Reading 51: arbitrage, replication, and carrying costs

Question 1

Derivatives pricing models use the risk-free rate to discount future cash flows because these models:
are based on portfolios with certain payoffs.
assume that derivatives investors are risk-neutral.
assume that risk can be eliminated by diversification.

Answer 1

Derivatives pricing models use the risk-free rate to discount future cash flows because they are based on arbitrage relationships that are theoretically riskless. (LOS 51.a)

Question 2

Arbitrage prevents:
market efficiency.
earning returns higher than the risk-free rate of return.
two assets with identical payoffs from selling at different prices.

Answer 2

Arbitrage forces two assets with the same expected future value to sell for the same current price. (LOS 51.a)

Question 3

The underlying asset of a derivative is most likely to have a convenience yield when the asset:
is difficult to sell short.
pays interest or dividends.
must be stored and insured.

Answer 3

Convenience yield refers to nonmonetary benefits from holding an asset. One example of convenience yield is the advantage of owning an asset that is difficult to sell short when it is perceived to be overvalued. Interest and dividends are monetary benefits. Storage and insurance are carrying costs. (LOS 51.b)

Question 4

An investor can replicate a forward on a stock that pays no dividends by:
selling the underlying short and investing the proceeds at the risk-free rate.
buying the underlying in the spot market and holding it.
borrowing at the risk-free rate to buy the underlying.

Answer 4

Borrowing S0 at Rf to buy the underlying asset at S0 has a zero cost and pays the spot price of the underlying asset minus the loan repayment of at time = T of S0(1 + Rf)T, which is the same payoff as a long forward at F0 = S0(1 + Rf)T, the no-arbitrage forward price. (LOS 51.a)

Question 5

The forward price of a commodity will most likely be equal to the current spot price if the:
convenience yield equals the storage costs as a percentage.
convenience yield is equal to the risk-free rate plus storage costs as a percentage.
risk-free rate equals the storage costs as a percentage minus the convenience yield.

Answer 5

When the opportunity cost of funds (Rf) and storage costs just offset the benefits of holding the commodity, the no-arbitrage forward price is equal to the current spot price of the underlying commodity. (LOS 51.b)