Chapter 12 & 13: Valuation of investments

Question 1

Clean price

Answer 1

Price excluding accrued interest = quoted market price

Question 2

Dirty price

Answer 2

The sum of the clean price and the accrued interest.
Price at which the bond is actually traded

Question 3

Zero-coupon spot yields

Answer 3

• AKA zero-rates, zero-coupon rates or spot rates
• Continuously compounded rate of return on a zero-coupon bond

Question 4

Bond yields

Answer 4

• 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.

Question 5

Par yields

Answer 5

• 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.

Question 6

Relationship between futures and forwards

Answer 6

Traditional difference: OTC forwards and exchange traded futures - forwards had no cashflow until maturity but for a future there are daily marking-to-market and settlement of margin requirements

If interest rates are equal then value of the cashflows are equal and prices must also be equal.

When interest rates vary unpredictably, unmargined forwards and futures prices aren’t the same because of daily cashflows from settlement and interest earned on cash received (or paid on borrowing)

Price of underlying asset strongly positively correlated with interest rates = long futures contract more attractive than long forward contract = futures prices higher than forward prices

Reverse holds true when asset price is strongly negatively correlated with interest rates

Question 7

Hedge

Answer 7

Defined as a trade to reduce market risk

Hedging reduces the risk by making the outcome more certain

Question 8

Basis

Answer 8

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

Question 9

Basis risk

Answer 9

Risk that the future price and the spot price will not move in line due to volatility in the basis

Question 10

Basis risk may arise if:

Answer 10

• 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

Question 11

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:

Answer 11

Normality of returns

• Leptokurtic
• ‘Fat-tailed’ feature can be modelled using a heteroscedastic model
• Longer time horizon = more normal the return distribution is

Independence of increments in asset prices

• variance of price changes do not increase linearly
• absolute values of returns and squared returns are significantly autocorrelated (thus, significant non-linear dependence)

Constancy of parameters (drift and volatility)

• non-linear dependence of squared returns suggest that the return series could be heteroscedastic
• financial market volatility varies in certain systematic ways
• markets also exhibit volatility “clustering” = non-linear dependence in returns series

Relationships between variables

• TS analysis of equity returns suggest little direct correlation between rates of equity growth for share price indices and rate of inflation.
• Some evidence - equity share returns are negatively correlated with inflation

Question 12

Why are interest rate derivatives more difficult to value than equity derivatives?

Answer 12

• behaviour of individual interest rates is more complicated than that of a stock price
• for 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

Question 13

Interest rate cap

Answer 13

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.

Question 14

Interest rate floors

Answer 14

Provides a payoff when the interest rate on an underlying floating rate note falls below a certain rate – useful if receiving the floating rate

Question 15

Relationship between price of interest rate caps and floors

Answer 15

cap price = floor price + value of swap

• swap is an agreement to receive floating and pay fixed rate RX

Question 16

Evaluating a securitisation

Answer 16

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

Question 17

Modelling of cashflows for a securitisation involves key features such as:

Answer 17

• 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

Question 18

Price of ‘plain vanilla’ CDS in theory

Answer 18

Derived from the yield on an associated bond, from the same issuer and for same maturity, in excess of the risk free rate

Question 19

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:

Answer 19

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

Question 20

Procedure for valuing a swap using forward rate agreements

Answer 20

1. Calculate forward rates for each of the reference rates that will determine the swap cashflows
2. Calculate swap cashflows on the assumption that the reference rates will equal the forward rates
3. Set the swap value equal to the present value of these cashflows