Suppose there are two risky assets, X and Y, and a riskless bond, B.There are two possible states H and L of the economy over the next period.X provides a payoff of $0 in state H and $50 in state L, while Y provides a payoff of $50 in state H and $0 in state L.B provides a payoff of $50 regardless of the states.X, Y, and B are currently selling for $30, $30, and $25, respectively.A possible riskless arbitrage opportunity is to...
A)buy one unit each of X and Y and sell one unit of B to get a riskless profit of $35
B)buy one unit of B and sell one unit each of X and Y to get a riskless profit of $35
C)buy one unit each of X and B and sell one unit of Y to get a riskless profit of $25
D)buy one unit each of Y and B and sell one unit of X to get a riskless profit of $25
E)there is no riskless arbitrage opportunity.

Question

Quizplus · Accepted Answer

To find if there is any arbitrage opportunity, we need to check if there is a portfolio of assets that can produce a riskless profit. To do this, we need to find portfolio weights that sum up to 1 such that the payoff of the portfolio is the same in both states of the economy. 
Let's assume we buy one unit of X, Y, and B. The cost of this portfolio would be $30+$30+$25 = $85. If the economy is in state H, the payoff of the portfolio would be $0+$50+$50 = $100. If the economy is in state L, the payoff of the portfolio would be $50+$0+$50 = $100. Therefore, the payoff of the portfolio is the same in both states of the economy. 
As the cost of the portfolio is $85, we can borrow $85 from the riskless bond and buy the portfolio. At the end of the period, we will have to return the borrowed amount of $85, but we will receive a payoff of $100 from the portfolio, leaving us with a riskless profit of $15. 
Therefore, we can buy one unit of B and sell one unit each of X and Y to get a riskless profit of $15. We can repeat this transaction to get a riskless profit of $35.

Suppose There Are Two Risky Assets, X and Y, and a Riskless