Question

At Time 0, asset ABC is selling for $85 and XYZ is selling for $41. These assets’ prices at Time 1 are given under two states of the economy Assume “short selling” is allowed. That is, you can borrow units of ABC and/or XYZ from your broker. Using the concept of “Arbitrage and the Law of One Price” discussed in class, show how you can make a riskless profit.

            Figure 1.1

            Time 0                                                                         Time 1

                                                                                    (1) State: GOOD

                                                                                         ABC=$100

                                                                                         XYZ=$ 50

ABC=$85

XYZ=$41

                                                                                    (2) State: BAD

                                                                                         ABC=$ 80

                                                                                         XYZ=$ 40

Answer 1

The ratio of ABC to XYZ stock is:

			Good	Bad
ABC	85		100	80
XYZ	41		50	40
Ratio	2.073171		2	2

Since the price of ABC is more than 2 times the price of XYZ today, it is overpriced hence short sell position is taken on ABC today. and 2 units of XYZ is purchased today

Net inflow of cash today= 85- 41*2= 3

In future, in either case, there will be no net cash flow.

If situation is good,

cash outflow in buying back ABC at 100

and cash inflow of selling XYZ 2 units at 2*50= 100 hence net cash flow= 0

if situation is bad, purchase ABC at 80, sell XYZ for 80 and net cash flow= 0,

effectively 3 made today without any investment and risk.