# R28 : Rebalancing

V4, P30~31 On the top of P30, it is said : portfolio rebalancing is required to keep the portfolio DURATION syncronized with the horizon date. Then in 4.1.1.5 and Example 6 & 7, the rebalancing of the “DOLLAR DURATION” is introduced. My questions : Which shall be rebalance ? DURATION or DOLLAR DURATION ? How to rebalance the DURATION (not introduced in the text) ? In example 7, what does it mean by : We choose to rebalace using the existing security proportions of “one-third each” ?

Simple duration based rebalancing does not cover the effect of market price changes on the portfolio risk . Dollar duration which measures the PVBP gives us the effect of moving to a different point-in-time to current prices. Duration is , after all , a forward looking estimate while the portfolio value ( based on current prices) , is a present value term. The two in combination gives you a measure of risk of prices and duration both changing at the same time.

You would want to manage duration. In order to do that, in general, you should calculate dollar duration, then calculate which amount of dollar duration should be adjusted and then perform that adjustment either using all or some existing instruments in the portfolio or use some other instruments. For example, you have a portfolio with market value of \$100 million with duration of 30. If you want to reduce duration to 25 using futures contracts with market value of \$300,000 and duration of 10 each, then dollar duration would need to be calculated to find out the number of futures contracts that need to be sold.

Shall we balance both DURATION and DOLLAR DURATION ? Can we balance both DURATION and DOLLAR DURATION at same time ?

If we define duration as % change in portfolio value for 100 bps change in interest rate, than rebalancing the dollar duration is the same as rebalancing the duration. My opinion only.

bell99 Wrote: ------------------------------------------------------- > If we define duration as % change in portfolio value for 100 bps change in interest rate, > than rebalancing the dollar duration is the same as rebalancing the duration. > > My opinion only. Is it that : Rebalancing of DURATION = Rebalancing of DOLLAR DURATION ? Anyone else can confirm ?

DOLLAR Duration rebalancing is a technique . Duration rebalancing is a goal or target.

janakisri Wrote: ------------------------------------------------------- > DOLLAR Duration rebalancing is a technique . > Duration rebalancing is a goal or target. I was trying to explain that earlier but your explanation is very concise and precise. In some sense it’s similar to delta hedging. You know that you want your delta to be equal to zero but you still have to calculate the number of underlying contracts to buy or sell and that depends on the position size. Similarly, you know what you want the portfolio duration to be but the number of contracts to buy or sell depends on the portfolio size. Dollar duration reflects both portfolio size and duration adjustment.

janakisri / maratikus, Can you (or anyone else) raise an example showing that the goal of duration rebalancing can be reached by rebalancing of the dollar duration ? Duration rebalancing means keep the portfolio DURATION syncronized with the horizon date (of the liability). That is : to make the portfolio DURATION always same as the period left to the horizon date (of the liability). In Example 6 on P30, the portfolio’s duration is 3.636. But in Example 7 on P31, after one year, the portfolio’s durations both BEFORE and AFTER the rebalancing are same (2.725). This means that rebalancing the dollar duration has nothing to do with the the rebalancing of the duration. The horizon date (the time period left) of the liability is not indicated in the examples. Then, how to rebalance the portfolio’s DURATION ?

2010 AM Exam Q6 This shall to be what I have been looking for. But I wonder why the cases are not illustrated in Reading 28 or elsewhere in the curriculum.