Suppose you run a convertibles arbitrage hedge fund. You’ve noticed a potential trading opportunity related to the different securities issued by ENM Corporation. In particular, you think there may be an opportunity associated with ENM’s convertible debt. The market conditions you’re facing are as follows:
-Interest rates are stable (i.e., you can ignore interest rate risk), and the yield curve is flat at 11.11%. In particular, the current market prices of riskless one and two years zeros ($100 face-value) are: B1 = $90 and B2 = $81
-The stock of ENM is currently trading at $70, and will either go up or down each of the next two years according to the following tree:
.............................120.33
..............91.78
70........................ 83.62
............63.78
...........................58.11
-You can trade (buy or write) puts and calls on ENM, at any maturity and with any strike. All the options are fairly priced by the market.
-As mentioned previously, you believe there might be a profitable trading opportunity associated with ENM’s convertible debt. ENM’s convertible bond is a risk-free zero maturing in two years, with a face value of $100. At the end of the first year, and only at the end of the first year, the bond may be returned to the company for one share of ENM common stock. This convertible bond is currently trading at $81.39
(a) What is the convertible bond’s fair price? Is it mispriced?
(b) Is there a true arbitrage opportunity here? That is, can you devise a profitable strategy that can’t lose money? What is the strategy? What are the cash flows to this strategy?
(c) Suppose you can lever your position 20 times. That is, suppose for every dollar you get shorting you:
Can use the proceeds to buy assets, which your broker will hold as collateral,
And you must leave an additional $:05 cash in a margin account, also with your broker.
This margin account earns interest at the rate rf – 2% = 9.11%, i.e., you’re “taking a haircut,” “rebating” 2% of the interest earned on this account to the broker
What is the return and standard deviation to your arbitrage strategy with this leverage?