In 2019, CFA Institute revised all of their Level III Fixed Income readings, and, in particular, came up with a 10-page blue box example that was absurdly complex, which I simplified here.
That example’s gone. Fortunately. (In point of fact, I’m sorry that the idea is gone from the curriculum, because it was interesting and useful. The problem was that the example was far too complicated for candidates, many of whom do not employ any fixed income in their day-to-day work, much less foreign fixed income.)
For 2022, CFA Institute replaced that Yield Curve Strategies reading with a new Yield Curve Strategies reading. I’m going to address the new reading here, and in the companion articles linked here. It’ll be interesting, but not as interesting as it could have been.
What are Yield Curve Strategies?
First, when we talk about yield curve strategies, we’re generally talking about investments in risk-free government bonds, either directly or synthetically. This is distinguished from credit strategies in which we’re talking about investments in corporate bonds, for example, for which potential changes in credit spreads can play a significant rôle in our investment decision; the bonds we consider in yield curve strategies have essentially no credit spread component. Thus, we may be talking about:
- Buying or selling government bonds (domestic or foreign)
- Taking the long or the short position in futures contracts on government bonds (domestic or foreign)
- Taking the long or the short position in forward contracts on government bonds (domestic or foreign) with reputable counterparties (i.e., those for whom the default risk is negligible)
- Buying or selling options on government bonds (domestic or foreign)
- Entering into plain vanilla interest rate swaps with reputable counterparties
- Entering into currency swaps with reputable counterparties
The objective in a yield curve strategy is, as you might expect for any investment strategy, to try to enhance the returns on our portfolio. This may be accomplished by:
- Adjusting the overall duration of the portfolio
- Adjusting the key rate durations of the portfolio
- Adjusting the convexity of the portfolio
- Adjusting the cash flow of the portfolio
Which of these approaches we will use depends on our view of what will happen to the yield curve (or yield curves, if we’re considering investments denominated in more than one currency) over our investment horizon (and, of course, on the scope we’re allowed based on the investor’s investment policy statement (IPS)). I’ll cover the possibilities, and help you to understand how to select an appropriate strategy given a particular view on the yield curve(s).
Making Money with Bonds
There are broadly two ways to make money with bonds:
- Coupons (more generally, to incorporate synthetic strategies using, for example, swaps: interest payments)
- Price changes
The curriculum breaks down the expected return on a bond in this manner:
\begin{align}E\left(R\right) &≈ Coupon\ income\\
\\
&\pm Rolldown\ return\\
\\
&\pm E\left(∆Price\ from\ investor’s\ view\ of\ benchmark\ yields\right)\\
\\
&\pm E\left(∆Price\ from\ investor’s\ view\ of\ yield\ spreads\right)\\
\\
&\pm E\left(∆Price\ from\ investor’s\ view\ of\ currency\ value\ changes\right)
\end{align}
For yield curve strategies we won’t be concerned with the fourth term (changes in yield spreads), and we’ll be concerned with the last term only when we discuss bonds denominated in foreign currencies, at the end of this article. Our main focus, therefore, will be on coupon income, rolldown return (i.e., the price change in a bond that results from the passage of time, assuming that the yield curve does not change), and price changes that result from changes in the yield curve.
Your View of the Yield Curve
Broadly (i.e., really, really broadly), there are two possibilities for the yield curve in the future:
- It can stay the same as it is today: a static yield curve
- It can change: a dynamic yield curve
Your choice of strategy begins with your view of how the yield curve will look at the end of your holding period: the same as today, or different. If you believe that the yield curve will remain static, you’ll choose from one set of strategies, but if you believe that the yield curve will change, you’ll choose from a different set of strategies. I’ll cover both possibilities (and their corresponding strategy sets) in these articles:
The Yield Curve
For the articles on yield curve strategies, I’ll start with this yield curve:
| Maturity, Years | Par Rate | Spot Rate | Forward Rate |
| 1 | 2.220% | 2.220% | 2.220% |
| 2 | 2.521% | 2.525% | 2.831% |
| 3 | 2.799% | 2.810% | 3.382% |
| 4 | 3.057% | 3.078% | 3.887% |
| 5 | 3.296% | 3.331% | 4.348% |
| 6 | 3.518% | 3.570% | 4.774% |
| 7 | 3.722% | 3.794% | 5.150% |
| 8 | 3.912% | 4.008% | 5.516% |
| 9 | 4.087% | 4.209% | 5.836% |
| 10 | 4.249% | 4.401% | 6.139% |
(OK, technically it’s three yield curves.)
