Lecture%2019 - $""&&"/0 1/0(2/0& 3/0 3...

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Unformatted text preview: ! #! $! " " % & % ' % ' ( ' ) &! "! ) ' * +' , (( % ,-( ,-( . ' /0 -(( . 1 /0 -(( ) ,#-(2/0-(( ' & 3 /0 -(( 3 4 ! A 1% move in the S&P 500 = .01*1400 = 14 points = S&P 500 futures contracts change by $250*14 = 3,500. A 1% move in my portfolio of stocks is equal to .01*$100 million = 1,000,000 To set the beta of my total portfolio (futures plus stock) to .5 sell futures contracts until a 1% decline in the S&P 500 will result in a $500,000 gain in futures. Sell 500,000/3,500 = 142.85 contracts short. At $25,000 margin per contract this only requires a little less than $3.6 million in margin! Example: Hedging intere st rate risk with eurodollar contracts Suppose I own a $100 million bond portfolio with duration and convexity such that a 10 basis point move in 3- month interest rates will result in a $100,000 change in the value of my portfolio. I wish to immunize my portfolio from interest rate risk by selling Eurodollar futures short. Assume a 1 basis point move in my portfolio will correspond to a 1 basis point move in Eurodollar yields. A one basis point decrease in Eurodollar yields results in a $25 increase in the Eurodollar contract. Therefore, if I wish to eliminate my interest rate risk I need to sell enough Eurodollar contracts short to eliminate my interest rate risk. A 10-basis point increase in yields results in a 100,000 decrease in the value of my portfolio, thus I must sell Eurodollar contracts short until a 10-basis point increase in yields results in a 100,000 decrease in the value the future contracts I have shorted. A 10-basis point increase in yields results in a 10*25 = $250 decrease in the value of the Eurodollar contract. Thus, I must sell 100,000/250 = 400 contracts short. ...
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