A. Spread Duration in concept is the same of Duration, however it measures price sensitivity to a change in spreads. Spread Duration is the % price change for a 100bps change in spreads Spreads can be versus risk free rates (i.e. the treasury curve), or versus the swaps curve. B. Duration Contribution and Spread Duration Contribution These measures are of critical importance to portfolio managers Portfolio managers many times wish to know how much of the total portfolio duration or spread risk is attributable to a bond, a sector, a specific risk type, etc. Duration x MV of the bond (or sector) / MV of the Portfolio = Duration Contribution Spread Duration x MV of the bond (or sector) / MV of the Portfolio = Spread Duration Contribution Example, purchase the following bond for a $6bn portfolio: Duration = 6.50 Price = 101-16 >> 101.5 Par Amount = $25,000,000 1. The duration contribution to the portfolio is: 6.50 x $25,375,000 / $6,000,000,000 = 0.027 years So if the yield of this bond alone changes by 100bps, the portfolio will impacted by .027%. Let's prove that out: Question 1 If comparable bonds yields shift up by 15bps, using the bond's duration, what will be the market value change of this bond? For that 15bps change in rates, by what percent does the bond's value change impact the portfolio: What would be the answer to the question above if the rate change was 100bps? Stated in years, this is the bond's duration contribution to the portfolio. (5pts) 2. For a fixed rate, bullet bond, the spread duration is very similar to the modified duration. (For bonds with cashflows that change when interest rates change, duration and spread duration will be different e.g. callable bonds, and MBS) (For bonds with coupons that change when interest rates change, duration and spread duration will be different e.g. variable rate bonds. (Discount Margin)) Spread Duration = 6.50 For the same bond, given the spread duration of 6.5, the spread duration contribution to the portfolio is: 6.50 x $25,375,000 / $6,000,000,000 = 0.027 years 3. So, if either the general level of interest rates change, or just the bond or sector spreads change by 100bps, we will change the discount rates used to PV the cash flows by 100bps, the bond value will change by 6.5%, and the portfolio value be impacted by .027% Question 2 If credit spreads of comparable bonds tighten by 15bps, using spread duration, what will be the market value change of this bond? And if credit spreads widen 15bps? (5pts) 4. Buying a corporate bond exposes us to credit risk and liquidity risk, in addition the to usual interest rates risk, reinvestment risk, inflation risk, etc. Investors are compensated for these risks by earning the credit spread (i.e. we discount it's cashflows at a higher yield; the risk-free rate + the credit spread) C. Hedging Duration Risk I can hedge the duration risk of a bond purchase by selling interest rate futures contracts with an offsetting amount of duration contribution 1. We may not want to keep the duration risk. If we just want to benefit from tightening credit spreads, we can hedge away any impacts from treasury curve shifts (i.e. the impact of changes to the 'general level of interest rates') 2. If I wanted hedge out the duration contribution to the fund of this $25mm bond purchase, I can use the 10yr futures contract (TY). Each TY contract has the following characteristics: Duration = 7.00 Price = 133-00 >> 133.00 Par Amount = $100,000 In order to remove .027yrs of interest rate duration from the portfolio, we solve for the notional amount of futures contracts that equals an .027 contribution to the portfolio: notional amt of futures x 7.00 x 1.33 / $6,000,000,000 = 0.027 Let's rearrange that and solve the notional amount of TY futures contracts: 0.027 / 7.00 / 1.33 x $6,000,000,000 = 17400644.4683136 We need to convert notional to number of contracts. Recall that each contract has a $100,000 notional = 174.00 contracts Selling 174 contracts as a hedge would make me neutral to changes in the market level of interest rates, but leave me long the spread duration. When we size a futures trade we work in # of contracts. When we size a bond trade we work in face amount (notional) Question 3 I am bullish on AAA credit spreads (i.e. my view is that AAA credit spreads will tighten) I wish to add .1yr of AAA credit risk to my $6bn portfolio A dealer is offering MSFT 3 1/2s maturing 11/15/42 (594918AR5). The offer price is 113-12, and the bond's duration is 15.385yrs How much of this bond do I need to buy to add .1yr of AAA credit spread exposure to my portfolio? (5pts) Question 4 If I then wanted to hedge the duration risk of that bond purchase and and keep the spread risk, how many 10yr futures contracts would I sell? (5pts) Question 5 I am bullish on AAA credit spreads, and wish to add exposure. However, I am fully invested and cash on hand to buy the MSFT bond is low. I want to add .2yrs of spread duration, not spread duration and rate duration. To raise cash, and hedge the rate exposure, I can sell some of the T 2.75% 11/15/2042 bonds I own in the portfolio That bond is bid at 110-05, and has a duration of 16.48 years. I buy .2yrs of the MSFT bond, how much of the Treasury bond should I sell in order to remove .2yrs of rate duration from my fund? (5pts) Question 6 Suppose instead I am bullish on rates, not credit, and I wish to get long TY contracts to add .2yrs of duration to my portfolio. How many contracts should I go long? (5pts)