NO.PZ201909280100001005
问题如下：
Anderson’s
conclusion about the profitability of the AVC convertible arbitrage trade is:
选项：
A.
correct
B.
incorrect, because the profit will be higher if the
share price decreases
C.
incorrect, because the profit will be higher if the
share price increases
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
AVC convertible bond is €1,000 × (115/100)/50 = €23, and the current
AVC share price is €28. 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).
经典的可转债套利策略是买入相对低估的可转债，做空相对高估的标的股票。如果可转换债券的现价接近转换价值，那么做多可转换股票和做空股票 delta 敞口的组合将造成这样一种情况，即股价的小幅变化而忽略股息和借贷成本，损益将是相同的。 AVC可转债当前转股价格为1000欧元×(115/100)/50=23欧元，当前AVC股价为28欧元。因此，通过购买可转换债券、卖空股票、行使转换选择权并以当前市场价格出售股票，无论股价如何变化，都可以锁定 5 欧元的利润。下表通过显示三种不同股票价格的相同交易利润 5 欧元来证明这一结果：
通过可转换债券获利的多头股 = 新股价格 - 当前转换价格
做空股票利润 = 当前股价 - 新股价
总利润 = 多头股票通过可转换债券利润 + 空头股票利润
因此，无论股价如何，可转换套利交易的总利润为 5 欧元
PS：1000是面值，但是题目中并没有提供，这个类似基础班上的例题：Convertible Arbitrage Strategy。由于转换率是50，也就是可以转换成50股，当成价格是28，也就是转换后的价值是50×28=1400.因为面值都是一个整数，而且价值差距不会太，不可能面值1万，或者100，那一边得亏死。所以先猜出来是1000元的面值。
例如跌到21，short stock就有7的profit，这也算lock in了5的profit吗？因为7>5?
