# Target duration = Cash duration

If the client states that they would like to maintain the current duration of the bond portfolio. And the cash duration is given. Should this (cash duration) be taken as the Target Duration when computing the numbers of future contract that needs to be bought/sold?

The answer considers Cash duration as Target duration. But I am under the impression that as client wants to maintain the current duration, the target duration = current duration of the bond. Could you help me understand?

Reference: 2016 mock exam: morning session: question number 31

You are confusing converting an asset position to cash with hedging an asset position. When fully hedging the portfolio, you want variation to equal zero, thus target beta/duration will equal to zero. In this case, you wish to convert your portfolio in cash equivalent (STIR). To do so you will need the duration of the cash position, which will not equal to zero. Also, always keep in minds that when converting to cash equivalent, you use FV of the portfolio at risk-free. Cheers!

Sorry for the confusion, I will re-raise my question -

The mock exam states that the client wants to move his 10% portfolio (i.e., 5.5 billion) from Bonds to Equity, maintaining his current duration(6.90) and beta(1.05). The extra information provides cash duration(0.25).

Bond = Future contract duration = 6.90 and MV of the future contract = 4.83 mio

Number of future contract (bonds) to sold =

Based on my understanding = ( ( 0 - 1.05) / 6.90) * (5.5 billion/4.83mio)

However CFA answer suggest = ( ( 0.25 - 1.05) / 6.9) * (5.5 billion/4.83mio)

Getting confused as to why cash duration is used, when the client want the exposure to move to equity and not cash.

Can anyone help on the above

you are converting the bonds first to short term cash - then using that cash to buy the equities. Hence the short term cash duration of 0.25 is used as the target duration for bond conversion. They do this in the book examples as well, read the blue box examples in the book where they convert from equities to bonds or vice versa using futures contracts.

To decrease the bond portfolio, the formula for the number of bond futures to sell uses cash duration (0.25) as the target duration: ( 0.25 - 1.05) / 6.9) * (5.5 billion/4.83mio) But to increase the equity portfolio, why does the formula for the number of equity futures to buy not use the cash duration? Answer is given as: ((1.15 - 0.00) / 1.05) * (5.5billion/1.525mio) So why are they using the cash duration of 0.25 in the bond futures but not in the equity futures?

You are converting the bonds to short term ones (0.25 duration)

Equity uses target beta, not duration.

Equity is assumed to have a duration of zero.

It’s not cash; it’s equity.

HI cany you quote which topic is this from as the same concept is covered in Fixed Income aswell as Risk management with futures and forwards. I am specifically interested in checking out the blue box example where they have used cash duration. Thanks in advance If the question asked to allocate more to bonds and less to equity instead, for bonds would it be from cash duration 0.25 to duration 6.9 or duration 0 to 6.9? Thanks

Zero to 6.9.

When you reduce your equity synthetically you end up with a zero-beta, zero-duration portfolio.