EFB344 Risk Management and Derivatives: 100%

Provide an example of index arbitrage using futures contracts. Compare and contrast the duration targeting formula and the beta targeting formula. Why might a hedge based on duration targeting not work? A stock index currently stands at 350. The risk-free interest rate is 8% p.a. (with continuous compounding) and the dividend yield on the index is 4% p.a. What should the futures price for a four-month contract be? It is 9 January 2013. The yield on a Treasury bond with a 12% coupon that matures in 12 October 2020 is quoted as 5.04%. What is the cash price? (Hint: There are 93 days until the next coupon payment on 12 April 2013 which will occur 182 days after the last payment). A 90-day bank accepted bill futures price changes from 96.76 to 96.82. What is the gain or loss to an investor who is long the two contracts? In industry, it is common to find people using rules of thumb to get a rough idea of what gains and losses like this are likely to be (before they get their new graduate to actually calculate it properly). As an example of this, a one basis point (ie – 0.01%) change in yield will lead to around a $24 change in the value a 90 day bill or futures contract over such a security. Looking again at the question, the 90-day bank accepted bill futures rate has increased by 6 basis points. The investor makes an approximate gain per contract of 24 × 6 = AUD 144, or AUD 288 in total. A one-year long forward contract on a non-dividend-paying stock is entered into when the stock price is AUD 40 and the risk-free rate of interest is 10% pa with continuous compounding. (a) What are the forward price and the initial value of the contract? (b) Six months later, the price of the stock is AUD 45 and the risk-free interest rate is still 10%. What are the forward price and value of the forward contract? Suppose that the risk free rate is 10% pa with continuous compounding and that the dividend yield on the stocks underlying an index is 4% pa. The index is standing at 400 and the futures price for a contract deliverable in four months is 405. What arbitrage opportunities does this create? On 1 August, a portfolio manager has a bond portfolio worth $10million. The duration of the portfolio in October will be 7.1 years. The December 10-year Treasury bond futures price is currently 95.12 with duration 7.8 years. How should the portfolio manager immunise the portfolio against changes in the interest rates (i.e. – remove market risk) over the next two months?