Earlier, you suggested that the rebalancing process could produce a negative cash required. But for this to happen, the dollar duration would have to increase between T5 and T4. This is theoretically impossible, because as time to maturity lessens, the duration should decrease. If I’m correct about this, then the demand for cash will accompany every rebalance, But again, why do we care about rebalancing the DD to what it was before? Why are they telling us to do this when the duration of the liability that we’re matching to is less?
Lets say duration of 1 year bond is $10 and 10 year bond is $140. You can get a exposure to 10 year bond by buying a 10 year bond or by buying 14 one year bonds. Equation does not feel like equal. But it is. The equation is neither matching cash flows and nor timing of cash flows and nor maturity. It is matching duration/sensitivity to rates. Why he want to get this exposure to this sensitivity? He thinks interest rates are going down and want more exposure to duration to profit. Interest rates went down and he sells off a month after, he should end up with same money with either of the instruments(assuming rates change parallelly). Or may be his liabilities have a similar exposure in opposite direction. When Investor says maintain duration of 10 years. He wants portfolio value to change as 10 years bond. He neither wants you to make sure you have cash flows every six months equal to 10 year bond coupon rate nor wants you to make sure portfolio matures after 10 years with same value as 10 year bond.
Sorry, I am still confused, my questions are : 1. P29 : The paragraph under 4.1.1.3 [In general, for an upward-sloping yield curve…] Shall the immunization target rate of return be determined at the beginning (as the 7.5% in Example 5 on P27) and the yield curve is irrelevant ? 2. P.30 : 1st line, because [portfolio rebalancing is required to keep portfolio duration synchronized with the horizon date.] Is the portfolio duration mentioned here the Macaulay duration of the portfolio ? How to keep portfolio duration synchronized with the horizon date ? 3. P.31 : Example 31 Why the portfolio dollar duration at the initial value shall be maintained ? What is the justification behind this ? Shall the Modified Duration (rathet than the Dollar Duration) be maintained ?
I get the math. I don’t get the rationale, at least from the textbook viewpoint. Why would someone desire to maintain a constant asset duration when clearly the liability duration is winding down? Or is liability duration completely irrelevant? Moreover, it’s very expensive to do this. In the example on page 31, you’re having to add $1 million to the portfolio (instead of exchanging existing bonds for longer duration bonds, which would take zero capital), Then what happens a year later when you have to do this all over again? Put in another million or two? But WHY?
IMO, the immunization target rate of return shall be the the target yield (as the 7.5% in Example 5 on P.29) at which the target value (as the $13,934,413) can be archieved. The immunization target rate of return is the “target yield” and it shall be determined at the beginning and it will remain same over the immunization time horizon (5 years in Example 5), regarless of the what is the yield curve at the beginning and how the yield curve changes thereafter. Anyone can advise what’s wrong with me ?
Reading 23, ALM, I am very much confused too ! Page 29, the 2nd paragraph under 4.1.1.3 Determining the Target Return “In general, for an upward-sloping yield curve…higher reinvestment return” I think that the target return is the target yield (as the 7.5% in Example 5 on p.27) and it shall be same over the entire investment horizon, irrespective of the yield curve (upward, flat or downward) at the inception or any change in yield curve after the inception. The target yield (return) of 7.5% in Example 5 is calculated by (13,934,413/9,642,899)^(5x2). Thatv is, the immunization target rate of return shall have nothing to do with the shape of the yield curve. Page 30, 1st line “portfolio rebalancing is required to keep the portfolio DURATION syncronized with the horizon date” What does this mean ? Page 31, Example 7 :Rebalancing, Why the dollar duration shall be maintained ? What is the rationale behind this ? Shall the duration be kept to be syncronized with the horizon date (as indicated in 1st line on P.30) ? Page 41, footnote 27 Is the duration of multiple liabilities calculated in the same way as the Macaulay Duration ? If so, then which composite asset duration (Macaulay Duration or Modified/Effective Duartion ?) must equal the composite duration of liabilities ? Any advice will be appreciated !
I’m totally with Hank Moody on this one and I had the same question in my mind going through the example. The example is so poorly chosen that I think they are loosing the whole point when they pretend that the value should be hedged back to the previous 5 year point. But given that is the objective, I guess it makes sense, but such a s****y example.
Hank, Heres how i look at it…
The liability that was 5 years at initiation got extended out 1 year at the end of the 1st year. Which means we have to rebalance to match duration to the new investment horizon. Yes our bond portfolios duration decreased by roughly 1 because 1 year passed, but we now have to increase duration to match the time horizon. Heres the catch, to get our DV01 to the appropriate level we are only allowed rebalance our exisiting bonds and keep them at 1/3 level. Obviously this is stupid, in the real world if you need to get a 5 duration and your bonds all have a duration under 4 than you sell the bonds and reposition the portfolio with bonds of higher durations and wont have to come out of pocket. But we are instructed to use our exisiting bonds, so if we cant adjust our duration the only way to match DV01s is by adding more to the market value. So now we have 4mil invested with a duration of 4yrs to match a liability that has a present value of 3Mil with a duration of 5.
So i beleive the takeaway is, we dont have to necessarily match duration, we can match dollar duration(or DV01), and when we match DV01 the market values dont have to be the same. I could have 1Mil bond with duration of 1yr immunizing a 10K libiality that has a 100 yr duration. Each year i would have to rebalance though.
My 2 cents…