Question

Given the following information, could you find any arbitrage opportunities in ABC stock? If so, what is your arbitrage procedure and profits? (Assume all the interest rates are periodically compounded.)

                                                            Bid                  Ask

6-month ABC futures:                                    $398.10           $399.50                       

ABC stock price:                                $392.65           $393.35

3-month T-bill rate:                            4.00%              5.00%

6-month T-bill rate:                            5.00%              5.00%

Answer 1

Ans:

Arbitarge means 100% guaranted profit to be earned on a position. There are 2 option available to check arbitrage opportunity.

1.

Borrow $393.35 @5% per year and buy stock ABC

Sell 6 month ABC Future at $398.10

Amount to be paid on borrowing after 6 months = $393.35 + $393.35 * 5% * 1/2 = $403.18

So loss will be on this position : $403.18 - $398.10 = ($5.08)

2.

If short selling possible:

Sell ABC stock @ $392.65 and Invest @5% per year

Buy 6 month Future @ $399.50

Amount to be received after 6 mion ths from investments = $392.65 + $392.65 * 5% *1/2 = $402.47

Arbitrage Profit = $402.47 - $399.50 = $2.97

Arbitrage profit available but only if short selling possible.

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