8006 Exam Dumps : Exam I: Finance Theory Financial Instruments Financial Markets - 2015 Edition

Since Macaulay duration is 6 years, the modified duration is 6/(1+5%) = 5.71. This means that if interest rates were to rise by 1%, the bond price would decrease by 5.71%. Since interest rates have risen by 10 bps, (100bps = 1%), the bond's price would fall by roughly 0.571%, or 57 basis points

To solve this question, we need to revisit how delta is calculated in a single step binomial model:

Consider a portfolio with just two positions: 1 Long Call option, and Δ Short Stock. We do not know what Δ (Delta) is.

Now if the current price of the stock is P, which can take the value P2 (higher value) and P1 (lower value) in the future at time T, then Δ needs to be such that the value of the portfolio is equal in both the cases. If the price goes up, the value of the option will be $1 (given) and the value of the short stock will be -Δ P2. If the price goes down, the value of the option will be $0, and the value of the stock will be -Δ P1.

Therefore, $1 - Δ P2 = $0 - Δ P1.

Solving for Δ, we get Δ = $1 /(P2 - P1) = $1 / ($102-$98) = 1/4.

The no-arbitrage futures price is given by exp(0.5*(4%-1%))*$1000 = $1015.11. Therefore Choice 'a' is the correct answer.