Correction Fixed Income Midterm 2006
1. The adequate FRA to use would be the June 2007 which is tells you what the markets expects the 3-month rate to be 15 months from now. The future june 2007 eurodollar contract trades at 94.885 which means the market expects the 3 month rate next June to be at 5.115% (100 – 94.885). We need to sell the FRA to hedge our mismatch.
The initial 1MM deposited will grow to 1MM (1+5.20%)15/12 = $1,065,000
After 15 months, if the FRA trades at 6.09/6.20, we can settle at 6.19%. The loss on the FRA position is therefore:
6.19 - 5.115 = 1.075% The amount dealt was 1,065,000 sop the loss amounts to :
1,065,000 (0.01075)/(4)=$2,691.
The amount roll over for the last 3 month is therefore : 1,065,000 – 2,691 = $1,062,300 invested for 3 month @6.09% = $1,078,100
Amount of the loan: 1MM (1 + 5.50%)18/12= $1,083,624
3. (7 + (100 – 101)/20 ) / (101/100) = 6.88%
To determine the dirty price, one must calculate the accrued interest: Number of days since last coupon (it’s a corp. bond so 30/360): 142 days Accrued interest = (142/360) x 7 = 2.76 or $27.60
Dirty price is therefore 1010 + 27.60 = $1037.60
120 bonds would cost me 120 x 1037.60 = $124,512
4. Price of the bond = 5/(1+5.5)1 + 5/(1+5.5)2 + 5/(1+5.5)3 + 5/(1+5.5)4 + 105/(1+5.5)5=
97.86
Weighted price :
5/(1+5.5)1 + 5x2/(1+5.5)2 + 5x3/(1+5.5)3 + 5x4/(1+5.5)4 + 105x5/(1+5.5)5 = 444.33
Modified duration = (444.33/97.86) /( 1+0.055)= 4.30
If the bond has a convexity of 120, a 50BP increase in yield will lower the price by : -(4.30 x 0.5) + (1/2 x 120 x (0.005)2 = -2%
The new bond price is therefore = 95.90
5. The fed requires 20 billion so there is $50 billion left. The highest bidder would be the bidder with the lowest rate.
GS gets its 15 billion JPM gets its 20 billion
MS gets 15 of the requested 22 billion ML gets nothing.
Fed’s price is the weighted average of the bidders that is n: (15 x 4.63 + 20 x 4.65 + 15 x 4.66 ) / 50 = 4.647%
6. Portfolio A with 78% of the 5-year note and 22% of the 10-year note, you get : (0.78 x 4.34) + (0.22 x 7.38) = 5.00
Portfolio B with 28% of the 30-year note and 72% of the 2-year bill, you get : (0.27 x 13.29) + (0.73 x 1.91) = 5.00
You would chose the portfolio with the highest convexity which is Portfolio B with a convexity of 74. (0.27 x 264.667) + (0.73 x 4.426)
1 x 12.84 + z x 1.85 = 0 z=-6.94
For each 30 year bond you buy, you must sell 6.94 2-year bond or 69.2 million face value of the 2-year bond. 69.2 million face means 69.2M/1001.30 = 69 110 bonds.
