NO.PZ2023010407000010
问题如下：
Johnson research a convertible arbitrage strategy and
analyzes transactions involving ABC company stocks and convertible bonds.
And collect selected data for ABC company, as shown in Exhibit 1
Exhibit 1
Based on comparisons with industry ratios, Johnson believes that the relative value of ABC's stock is overvalued, while convertible bonds are undervalued. And believe the potential profit outcomes of a long position in the convertible bond combined with a short stock position,assuming that the stock price changes very little, ignoring dividends and borrowing costs. He came to the following conclusions:
"Regardless of whether ABC's share price is falling or rising, the profit of a convertible arbitrage transaction is the same."
Johnson’s conclusion about the profitability of the ABC convertible arbitrage trade is:
选项：
A.Correct
incorrect, because the profit will be higher if the share price decreases
incorrect, because if the stock price rises, the profit will be higher
解释：
A is correct. The
classic convertible bond arbitrage strategy is to buy the relatively
undervalued convertible bond and take a short position in the relatively
overvalued underlying stock. If the convertible bond’s current price is near
the conversion value, then the combination of a long convertible and short
equity delta exposure will create a situation where for small changes in the
share price and ignoring dividends and borrowing costs, the profit/loss will be
the same. The current conversion price of the ABC convertible bond is € 1000×(120/100)/50=€24, and the current AVC share
price is €29. Thus, by purchasing the convertible bond, selling short the
shares, exercising the conversion option, and selling the shares at the current
market price, a profit of €5 can be locked in regardless of changes in the
share price. The following table demonstrates this result by showing the same
trade profit of €5 for three different stock prices:
where
Long stock via convertible bond profit = New share price – Current conversion price
Short stock profit = Current share price – New share price
Total profit = Long stock via convertible bond profit + Short stock profit
Thus, regardless of the share price, the total profit on the convertible arbitrage trade is €5
B is incorrect because if the convertible bond’s current price is near the conversion value, then the combination of a long convertible and short equity delta exposure will create a situation where the profit/loss will be the same (not higher if the share price decreases).
C is incorrect because if the convertible bond’s current price is near the conversion value, then the combination of a long convertible and short equity delta exposure will create a situation where for small changes in equity price, the profit/loss will be the same (not higher if the share price increases).
如果股价低于了$24，这个时候可转债不会转股，而 short stock的头寸会超过$5，所以在股价下跌的时候，arbitrage的profit会更高
麻烦老师看一下，为什么这种理解有问题呢？
