The spot price of a stock index is $1000, the risk-free interest rate is 7%, and the continuous dividend yield on the index is 2%. What is the cost of carrying this asset over time?

Question

BlackTom AI · Accepted Answer

To evaluate the question, first identify what the cost of carrying a stock index involves: the cost of financing the position minus the income from dividends. For a continuously paying dividend yield q and a risk-free rate r, the carrying cost is typically r − q.
Option 1: 0% would imply no net carry, which would only occur if r = q. Here r = 7% and q = 2%, so the net carry is not zero.
Option 2: 3% would correspond to a carrying cost of r − q = 3%, which would require q = 4% given r = 7%. Since the actual q is 2%, this option misaligns with the data.
Option 3: 5% matches the calculation r − q = 7% − 2% = 5%. This is the correct net cost of financing minus dividends for the asset.
Option 4: 2% would reflect just the dividend yield rather than the net financing cost, and it ignores the effect of the financing rate. The cost of carry is not equal to q alone when there is a positive interest rate.
In summary, the correct framework shows the net cost of carrying the index equals the risk-free rate minus the continuous dividend yield, yielding 5% for these given values.

BUSFIN 4229 SP2025 (4930) MIDTERM EXAM II- Requires Respondus LockDown Browser

The spot price of a stock index is $1000, the risk-free interest rate is 7%, and the continuous dividend yield on the index is 2%. What is the cost of carrying this asset over time?

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