BUS 550 WEEK 9 HOMEWORK

Your first question is #3, and it is split up in the course shell, but you can answer it all at once. As you can see in the question, Ms. Klein manages a financial portfolio and anticipates a shift in the yield curve. A basic concept in finance is that any change in interest rates will change the value of a financial portfolio, so Ms. Klein wants to protect her position using a hedging strategy. Some information about her portfolio and bond futures contracts are given in the text.

Part (a) requires no math and is conceptual. This will require some thought about why futures contracts are a good choice for hedging.

Part (b) requires you to calculate the number of contracts needed to protect this portfolio. You first have to find the value of each contract based on the information provided in the question. Then you use one of two ways to calculate the number of contracts needed. The first method is the ‘modified duration’ approach, which considers a change in the value of the portfolio as a result of the changes in duration versus the changes in value of the portfolio. The second method uses a ‘basis point’ method of calculation. Here are the equations:

Using modified duration,

Target Change in Value using MD

= Change in Value using MDhedge + Change in Value using MDportfolio

= (MDhedge x change in yield x Valuehedge) +

(MDportfolio x change in yield x Valueportfolio)

= (MD per futures x change in yield x N x contract value) +

(MDportfolio x change in yield x Valueportfolio)

where N = the number of futures contracts.

Because the target MD is zero, then:

N = -(MDportfolio x Valueportfolio)/(MD per futures x contract value)

Using basis point value,

BPVtarget = BPVportfolio – BPVhedge

BPVtarget = BPVportfolio – (N x BPV per futures)

And N = (BPVtarget – BPVportfolio)/BPV per futures

Use those equations above to get the answer for the number of contracts needed. You will get the same answer using each equation.

Part (c) also requires some calculations. The question states that the interest rates may increase by 10 basis points, which would cause an immediate decrease in the value of the portfolio. However, this decrease is offset by increase in value of the futures contracts. You are to demonstrate mathematically how the cash flow will occur in the contracts if the interest rates do change as anticipated.

Part (d) is conceptual and is a good question for getting you to think about why hedging does not fully protect your portfolio.

Part (e) requires a graph, which will be a lot easier than the SML graph we did earlier this quarter.

Question 3 is clearly the more difficult question that requires the most calculations and thought. Question 5 on the other hand is not that difficult. This question demonstrates how you can make a profit from an ‘arbitrage’ which is a risk free way to use someone else’s money to make a profit. You are to first describe the components of a ‘cash and carry’ arbitrage transaction and then show the math as to how you can profit from such a transaction. Its relatively straight forward, but as always, I will gladly help along the way.