Stock YMH is trading at $16 per share and is scheduled to pay a $0.32 dividend per share in six months. The effective 6-month interest rate is 2.7% and the YMH forward contract with 6-month maturity is trading at $16.43 (the forward contract expires right after the dividend is paid). If you have $3200 now, but cannot borrow, what is the maximum riskless profit you can generate in six months (i.e., at maturity)?

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BlackTom AI · Accepted Answer

We need to consider a no-borrow arbitrage strategy using the given information and determine the maximum riskless profit in six months.

First, restate the setup clearly: you have $3200 today and cannot borrow. Stock YMH is trading at $16 now. A dividend of $0.32 per share is paid in six months. The 6-month effective interest rate is 2.7%. A 6-month forward contract on YMH is priced at $16.43, with maturity exactly after the dividend is paid (i.e., at the same time as the dividend cash flow).

Next, examine a classic cash-and-carry arbitrage given these facts:
- Buy the stock now with your $3200. At $16 per share, you can purchase 200 shares (200 × 16 = 3200).
- Simultaneously, enter into a short forward contract to sell 200 shares at $16.43 in six months. This locks in selling the stock for 16.43 × 200 = 3286 at maturity.

Consider the cash flows:
- Today: You spend $3200 to buy 200 shares. No borrowing is allowed, so you use all of your cash to acquire stock.
- At six months: The forward matures. You deliver 200 shares and receive 3286 in cash from the forward contract.
- Also at six months: The stock pays a dividend of $0.32 per share. Since you own 200 shares, you receive 200 × 0.32 = 64 in dividend cash at the six-month mark.

Now total cash at six months from this strategy:
- From the forward settlement: 3286
- From the dividend: 64
- Total inflow at six months: 3286 + 64 = 3350

Compare this to the initial outlay you made: $3200 at time 0. The realized profit from this riskless arbitrage is 3350 − 3200 = 150.

Check for consistency with the no-borrow condition: you started with 3200 and did not borrow; you simply allocated your cash to buy stock and used the forward to lock in a sale price. There is no need to borrow funds to finance this position, so this profit is achievable under the given constraint.

Alternative checks (why other naive constructions don’t apply here):
- If you did not hold the stock (i.e., stayed cash and entered a forward only), there would be risk since you don’t own the asset to deliver; the forward would not produce a guaranteed payoff without financing the position. 
- If you attempted to exploit a mispricing by buying or selling the forward alone without the accompanying stock position, you would be exposed to price risk or funding constraints given you cannot borrow.

Conclusion (interpreted from the reasoning above): the maximum riskless profit you can generate in six months with $3200 and no borrowing is $150. The core idea is to go long the stock and short the forward to lock in the price differential plus the dividend cash flow, yielding a certain payoff of 3350 in six months minus your initial 3200.

COEC_V 371 001 002 2025W1 Lecture 8 Practice Quiz

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