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UNIVERSITY OF ILLINOIS College of Business - Department of Finance - Finance 300 (Financial Markets) Professor James Jackson # Bonds (t periods) Coupon (C\$) PV (C\$) Duration (D i ) Convexity (C i ) 1000 1 \$50.00 \$49.02 0.0440 0.0880 2 \$50.00 \$48.06 0.0863 0.2588 3 \$50.00 \$47.12 0.1269 0.5074 4 \$50.00 \$46.19 0.1658 0.8291 Face Value \$1,000.00 \$923.85 3.32 16.58 Bond Price (∑ PVCF) = \$1,114.23 ∑/2 = Duration (Years) ∑/4 =Convexity (Years 2 ) 1.870 4.566 Years to Maturity Coupon Rate Market Rate (YTM %) Current Yield Modified Duration Price Change (MD Only) Modified Convexity Price Change per + 1.00% YTM 2.00 10.00% 4.00% 8.97% -1.833% -\$20.42 2.19 -\$20.18 Futures Contract Face Contract \$ per 1/32% YTM % \$100,000.00 \$31.25 + 1.00% 1. Portfolio \$ change per + 1.00% YTM? [1000 bonds] *[ -\$20.18] = -\$20,180.00 2. Hedge Ratio? [ -\$20,180.00 / ( \$ 31.25 * ( 32 /32 ))] = -20.18 ** 3. Number of Futures Contracts? –20.00 Contracts (Rounded Hedge Ratio) 4. Long or Short Futures? Short ( Opposite Direction of YTM ∆29 5. Initial Margin per Contract (\$). \$2,700.00 (Set by the CBOT (t=0)) 6. Total Initial Margin Required (\$)? \$2,700.00

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