Derivatives - Futures Contracts

When reallocating a portfolio between stocks and bonds, why don’t we use the duration of cash (if applicable) when we go from cash to equity, but we use the cash duration when going from fixed income to cash.

i.e. current allocation 50/50 stock bond. Target 60/40 (i.e. need to sell bond futures and buy equity futures)

cash duration .25

fixed beta 4

equity beta 1.5

fixed future contract beta 3

equity future contract beta 1.7

fixed (0.25-4/3)

equity (1.5-0/1.7)

I’m curious by the equity won’t be (1.5-.25/1.7) since we used duration of .25 for cash when reducing allocation of bonds?

Cash duration should be zero on both sides. That’s how the curriculum teaches it anyways. I’m confused by your example though. In the data you have a cash duration of .10 and a cash duration of .25 in your calculations. I’ll assume it’s a typo.

Edit - I stand corrected. There is an example in the curriculum where a duration of .25 is used on a 6 month instrument (Exhibit 7 in reading 26). I’ll have to look it over.

JayWill, yeah sorry that was a typo. I can understand why going from cash (which has a duration of zero would be correct, but not completely sure why going from fixed to cash is 0.25.

It’s not a typo. In curriculum and all practicing examples is assumed that cash duration is 0 what is likely not in his example above.

jay - they do use a cash duration of 0.25. I believe I recall a problem on the curriculum where they do that.

Excerpt from book

Fixed Income Money Advisors (FIMA) –

Currently, it would like to alter a $30 million segment of its portfolio that has a modified duration of 6.5. To increase liquidity, it would like to move $10 million into cash but adjust the duration on the remaining $20 million to 7.5.

continuing on in the writeup:::

Action The bond futures contract that FIMA will use is priced at $87,500 and has an implied modified duration of 6.85. To convert $10 million of bonds at a duration of 6.5 into cash requires adjusting the duration to that of a cash equivalent. A cash equivalent is a short-term instrument with a duration of less than 1.0. The equivalent instruments that FIMA would use if it did the transactions in cash would be six-month instruments. The average duration of a six-month instru- ment is three months or 0.25. The interest rate that drives the long-term bond market is assumed to have a yield beta of 1.0 with respect to the interest rate that drives the futures market. FIMA could solve this problem in either of two ways. It could lower the duration on $10 million of bonds from 6.5 to 0.25. Then it could raise the dura- tion on $20 million from 6.5 to 7.5. If FIMA converts $10 million to a duration of 0.25 and $20 million to a duration of 7.5, the overall duration would be (10/30)0.25 + (20/30)7.50 = 5.08. As an alternative, FIMA could just aim for lowering the overall duration to 5.08, but we shall illustrate the approach of adjusting the duration in two steps.

Bond to Bond they make the adjustment to Cash. But Equity to Bond - they assume a beta of zero.

I think that is the rule of thumb?

That makes sense. So basically:

If they provide duration to cash and going from bonds to cash don’t use 0, use cash duration number.

When going from cash to equities always use 0 for cash duration

Okay, after looking it over, in Exhibit 7 where a .25 duration is used for cash is a Bond portfolio example where the goal is actually generating cash to meet a liquidity requirement with a portion of the portfolio, not simply modifying the asset allocation. The equity example below that in Exhibit 8 is shifting exposure of a portion of the portfolio to a different capitalization category (Lg Cap to Mid Cap).

I think the simple answer is to follow the examples in the curriculum. If you’re changing the asset allocation and/or shifting the beta or duration of a portfolio up or down, use 0 for the cash beta/duration unless stated otherwise (which I doubt you’ll see on the exam).

In the example I was doing it was a modifying asset allocation question and they did use cash duration.

Yeah cpk, I think the key here is that in the example, cash is technically being generated by the futures sale on a portion of the portfolio value that is not going anywhere else for the time being. Thus a slightly longer term rate is being assumed on a 6 month cash instrument that has a duration of .25. I think I’m interpreting this correctly anyways.

Hmm. A 3rd party prep provider practice question I assume?

There is a statement in the curriculum that I think confirms my thinking, which comes from their asset allocation adjustment example …

“The sale of stock index futures provides $90 million of synthetic cash that is now converted into bonds using bond futures. Because no movement of actual cash is involved in these futures market transactions, the modified duration of cash is effectively equal to zero.

It’s from the CFAI site actually. I adjusted numbers and didn’t write specifics since I don’t want to violate any rules…

Okay, give me the Example or Exhibit number then if you don’t mind. I assume this is in Reading 26?

Edit - oh, by “site” you may mean the topic tests. Sorry, my brain is fried. If so, what is the name of the item set?

It’s not in the reading, it’s from the website where people made mock vignette, but it was my understanding it’s a violation to copy, paste, etc problems from that site since this is public forum.

No worries. My brain was like that yesterday after my 8 hour session on Sunday. Maybe I’m just being paranoid, but I don’t think I can say that can I? hahaha

You can reference the name of it, just not completely copy/paste a question (I believe). Either way, I found it. Thankfully it was the first one available.

So, my personal answer is (drumroll) …

I have no idea. LOL!

Seriously. They don’t teach this anywhere in the curriculum, and it actually contradicts the sentence I referenced above. The way I see it, if cash has an assumed duration of something above 0, it should be used in calculating the number of contracts on both sides of the reallocation.

Funny enough I did this item set a month ago and don’t remember this question at all. I might have to take another pass through these if I can find the time.

Bill (S2000magician) chimed in on this same question. I concur with his reasoning.

Thanks JayWill. I had the same thoughts going through this. It never made sense to me to use duration going into cash but not re-investing it. I’m not a super huge fan of some of the questions they present for this exact reason. IMO the way they set up the question is not similar to what it will be like on the actual exam and there are sometimes errors in the questions that end up wasting everyone’s time trying to figure out if we need to know it or if someone just screwed up. With so much emphasis put on due diligence in the curriculum, I always find it ironic. Thanks again for all the help!