21-Liquidity Preference and Duration

# Price per bond 9938 verify suppose you buy 1000 bonds

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• shi1hong
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Price per bond = \$99.38 (verify) Suppose You buy 1000 bonds (\$99,380)

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Credit Spread Soon after buying: Credit spread hasn’t changed But yield curve jumped by 20bp YTM on defaultable bond=.082 New bond price=\$94.01 You just lost \$5,365.57! Return = -5.4% To hedge interest rate risk create a portfolio with zero modified duration.
Hedging Interest Rate Risk D* of defaultable bond=30/1.08=27.78 Suppose you can trade default-free bonds: 10 year zeros (YTM=2% initially), D*=10/1.02=9.80 1 year zeros (YTM=2% inititally), D*=1/1.02=0.98 How can we use these zeros to create a portfolio with D*=0?

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Modified Duration of a Portfolio The modified duration of a portfolio is the weighted sum of the modified durations of the assets in your portfolio. We want a portfolio with a weight of 1 in the defaultable bond, and a position in the other default-free bonds such that the modified duration of our portfolio is zero. * * 2 2 * 1 1 * ... n n p D w D w D w D + + + =
Hedging Interest Rate Risk w=-3.15 Equity=\$99,380 Value of defaultable bonds purchased Short 3.15*99,380=\$313,047 in 10-year zeros Use proceeds to buy 1-year zeros 0 98 0 8 9 78 . 27 * = + = . )-w* . w*( D p

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Hedging Interest Rate Risk
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