Hedge Fund Strategies：练习题

Which of the following hedge fund strategies primarily seeks to exploit mispricings between a convertible bond and its underlying common stock, typically by buying the convertible bond and shorting the underlying stock?

A convertible bond is currently trading at its conversion value (parity) with an implied delta of \(\Delta = 0.65\). The bond has a par value of \$1,000 and is convertible into \(25\) shares of common stock. If a hedge fund manager establishes a delta-neutral convertible arbitrage position by purchasing \(100\) convertible bonds, how many shares of the underlying common stock must the manager short?

A fixed-income arbitrage hedge fund identifies that the 5-year swap spread (defined as the 5-year swap rate minus the 5-year Treasury yield) is historically wide at \(60\text{ bps}\) and expects it to mean-revert to its long-term average of \(35\text{ bps}\). Which of the following trades should the fund execute to profit purely from the narrowing of the swap spread?

In an equity market-neutral strategy, a manager aims to eliminate exposure to systematic risk by maintaining which of the following portfolio characteristics?

Which of the following biases in hedge fund database reporting arises when unsuccessful funds cease reporting their performance and are subsequently removed from historical databases, thereby causing historical performance metrics to be overstated?

A hedge fund analyst is evaluating a proposed merger arbitrage opportunity. Firm A has announced a definitive agreement to acquire Target Firm T in a stock-for-stock transaction. Under the terms of the agreement, shareholders of Target Firm T will receive \(0.60\) shares of Firm A for each share of Firm T held.

Currently, the market prices are:

Price of Firm A stock (\(P_A\)) = \$50.00\)
Price of Target Firm T stock (\(P_T\)) = \$27.60\)

(a) Calculate the current gross merger spread per share of Target Firm T.

(b) The arbitrageur decides to implement a classic merger arbitrage trade using \(10,000\) shares of Firm T. Specify the exact position (long or short) and number of shares to trade in Firm A to hedge the market risk of the exchange offer.

(c) Suppose the merger successfully closes after exactly \(6\) months, and no dividends are paid by either company during this holding period. Calculate the annualized rate of return on the capital invested (assuming the initial capital outlay equals the net cost of purchasing the shares of Firm T and margin requirements on the short sale are covered by the short sale proceeds without additional financing drag).

(d) Identify the primary downside risk to the arbitrageur in this transaction and state the effect on the position's payoff if regulatory approval is denied.