Answer-first summary for fast verification
Answer: a) Cash and carry will realize $1.92 in future profit
### Step 1: Compute the theoretical forward price Because the asset pays income at a rate of **5% every six months**, the one-year income yield is compounded semi-annually: \[ F_0 = \frac{S_0 e^{rT}}{(1.05)^2} \] Substitute the values: \[ F_0 = \frac{60 \cdot e^{0.03}}{1.1025} \approx 56.08 \] ### Step 2: Compare with the market forward price - Theoretical forward price: **56.08** - Market forward price: **58.00** The market forward is **overpriced** relative to theory. ### Step 3: Arbitrage strategy Use a **cash-and-carry** arbitrage: 1. Borrow money and buy the asset today. 2. Short the forward contract at 58.00. 3. Collect the income payments. 4. Deliver the asset at maturity and receive 58.00. ### Step 4: Arbitrage profit \[ \text{Profit} = 58.00 - 56.08 = 1.92 \] ### Answer **A) Cash and carry will realize $1.92 in future profit**
Author: Manit Arora
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Question 716.2. An investment asset has a current price of $60.00 while the risk-free rate is 3.0% per annum with continuous compounding. The asset pays income twice a year and the income is equal to 5.0% of the asset price at the time of income payment; in other words, the asset's yield is 10.0% per annum with semi-annual compounding. If a one-year forward contract on the asset has a price of $58.00, and if we make the typical theoretical cost of carry assumptions (e.g., no trading transaction costs), then which of the following best summarizes the arbitrage opportunity? [note: inspired by Hull's Example 5.3]
A
a) Cash and carry will realize $1.92 in future profit
B
b) Cash and carry will realize $2.44 in future profit
C
c) Reverse cash and carry will realize $3.83 in future profit
D
d) There is no arbitrage opportunity: the forward is not mis-priced
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