Lecture 1 Flashcards
What are the rows (columns) representing within the payoff matrix (Hint: Either States of the world or securities)
Rows - Securities
Column - State of the world
Define the “Asset Span”
The Asset Span is the number (a better word is dimension) of different payoff profiles one can construct via trade in the available assets
The Asset Span is the set of different portfolio payoffs that we can achieve in the future via trade in the existing assets today
When are Markets referred to as “Complete Markets”
Markets are said to be complete iff any newly issued payoff profile can be constructed through buy and sell orders of the existing assets
When do we have “Incomplete Markets”
Not every newly introduced payoff can be replicated by a portfolio of the existing assets
This means that there are less than S securities with independent payoff profile
Either there are less than S securities in the economy (Dimension of the market > S) or one can construct a portfolio of the existing securities to replicate the payoff profile of some other existing securities
What is equilibrium pricing
Analytical solution of a GE maximization problem with specific reference to preferences, endowments and production functions
Tells us how prices of traded securities are formed and how we should price newly issued one
What is arbitrage pricing
No reference to preferences, endowments or production functions. Only the assumption that agents prefer more to less
Tells us how to price using the concept of the replicating portfolio
What criteria have to be meet for an arbitrage opportunity
It exists if a payoff is possible in at least one future states of nature, with no initial investment and no possible losses.
You exploit an arbitrage opportunity when you make a certain profit starting with zero initial capital
How can you exploit an arbitrage opportunity
One can exploit an arbitrage opportunity by forming a portfolio of existing traded assets that has a positive payoff tomorrow but costs nothing or even has negative price (in essence the trader receives money today), i.e. hX 0 and ph0 0 with one strict inequality, where p = (p1, …, pJ)
What is “strong arbitrage”
A strong arbitrage is when one can form a portfolio that has a positive or zero payment tomorrow at every state but gives a positive payment today, i.e. hX >= 0 and ph0 < 0
Can arbitrage opportunities exist long term?
Arbitrage opportunities cannot consistently exist, since agents would take advantage of them and thus move prices until arbitrage opportunities are vanished
What are/is the assumption for an arbitrage opportunity to exist
It only assumes that agents in the economy prefer more than less
What is the Law of one price
Every security or portfolio with the same payoff profile should be worth the same today. If this was not the case and two securities with the same payoffs but different prices where traded today, then one would sell the expensive and buy the cheap, since he prefer “more” than “less”
When is asset referred to as “redundant”
We call an asset redundant when we can form a portfolio of existing assets to replicate its payoff in every state of the world
What is next to positive prices necessary so that no arbitrage opportunity exists
They have to satisfy the law of one price
What is the relationship between the current exchange rate, the forward rate, the domestic interest rate and the foreign interest rate (Covered Interest Rate Parity)
F_{0,T} = S_0 * \frac{1+r_{0,T}^*}{1+r_{0,T}}
The current exchange rate is defined as S_0
The forward exchange at period T is defined as F_{0,T}
The domestic interest rate is r_{0,T}
The foreign interest rate is r_{0,T}^*
