Question

consider that we have one stock, ZEE Electronics, that today is worth $50 and one period later will be worth either $75 or $40. We will denote these prices as ZEE = $50, ZEE+ = $75, and ZEE– = $40. Another stock, CYT Technology, is today worth $38 and one period later will be worth $60 or $32. Thus, CYT = $38, CYT+ = $60, and CYT– = $32. Assume that the risk- free borrowing and lending rate is 4%. Also assume no dividends are paid on either stock during the period covered by this example. Find arbitrage return for ZEE and CYT technology, if exist

Answer 1

Price of ZEE Electronics today = $50

Price of ZEE Electronics one year later= $75 or $40

Price of CYT Technology today = $38

Price of CYT Technology one year later= $60 or $32

Risk free borrowing and lending rate = 4%

Arbitrage return:

Step 1: Short Sell say 500 ZEE stocks and receive $25,000 (500*$50)

Step 2: Buy 625 CYT Technology stocks and pay $23,750 (625*$38) (please refer note below).

Step 3: Invest in risk free for the balance of $1,250 ($25,000-$23,750) at a rate of return of 4%

Net Investment out of own funds today = -$25,000+$23,750+$1,250 = 0

After 1 year:

Scenario 1 : If the prices of Zee Stocks and CYT Technology are at the high levels of $75 and $60

Step 4: Sell 625 CYT Technlogy shares and receive $37,500 (625*$60)

Step 5: With those funds, buy 500 Zee stocks by paying $37,500 (500*$75)

Step 6: The risk free investment made at $1,250 would have become $1,300 ($1,250*(1+4%))

Net Receipt : $37,500-$37,500+$1,300 = $1,300

Scenario 2 : If the prices of Zee Stocks and CYT Technology are at the low levels of $40 and $32

Step 4: Sell 625 CYT Technlogy shares and receive $20,000 (625*$32)

Step 5: With those funds, buy 500 Zee stocks by paying $20,000 (500*$40)

Step 6: The risk free investment made at $1,250 would have become $1,300 ($1,250*(1+4%))

Net Receipt : $20,000-$20,000+$1,300 = $1,300

Thus, with the net investment of zero at the beginning, the net receipt or gain at the end of the year is $1,300 regardless of whether the price of Zee Stock and CYT Technology stock hits the upper level or the lower level.

Thus, arbitrage gain on the transaction = $1,300

Return % = 100% (as there is zero initial investment).

Note: The upper level price of Zee is $75 which is 1.25 times of CYT Technology price of $60 ($75/$60). Similarly, the lower level price of Zee is $40 which is 1.25 times of CYT Technology price of $32 ($40/$32). Thus in order to ensure that one year later, there will be no net cash-outflow, 1.25 times of Zee stocks sold needs to be bought in CYT techonology stocks at the beginning of the year. Thus, 1.25*500 = 625 CYT Technology stocks are purchased at the beginning (in step 2).