Arbitrage

Question 1

what is arbitrage strategy

Answer 1

the act of buying a security in one market and simultaenously selling it in another to make a profit
- profit off of price inefficiencies

without bearing any price risk = riskless trade
- can make money without taking on more risk

Question 2

what is arbitrage principle equilibrium

Answer 2

in equilibrium - prices reflect absence of arbitrage opportunities
- cant make a profit
- because of law of one price = eliminates arbitrage opportunities

Question 3

how is it possible to make a profit in the exchange market?

• what would equilibrium be?

Answer 3

• making use of price differences
• take a loan of £1 , buy $1.50, use $1.50 to buy #1.80, sell #1.80 for £1.20 - made 20p profit

equilibrium = when no arbitrage opportunities - cant make a profit without risk
- happens because you keep doing it above and eventually ER will change to stop

Question 4

example of arbitrage in bond market

when is market equilibrium

Answer 4

• rate or return on bond is higher than interest rate on loan
  = borrow at rate r and buy bonds = higher return = make profit
• rate of return on bond is lower than interest rate on loan
  = short sell bonds and lend at rate r

equilibrium –> rate of return on bond = r
r = v-p / p
p = 1/1+r *v

Question 5

notations
xi
x
v(x,k)

Answer 5

xi = shares of asset i
x = portfolio
v(x,k) = payoff of portfolio x in state k

Question 6

what are the 2 conditions that arbitrage portfolio must satisfy

Answer 6

1. zero initial outlay
   * the value of the arbitrage portfolio = value of original portfolio
   * if you want to buy you have to sell
   * change in the value of your portfolio after trade = 0
2. risk free
   * the change from original portfolio to arbitrage is riskless
   - you never lose money
   - the payoff is never less than 0

Question 7

when is there an arbitrage opportunity?

Answer 7

• prices that mean the arbitrage can exist = profits to be made
• portfolio where you can rearrange what you have and there is atleast one state your payoff is positive

Question 8

when is there no arbitrage opportunities?

Answer 8

• cant make money in each state by rearranging portfolio
• some states payoff is positive - some states its negative

Question 9

market equilibrium when

Answer 9

demand to hold assets is no greater than the supply available

• any trade involves risk

Question 10

arbitrage example:

Answer 10

• A yields higher than B but A is more expensive