How to Adjust Portfolio Duration for CFA L3 Problems

The Risk Management Application of Derivatives material (Study Session 15 in 2018) is a long, difficult, and important set of readings for the CFA Level 3 exam. 

You need to walk away with a good understanding of how to use forwards, futures, options, floors and caps, and swaps to adjust a portfolio's risk factors. From a calculation perspective, you will need to know how to adjust a portfolio’s beta or duration, switch exposure between stocks and bonds, and create a synthetic cash position. But this material isn't just calculation focused, L3 may have questions probing the advantages and disadvantages of each derivative strategy, including the challenges associated with maintaining a dynamic hedge.

This post tackles arguably the most important of these derivatives (at least for exam purposes): namely using futures to adjust portfolio duration. 

Remember the difference between forwards and futures?

Forwards and futures are quite similar, however, there are some key distinctions.

A futures contract is standardized and has minimal default risk/eliminates counterparty risk because it uses central clearinghouses. It is more regulated and more transparent than a forward contract, but it also requires a margin deposit.

A forward contract is customizable to any terms the parties agree to. It has higher default risks because you are exposed to the credit risk of the counterparty and less liquidity because each contract is customized. The advantage obviously is more flexibility. You can structure forwards in any way you want.

Both futures and forwards contracts are often used to manage/hedge risk by changing the underlying characteristics of a portfolio, or more accurately, by changing the overall payoff of the combined position given a particular market movement. 

When it comes to risk management you are more likely to be tested on futures contracts which is why in the following set of scenarios we default towards using a futures contract, but you could also use a forward contract in the same manner.

How to Use Futures to Adjust Portfolio Duration 

If we have a portfolio of fixed-income assets we may be concerned about the duration, or sensitivity, of our portfolio to changes in interest rates.[1] If we expect interest rates to increase (decrease) we may want to manage that risk by decreasing (increasing) duration.

Now we’ve talked about the idiosyncratic nature and high transaction costs of trading specific bonds before. The reality is that a portfolio of fixed-income assets can sometimes be difficult to trade in and out of. Hence we want to change a portfolio’s duration without having to trade in and out of the underlying assets. Enter futures contracts. Futures are more liquid, less expensive, and more easily shorted than bonds themselves, which makes them an ideal derivative to more easily alter the duration of a bond portfolio.

Testable Concept 1: Knowing when you buy or sell futures to increase or sell duration

  • To INCREASE the duration of a bond portfolio BUY bond futures
  • To DECREASE the duration of a bond portfolio SELL bond futures

In practice, we’ll set a specific modified duration target (MDT) for our fixed-income portfolio and then buy or sell the right number of futures contracts to hit that target from our initial portfolio duration (MDP). If we want to eliminate risk completely our target MD would equal zero:

futures modifying duration CFA Level 3


MDT = Target modified duration

MDP = Portfolio modified duration

MDF = Futures modified duration

VP = Portfolio value

Yield beta = Sensitivity to interest rate changes of the cheapest-to-deliver bond vs. original bond[1]

Multiplier = # indicating index value per contract (1 futures contract buys X units of index)

What next?

After you understand using futures contracts to modify portfolio duration you can turn to using futures to modify portfolio beta. This is a closely related concept, but deals with adjusting equity exposure vs. adjusting bond exposure. Once you've covered the two applications separately its time to combine them to build strategies for shifting exposure from fixed-income to equity and vice versa using futures





[1] Note, to understand yield beta and the more nuanced aspects of this process you can circle back to its coverage in reading 22.

[1] Duration, which measures the size and timing of the cash flows paid by a portfolio of bonds in terms of its weighted average maturity, is the primary measure of the change of a bond price in response to a move in interest rates.