Ch 11 +12 - Valuation of Investments

Question 1

Hedge

Answer 1

Defined as a trade to reduce market risk

Hedging reduces the risk by making the outcome more certain

Question 2

Basis

Answer 2

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 3

Basis risk:

Answer 3

Is the risk that the basis cannot be predicted in advance with complete certainty

Question 4

Basis risk may arise if:

Answer 4

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 5

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 5

Normality of returns

• Leptokurtic
• Modelled using a heteroscedastic model
• Longer time horizon = more normal the return distribution is

Independence of returns

• variance of returns 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
• volatility varies in certain systematic ways
• markets also exhibit volatility “clustering”

Question 6

When the price of an underlying asset is positively correlated with interest rates, a long futures contract…

Answer 6

More attractive than a similar long forward contract.

• Therefore higher price than forward
• And lower rate

Because:
-If the asset price increases, then the long futures position makes an immediate gain because of the daily margining procedure of marking to market

-Gain will tend to be invested at higher than average interest rates

Question 7

When the price of an underlying asset is negatively correlated with interest rates, a long futures contract…

Answer 7

Less attractive than a similar long forward

• Therefore lower price
• And higher rate

Question 8

The payoff per annum from a vanilla CDS is equal to

Answer 8

Excess return on the bond over the risk-free rate

Question 9

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 9

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

Illiquid and requires funding (package)

• harder to sell than regular gov bonds
• will be negative when funding is expensive

Different supply and demand dynamics in different markets