NO.PZ2024020101000012
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
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 B.incorrect, because the profit will be higher if the share price decreases C.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
在convertible arbitrage中，我们都是long convertible bond，同时short stock。此题中没有告诉我们面值是多少，但是根据题目我们可以知道conversion ratio是50，价格是面值的1.2倍，1.2/50=0.024，所以我们推断的面值应该是1000，这样可转债转成股票的价格就是0.024*1000=24，这个是因为可转债转股的价格和股票的差异不可能非常大，long 可转债就相当于我们能够以24块的价格买股票，同时以29的价格short stock，这样就会一直保持一个5块的价差。
假如股价跌到10元，那short stock的收益就是19，long CB带来的不对称的损失会小于15诶，为什么还要选A?
