Comparing IEF and Treasury Futures with Roll-Adjusted Returns

# US Treasury - IEF vs ZN Cumulated Return Comparison


# US Treasury - IEF vs ZN Cumulated Return Comparison












I have been trying to explore the possibility of replacing my IEF (10 years treasury ETF) positions with ZN (10 years treasury futures) for better leverage.

Reading the posts here, I understand that their return should be similar, except for the drag of financing cost. Not an issue for me as I will hold some short-term treasury to compensate for that.

In order to prove that their returns are indeed similar, I got their prices from the two sites below and computed the cumulated return.

https://www.nasdaq.com/market-activity/futures/zn/historical

https://finance.yahoo.com/quote/IEF/history?p=IEF

It turns out that they are very different and the difference (approximately 4% a year) is far beyond the financing cost. Please let me know what I am missing here. Am I fundamentally wrong about how I use the futures prices? Thanks.

## Answer by Helin (score 4, accepted)

https://quant.stackexchange.com/a/60263

I ran some quick simulations and the differences don't seem particularly drastic:

The black line above is the cumulative total return (inclusive of dividends) of IEF. The yellow line is the so-called "excess return" index for TY (aka ZN), which is the cumulative return of buying and holding TY contracts. To compute this index, I assume that you buy and hold the front-month TY contract until a week before the delivery month, at which point you roll into the next contract. Finally, the green line is the "total return" version, which is simply TY's excess return index with return on cash added back (i.e., it assumes that your futures positions are fully collateralized). The annualized return difference between the two total return indices is <70 bps (I used fairly conservative cash return assumptions and the differences will be even smaller for most institutional investors).

The blue line is likely what you retrieved from NASDAQ. It's simply the rolling front-month TY contract prices. The problem is that this series doesn't properly account for the roll between contracts – if you roll from a contract priced at 120 to another priced at 119, you don't lose a dollar, but that's what that time series would suggest.

The underperformance of TY is to be expected, since IEF tracks the 7- to 10-year part of the curve, while TY has generally tracked the shortest bonds in the delivery basket thanks to the low yield environment. The chart below shows the time to maturity of the cheapest-to-delivers of the front-month TY contracts since 2010.

For an alternative perspective, the next chart compares TY's duration against the duration of Treasuries in the 7-10y sector (based on index-weights).

## Answer by AlRacoon (score 1)

https://quant.stackexchange.com/a/60242

IEF as an ETF will also have management costs. Also the duration of IEF is lower since it is holding a basket of 7-10 Yr US Treasuries vs a 10 Yr note future, which is a future on just the 10Yr Note (actually a 10Yr 6% Note). There may be some optionality, such as Cheapest-to-deliver, at play with the future.

Also, you will incur roll risk and costs of the futures if your strategy is to hold the position for an extended period of time. The ETF will also incur costs as bonds roll down and no longer meet the maturity requirements but these costs will be different from the roll costs, which will occur quarterly if you are investing in the near futures.

## Answer by Edward Watson (score 0)

https://quant.stackexchange.com/a/60243

In addition to adding the return for your invested cash you have to roll the futures every quarter buy selling the front month and buying the back month a few days before the delivery cycle starts. You'll need some different contract specific data to do that. That should get you pretty close.

## Answer by Kim Gold (score 0)

https://quant.stackexchange.com/a/60249

You need to include the Roll Yield https://www.investopedia.com/terms/r/roll-yield.asp#:~:text=Roll%20yield%20is%20the%20return,premium%20to%20longer%2Ddated%20contracts.

Future contracts are usually rolled 4 times a year. When you do the roll, there is a price difference between contracts, and you need to include that. CBOE has a "Pace of the Roll" Tool which is really useful for such problems.

With roll yield added, adjustment for duration and considering the interest cost for the two cases, the return is the same.