Consider a non-dividend-paying stock with a current price of $2.96. The effective 1-year spot rate is 3%.

Today, you borrow at 3% enough to purchase 100 shares of the stock, and short 75 one-year forward contracts on the stock, each for 1 share, at the no-arbitrage forward price.

One year from now, the stock price is $3.54.

What is the total cash flow at maturity from this portfolio (including all positions)?

Enter your final answer rounded to two decimal places. For example, enter 1.23 if your answer is $1.234, and enter -1.23 if your answer is -$1.234.

Question

Consider a non-dividend-paying stock with a current price of $2.96. The effective 1-year spot rate is 3%.

Today, you borrow at 3% enough to purchase 100 shares of the stock, and short 75 one-year forward contracts on the stock, each for 1 share, at the no-arbitrage forward price.

One year from now, the stock price is $3.54.

What is the total cash flow at maturity from this portfolio (including all positions)?

Enter your final answer rounded to two decimal places. For example, enter 1.23 if your answer is $1.234, and enter -1.23 if your answer is -$1.234.

BlackTom AI · Accepted Answer

We start by clearly restating the setup and the cash flows involved at maturity.
- Initial actions: Buy 100 shares at 2.96 each, funded by borrowing. Short 75 one-year forward contracts on the stock at the no-arbitrage forward price.
- Given data: S0 = 2.96, one-year spot rate r = 3%, forward price F = S0(1 + r) = 2.96 × 1.03 = 3.0488 per share.
- Maturity stock price: S1 = 3.54.
- At maturity, you will have: (a) the forward settlements, (b) the stock you still hold after delivering 75 shares via the forwards, and (c) a repayment obligation for the initial loan.

Step 1: Determine the loan repayment amount at maturity.
- You borrowed enough to buy 100 shares at 2.96, a total of 296.
- With a 3% effective annual rate, the loan grows to 296 × (1 + 0.03) = 296 × 1.03 = 304.88 to be repaid at t = 1.

Step 2: Compute the cash received from the forward contracts at maturity.
- You are short 75 forwards at F0,1 = 3.0488 per share, so at maturity you deliver 75 shares and receive 75 × 3.0488 = 228.66 in cash.
- Because you hold 100 shares, delivering 75 leaves you with 25 shares remaining after the forwards settle. You do not owe any additional cash for the delivery itself beyond the shares you place into the forward contracts.

Step 3: Evaluate the value of the remaining stock at maturity if you liquidate.
- The 25 remaining shares are worth 25 × 3.54 = 88.50 at t = 1.
- If we are counting all cash flows at maturity, including liquidating remaining holdings, this 88.50 is a cash inflow from selling the remaining shares.

Step 4: Net cash flow calculation at maturity.
- Cash inflows: 228.66 (from the forward settlements) + 88.50 (from selling the remaining 25 shares) = 317.16.
- Cash outflows: 304.88 (repayment of the loan).
- Net cash flow = 317.16 − 304.88 = 12.28.

Alternative framing if you do not liquidate the remaining stock: you would still have 25 shares valued at 3.54 each (88.50 in market value) but only realize cash if you sell them. In that case, the explicit cash flows would be 228.66 (forwards) minus 304.88 (loan repay) plus the value of the 25 shares if liquidated (88.50), yielding the same net cash flow of 12.28 upon liquidation. If you strictly count only cash that changes hands at t = 1 without liquidating the remaining stock, you would report the forward cash inflow of 228.66 and the loan repayment of 304.88 as the primary cash movements, with the stock value treated as an asset on hand rather than a cash flow.

Summarizing the arithmetic clearly:
- F × 75 = 3.0488 × 75 = 228.66
- Value of 25 remaining shares = 25 × 3.54 = 88.50
- Total inflows if liquidating remaining stock = 228.66 + 88.50 = 317.16
- Outflows = 304.88
- Net cash flow (assuming liquidation of remaining stock) = 317.16 − 304.88 = 12.28

Thus, the computed total cash flow at maturity from this portfolio (including all positions, with liquidation of the remaining stock) is 12.28 when rounded to two decimals.

COEC_V 371 001 002 2025W1 2025W1 COEC 371 Final Exam Dec 16 - Requires Respondus LockDown Browser

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