# P2.T8.26. Arbitrage strategies (Stowell)

Discussion in 'Today's Daily Questions' started by David Harper CFA FRM, Apr 17, 2012.

1. ### David Harper CFA FRMDavid Harper CFA FRM (test)

AIMs: Describe the mechanics of an arbitrage strategy using an example. Discuss event-driven strategies, including: Merger arbitrage

Questions:

26.1. A convertible bond trades at 101.0% of its $1,000 par/face value, has a delta (with respect to the underlying convertible-into stock) of 0.60 and is convertible into 30.0 shares per$1,000 in face value. If the current share price is $29.00, what is the net initial cost of a market-neutral (delta-neutral) trade that is long the volatility, assuming no transaction costs? a. Initial net cost of$488
b. Initial net cost of $117 c. Initial net inflow$10
d. Initial net inflow $522 26.2. A fixed income arbitrate strategy manager takes two positions: she takes a short position in an interest rate swap (she is the floating-rate payer) with a notional of$10.0 million and a short position in Treasury bond with current value (price) of $7.0 million. The modified duration of each position is 4.0 years, to ensure an arbitrage, the net dollar (value) duration of the combined position is zero. The Treasury spot rate yield curve is flat at 2.0% and the swap rate curve is flat at 3.0%. If we ignore convexity and rely only on a linear approximation, and we further assume that swap spreads cannot become negative, what is the upside on this trade? (variation on example 30.5 in FRM Handbook, 6th Ed, page 764) a. Zero b.$280,000
c. $700,000 d. Unlimited 26.3. An acquisition has been announced by Acquirer (Company A) to merge with Target (Company T). Before the announcement, Aquirer A's shares traded at$21.00 and Target T's shares traded at $6.00. The proposed share-for-share exchange ratio was 1:2, which was a 75% premium over the$6.00 price. Subsequent to the announcement, Aquirer A's shares trade down to $20.00 and Target T's shares trade up to$8.00. At this time, a merger arb (risk arb) hedge fund takes a short position in Aquirer's A's stock hedged by a long position in Target T's stock. The merger is successful and the prices close at $28.00 (Acquirer) and$14.00 (Target). What is the gain per each share of Acquirer A? (variation on example 30.7 in FRM Handbook, 6th Ed, page 765)

a. zero per share of Target T
b. -$2 loss per share of Target T c. +$1 gain per share of Target T
d. +\$4 gain per share of Target T