield curve can have dips at certain tenors due to liquidity issues, staleness, or bad data
- difficult to correct bootstrapping issues
Nelson-Siegel:
- correct discontinuities using a parametric form
State the formula for pricing a semi-annual floating rate bond with a spread s
Price = Z(t, T_i+1)N(1 + r_2(T_i)/2)
State the price formula for an (leveraged) inverse floater
Price = NPrice(ZCB) + Price(ZCB at fixed rate) - NPrice(floating rate bond)
- Coupon = Fixed Rate - N*Floating Rate
State problems and potential solutions for bootstrapping
Number of Bonds > Number of Maturities
- use linear regression (C^TC)C^T*P(0)
Number of Bonds < Number of Maturities
- use Nelson-Siegel or splines
State one issue that is hard to correct with bootstrapping
The yield curve can have a dip at certain tenors
- liquidity issue
- staleness
- bad data
Key Point: hard to correct for these issues with bootstrapping
Define duration
Sensitivity of the price to a small parallel shift in the IR curve: (-1/P)(dP/dr)
Explain how the duration depends on the coupon rate and the interest rate
Higher coupon rate = lower duration
- higher coupon rate = cash flows larger in the near future
- cash flows arriving sooner are less sensitive to the IR
Higher interest rate = lower duration
- higher IR implies ST cash flows have a higher weight in the value of the bond
Define dollar duration
DD = -dP/dr = P*dP
Define VaR
The maximum loss that the portfolio can suffer over a time horizon T with an a% probability
Describe two methods of interest rate risk management
Cash flow matching - attempt to replicate cash flows exactly
Immunization - replicate present value and duration of the liabilities
- allows for selection of bonds with favorable liquidity and transaction costs
Define convexity
Percentage change in the price of the security due to the curvature of the price w.r.t the IR: (1/P)(d^2P/dr^2)
Use duration and convexity to approximate change in portfolio value from interest rates
dP = -DdrP + 1/2Cdr^2*P
State the number of zero coupon bonds to purchase for duration-convexity hedging
K_1 = (-P/P_1)(D*C_2 - C*D_2 / D_1*C_2 - C_1*D_2) K_2 = (-P/P_2)(D*C_1 - C*D_1 / D_2*C_1 - C_2*D_1)
Describe factor models
Factor model assumes the IR is driven by a set of factors (slope, level, curvature, etc)
State relationships between the spot rate curve and the forward rate curve
Spot curve increasing, forward curve above spot curve
Spot curve decreasing, forward curve below spot curve
Spot curve flat, forward curve = spot curve
Describe a Forward Rate Agreement
One counterparty pays the forward rate, while the other counterparty pays the future floating rate
- Payment at Maturity: NDelta[f(0, T_1, T_2) - r(T_1, T_2)]
State the formula for calculating the value of an FRA
NZ(t, T_2)Delta*[f(0, T_1, T_2) - f(t, T_1, T_2)]
Define a forward contract
One counter party agrees to purchase and the other counterparty agrees to sell a given security in the future at the forward price
Compare the curve bootstrapped from swaps (LIBOR) vs Treasury Bonds
LIBOR curve is slightly higher than the Treasury curve
- spread is a result of credit risk and lower liquidity
State advantages of hedging with futures
Higher liquidity
Lower credit risk
- clearinghouse guarantees futures contract payments
- use of margin accounts
State disadvantages of hedging with futures
Higher basis risk
- characteristics of the underlying instrument do not match the characteristics of the instrument to be hedged
Tailing of the hedge
- need to account for time value of money from the cash flows
Describe a swaption
Payer - call on the swap rate, right to enter a swap to pay the strike rate K
Receiver - put on the swap rate, right to enter a swap to receive the strike rate K
What are three sources of interest rate data for bootstrapping a LIBOR curve
LIBOR - less than 3 months
Eurodollar - up to 3 years
Swaps - over 3 years
Compare options with forwards/futures
Options have no downside but have an initial upfront cost
- other contracts can also result in cash outflows for the firm
Describe different types of option strategies that can be used as hedges
Deductibles - purchasing OTM options to only hedge against an extreme adverse event
Collars - buy call option and sell put option to earn premium to offset the cost of the call
Yield enhancing strategies - make the coupon of a bond sold at par higher by augmenting the bond with a short option position
