Using the Black-Scholes formula and the cumulative normal distribution (i.e. see Table 21.2, p. 740 of the prescribed textbook), compute the call and put option prices using the data from Table 2. Table 2: Option information Stock price, S0 38 Exercise price, X 34 Interest rate, r 0.051 (5.1% per year) Time to expiration, T 0.5 (6 months or half a year) Standard deviation, 0.25 ( 25% per year) First compute d1 and d2, then using Table 21.2 in the textbook, find the N(d)s and use interpolation if needed to find the exact call and put prices. e. Assume the current futures price for gold for delivery 10 days from 8 February is US$1,259.50 per ounce. Suppose that from 9 February 2017 to 22 February 2017 the gold prices were as in Table 3. Assume one futures contract consists of 100 ounces of gold. Also, assume the maintenance margin is 5% and the initial margin is 10%. Calculate the daily mark-to-market settlements for each contract held by the long position. Briefly discuss basis risk (i.e. you can give an example if it makes it easier to discuss) [Hint: see Chapter 22 and examples 22.1 and 22.2 of the textbook]. Table 3: Gold prices in US Dollars per ounce Day Futures Price (US Dollar per ounce) 8 Feb 2017 1,259.50 9 Feb 2017 1,253.50 10 Feb 2017 1,256.50 11 Feb 2017 1,261.10 12 Feb 2017 1,251.80 15 Feb 2017 1,254.80 16 Feb 2017 1,258.20 17 Feb 2017 1,269.10 18 Feb 2017 1,271.70 19 Feb 2017 1,266.10 22 Feb 2017 (delivery) 1,265.60 f. Evaluate a funds portfolio performance in terms of the market (e.g. outperformance or underperformance) using the Sharpe ratio, Treynor measure, Jensens alpha, and Information ratio using data from Table 4. Assume the risk-free rate is 5.3%. Briefly discuss each of the four measures plus the Morningstar risk-adjusted return model. Table 4: Portfolio performance data Fund Portfolio Market Average return, x 11% 8% Beta, 1.10 1.0 Standard deviation, 31% 25% Tracking error (nonsystematic risk), (e) 13% 0
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