Question

Lorenzo notes that the market includes securities A and B whose prices in one-year depend only upon whether the market is “up,” “steady,” or “neutral.” A, which has a current share price of $25, will sell for $32,$25, or $22 respectively, while B, with a current share price of $14, will sell for $16, $14, or $12, respectively. Explaining how Lorenzo has an arbitrage opportunity, assuming there are no costs associated with trading A and B.

Answer 1

In order to arbitrage from the above situation Lorenzo should buy 1 Share of security A and should short sell 2 share of security B at current market price.

So total investment in the above trade= Buy price of A – Sell price of B

= $ 25 – 2* $ 14

= (-) $ 3

(-) Indicates inflow of $3 from the above trades.

After one year he has to sell the security A and buy back 2 share of security B, since there are three possibilities. Let us consider each one.

If market is UP, Security A will trade $ 32 and B will trade $16

So Inflow or outflow from the trade= Sell price of A – Buy price of B

= $ 32 -2 * $ 16

= $ 0

Since no outflow so there will be gain of $ 3 that was earned when taking the trade.

If market is STEADY, Security A will trade $ 25 and B will trade $14

So Inflow or outflow from the trade= Sell price of A – Buy price of B

= $ 25 -2 * $ 14

= (-) $ 3

Since outflow is $ 3, so there will be no gain.

If market is NEUTRAL, Security A will trade $ 22 and B will trade $12

So Inflow or outflow from the trade= Sell price of A – Buy price of B

= $ 22 -2*$12

= (-) $ 2

Since outflow is $ 2, there will be gain of $1 ($3-$2).