SEEM 3590 Investment Science YANG Chen, Fall 2024 Homework Set 5 (Due on November 29, 2024, 23:59) Assignment 1. While studying the performance of a fund on the quarterly returns using the Fama-French three-factor model, an investor found that the historical estimates of the mean and standard deviation of the fund’s return are 2.2% and 5%, respectively. She also estimated the mean and standard deviation of the market portfolio’s return to be 4.5% and 10%, respectively, and the correlation between the return rates of the fund and the market is 0.60. The risk-free return rate is constant at 1% in the past. The portfolio loadings for SMB and HML are estimated to be 0.35 and 0.45, respectively. The expected payoffs for the zero- cost strategies associated with SMB and HML are estimated to be 0.75% and 0.85%, respectively. (a) What is the beta of this fund? (b) According to the Fama-French three-factor model, is the strategy of this fund a good one? Why? 2. There are one risky asset and one risk-free asset in the market. Assume there are three possible market states after 3 months, a, b, and c, with probability pa, pb, pc, respectively, such that pa + pb + pc = 1 and pa > 0, pb > 0, pc > 0. Over this 3-month period, the net rates of return of the risky asset in the a, b, and c states are ra, rb, rc, respectively, such that ra < rb < rc. The risk-free asset has a net rate of return of rf (constant) regardless of the state. If rf ≥ rc, by using the risky asset and the risk-free asset, construct a zero-cost strategy that corresponds to an arbitrage opportunity, and explain why this strategy leads to arbitrage. Repeat this for the case if rf ≤ ra. 3. A financial institution entered into an interest rate swap with company X two years ago to receive 4.0% fixed rate (per annum) and pay 6-month HIBOR on a principal of $10 million in three years. Therefore, the remaining life of the contract today is 1 year. The payments are made semiannually and the rates are quoted with semiannual compounding. The following are the discount factors two years ago when the swap was signed: Time-to-Maturity (months) Discount factor 6 0.9750 12 0.9550 18 0.9360 24 0.9180 30 0.9010 36 0.8950 1 SEEM 3590 Investment Science YANG Chen, Fall 2024 How much did the financial institution pay to or receive from company X two years ago to enter into the swap? 4. Suppose that spot interest rates with continuous compounding are as follows: Maturity (months) Rate (% per annum) 3 4.8 6 5.2 9 5.6 12 6.0 Calculate the forward interest rates with continuous compounding for the sec- ond, third, and fourth quarters. 2 51作业君版权所有