Question

There is a futures contract calling for delivery of one share of XYZ six months from today. You observe the following data today:

• XYZ stock price is $125.00.

• Dividend yield over the 6-month period of 4.00%

• You can borrow and invest at the same riskless interest rate of 3.00%, over the 6-month period. Investors can short-sell shares of XYZ at a zero cost.

a) Based on the data above, calculate the cash and carry value.

b) Suppose that XYZ futures price is $126.00.
Based on the data above, is there an arbitrage opportunity for an investor with zero initial investment?
If yes, design the arbitrage and calculate the profits.

c) What will happen to spot and futures prices as market participants pursue the arbitrage?

d) Suppose now, that XYZ futures price is $124.00 and the riskless interest rate over the period is 5.00%. Is there an arbitrage opportunity? If yes, design the arbitrage and calculate the profits.

Answer 1

Note we are not specifically given futures price for part (a) of the question and it shall be solved with an assumption of FP= S0*(1+r)t = 125*(1+0.03)^0.5 = $126.86. The interest rate for 6 months would be 1.5% and dividend yield would be 2%.

a. )Cash and carry value assuming we borrow $125 at the risk-free rate of 3%p.a. for 6 months and FP = S0*(1+r)t will give us positive earning only from dividend yield i.e., 125*(0.04)^0.5 = $2.50

c.) As more and more market participants exploit the arbitrage principle, the profits will vanish away and FP = So*(1+r)t leading to zero profits.

Part b and d are attached in screenshot