Fund #1: Allocating 0.10 of the beta budget to Fund #1 with a beta of 0.50 results in an asset allocation of 20% (i.e., 0.10/0.50), a weight that is below the pre-established limit of 25% for this asset. Fund #2: Allocating 0.10 of the beta budget to Fund #2 with a beta of 0.50 results in an asset allocation of 20% (i.e., 0.10/0.50), a weight that coincides with the pre-established limit of 20% for this asset. (Section 30.3.3) Chapter 31 Exercises 1.Consider this simplified example that relates to alpha and beta estimation. Suppose that two people each buy one lottery ticket each day for a month. The lottery tickets offer a fully random one-in-one-million chance to receive $1,000,000 and are fairly priced at $1 each. One person wins once during the month and the other person is winless. Describe the ex ante alpha of the gambles and the true beta (systematic risk) of the gambles based on your understanding of the facts. Then describe the likely estimations of alpha and beta that would be made based on an historical analysis of the outcomes during the month. 2.Describe portable alpha. 3.Describe the relative importance of strategic and tactical allocation decisions for active and passive investors. 4.Describe appropriate risk and return expectations for enhanced index products. 5.Suppose an index is trading at $950 and the futures contract on that index represents a multiple of 250 times the index. Assuming that the index has a beta of 1.0 relative to the index and setting the basis equal to zero for simplicity, calculate the notional value of futures contracts (per contract). 6.Continuing with the previous exercise, consider a $50 million portfolio with a beta of 1.4 relative to the index. Setting the basis to zero for simplicity, calculate the number of contracts necessary to hedge the $50 million long position in the portfolio. 7.The manager of a €200 million portfolio benchmarked to the equity index of Country A has decided to allocate €30 million to a hedge fund with an ex ante alpha of 100 basis points per year and a beta of 0.80 to the stocks of Country B. The remainder of the portfolio remains in a strategy that has no ex ante alpha and virtually no tracking error to the equity index of Country A. Futures contracts trade on the equity indices of Countries A and B. Country A’s equity futures contract trades at 200 times the index, with a current index value of €1,200. Country B’s equity futures contract trades at 300 times the index, with a current index value of €100. Assume riskless interest rates and dividend rates are
97 zero, and ignore transaction costs. With respect to the €30 million allocation to the hedge fund, what position should be established in the futures contracts of the equity index of Country A, what position should be established in the futures contracts of the equity index of Country B, and how much ex ante alpha should the asset allocator expect to obtain expressed on the basis of the entire €200 million portfolio?
- Winter '18
- Juliet Gloria
- Fund ONE