Chapter 12 & 13: Valuation of investments Flashcards
Clean price
Price excluding accrued interest = quoted market price
Dirty price
The sum of the clean price and the accrued interest.
Price at which the bond is actually traded
Zero-coupon spot yields
- AKA zero-rates, zero-coupon rates or spot rates
- Continuously compounded rate of return on a zero-coupon bond
Bond yields
- AKA gross redemption yield
- Single interest rate such that the discounted present value of the payments on a bond is equal to the market value of the bond.
Par yields
- Coupon rate that would be required to make the theoretical value of the bond equal to its nominal value under the prevailing pattern of zero-coupon interest rates.
Relationship between futures and forwards (formula)
Called the convexity adjustment
Relationship between quoted price for a futures contract and the contract price
Forward interest rate
The interest rate implied by current zero coupon rates for a specified future time period. Forward rates can be calculated from zero rates using:
Instantaneous forward rate
Forward rate agreement (FRA)
A forward contract where the parties agree that a specified interest rate will apply to a specified principal amount during a specified future time period
Arbitrage price of a forward
Hedge
Defined as a trade to reduce market risk
Hedging reduces the risk by making the outcome more certain
Basis
Difference between the spot price of the asset to be hedged and the futures price of the contract used to hedge
Provides a measure of the discrepancy between the elements involved in a hedge
If there is no basis then the hedge is perfect and all market risk is eliminated
Basis risk
Risk that the future price and the spot price will not move in line due to volatility in the basis
Basis risk may arise if:
- The asset whose price is to be hedged is not exactly the same as the asset underlying the futures contract = cross hedging
- The hedger is uncertain as to the exact date when the asset will be brought or sold
- The hedge requires the futures contract to be closed out well before its expiration date
Optimal hedge ratio
Empirical studies of asset prices and interest rates have identified departures in price and returns data from the assumptions commonly used in asset models.
These assumptions include:
- Normality of increments in (log) asset prices
- Independence of increments in asset prices
- Constancy of parameters (drift and volatility)
Why are interest rate derivatives more difficult to value than equity derivatives?
- behaviour of individual interest rates is more complicated than that of a stock price
- for the valuation of many products , it’s necessary to develop a model describing the behaviour of the entire yield curve.
- volatilities of different points on the yield curve are different
- interest rates are used for discounting as well as for determining payoffs from the derivative
Converting yield volatilities to price volatilities
Interest rate cap
Over-the-counter interest rate option, designed to provide insurance against the rate of interest on an underlying floating rate note rising above a certain level, the cap rate.
Interest rate floors
Provides a payoff when the interest rate on an underlying floating rate note falls below a certain rate – useful if receiving the floating rate
Relationship between price of interest rate caps and floors
cap price = floor price + value of swap
- swap is an agreement to receive floating and pay fixed rate RX
Evaluating a securitisation
Concentrates on the predictability and sustainability of adequate cashflow & considers factors such as:
- Lease terms
- Rental prospects
More generally:
- Degree of potential competitors
- Barriers to competitive entry
Agreements may include covenants.
Analysis of credit risk is key feature when evaluating a securitisation
Modelling of cashflows for a securitisation involves key features such as:
- statistics (early repayment experience)
- probability (default/recovery and timing)
- treasury management (payments in / payments out)
- structuring and security issuance
Difficult to determine suitable discount rate for each tranche of security
Price of ‘plain vanilla’ CDS in theory
Derived from the yield on an associated bond, from the same issuer and for same maturity, in excess of the risk free rate
The “basis” (CDS price less the yield in excess of risk-free) is not zero and can in fact be quite volatile. The factors that affect this are:
Not risk-free (the package of CDS+bond)
- Counterparty credit risk on CDS
- The no-default value of the bond may be higher or lower than face value due to changes in interest rates
- Documentation differences
Package of a bond and a CDS is lliquid and requires funding
- basis is negative when funding is expensive
- harder to sell than regular gov bonds
Different supply and demand dynamics in different markets
Procedure for valuing a swap using forward rate agreements
- Calculate forward rates for each of the reference rates that will determine the swap cashflows
- Calculate swap cashflows on the assumption that the reference rates will equal the forward rates
- Set the swap value equal to the present value of these cashflows
