[Questions 20-21] An investor owns a stock. Daily change in stock price, AS, has the standard deviation of 13. To hedge risks of the stock price, the investor considers cross-hedging using one of the following futures contracts. The following table shows each futures contract's standard deviation of of futures price change. AF, and the correlation coefficient p between AS and AF. Futures contract of P A 22 0.7 B 20 0.9 15 0.6 D 100.8 If the investor shorts h units of futures, the change in the portfolio value is AS - HAF. 20. Which futures contract results in the smallest variance, Var (AS - HAF)? (Assume that for each futures, we use respective minimum-variance hedge ratio). (a) contract A (b) contract B (c) contract C (d) contract D 21. What is the minimum variance if we use the futures contract found in question 20? (a) 5.67 (b) 32.11 (C) 60.84 (d) 86.19 [Questions 22-23] The current term-structure of spot rates is as follows (with con- tinuous compounding): Maturity (years) Zero-rate(%) 1 3.0 2 4.5 3 5.5 22. What is the implied forward rate ro(2, 3)? (a) 6.00% (b) 6.75% (c) 7.50% (d) 7.53% 23. A bank offers a special bond A through which investors can borrow (lend) $100 in year 2 and repay (receive) $100x60.07 in year 3. Is there an arbitrage? If so, what is the arbitrage's net cash flow in year 0? (Consider an arbitrage strategy where we use one unit of bond A and the net cash flows are zero from years 1 through 3) (a) 0.392 (b) 0.456 (c) 0.499 (d) 0.538 24. Consider non-dividend-paying assets A and B. The asset prices one year from now will depend on the state of economy as follows: Asset price in one year Boom Recession 50 20 30 30 asset A asset B Currently asset A sells for $15 and asset B sells for $27. Which of the following strategies results in an arbitrage? (a) buy 1 unit of asset A and sell 0.6 unit of asset B (b) sell 1 unit of asset A and buy 0.5 unit of asset B (c) sell 2 unit of asset A and buy 1.2 unit of asset B (d) None of the above leads to an arbitrage 25. Consider non-dividend paying stocks A and B. The current stock prices in time 0 are $45 for A and $32 for B. The stock prices two years from now depend on the state of economy as follows: Stock price in two years Boom Recession 80 40 30 40 stock A stock B What is the 2-year risk-free interest rate per annum? (a) 4.48% (b) 7.25% (c) 14.38% (d) 14.50%