(For some of the graphs I’ll extend the par curve to 30 years, but for calculations we’ll mainly stick to 10 years maximum.)
Here’s how they look for 10 years:
and here’s how they look for 30 years:
The Strategies in a Nutshell
Buying or Selling Government Bonds
This is about as straightforward as it gets: you have a bond portfolio, so you buy some bonds. Then, perhaps, you sell some of those bonds and buy other bonds.
By selling one bond and buying another, you can:
- Adjust the overall duration of the portfolio (sell a bond with one duration, buy a bond with a different duration)
- Adjust the key rate durations of the portfolio (for example, by switching from a bullet portfolio to a barbell portfolio with the same duration)
- Adjust the convexity of the portfolio (for example, a laddered portfolio will have more convexity than a bullet portfolio with the same duration)
- Adjust the cash flow of the portfolio (sell a bond with one coupon rate, buy a bond with a different coupon rate)
You can also adjust your currency exposure by selling a bond denominated in one currency and buying a bond denominated in another currency.
Taking the Long or the Short Position in Futures Contracts on Government Bonds
Although this is extremely similar to buying or selling (respectively) government bonds, there are some significant differences:
- Futures contracts require no upfront payment (although you will likely have to post a margin); therefore, they are leveraged positions (which can increase or decrease your total return significantly)
- Futures contracts do not pay coupons, so their duration is generally greater than the duration of the underlying bond, and their convexity is generally less than the convexity of the underlying bond
Apart from these, taking a long position in a forward contract is much the same as buying the underlying bond, and taking the short position is much the same as selling the underlying bond.
Taking the Long or the Short Position in Forward Contracts on Government Bonds
This is nearly identical to taking the long or short position in futures contracts. The main difference is that these are custom contracts, so you can adjust such characteristics as the underlying bonds, the time to maturity, and the collateral (if any). Apart from that, they work much as the futures contracts (above) work.
Buying or Selling Options on Government Bonds
The effects of options on government bonds are:
- Long call options increase duration and increase convexity
- Short call options decrease duration and decrease convexity
- Long put options decrease duration
- Long out-of-the-money puts increase convexity
- Long in-the-money puts may decrease convexity negligibly
- Short put options increase duration
- Short out-of-the-money puts decrease convexity
- Short in-the-money puts may increase convexity negligibly
Entering into Plain Vanilla Interest Rate Swaps
The fixed leg on a plain vanilla interest rate swap has an effective duration that is roughly 75% of the maturity of the swap, while the floating leg has an effective duration that is roughly half the time between swap payments. Therefore, if you enter into a pay-fixed, receive-floating swap you will reduce the duration (and the convexity) of your portfolio, and if you enter into a pay-floating, receive-fixed swap you will increase the duration (and the convexity) of your portfolio.
Note that this will also have an effect on your cash flow, but apart from the payment at the first settlement date, you cannot say for certain whether it will increase or decrease your cash flow.
Entering into Currency Swaps
A fixed-for-fixed currency swap isn’t likely to change the duration or convexity of the portfolio much, nor will a floating-for-floating currency swap; however, a fixed-for-floating currency swap can change the duration much as a plain vanilla interest rate swap does. It can also change your cash flows, similar to a plain vanilla interest rate swap.
Of course, in this case the two legs of the swap will pay different currencies, so they’ll be subject to different yield curves. Additionally, a currency swap will be subject to changes in currency exchange rates, which adds another dimension to the effect they will have on a fixed income portfolio.
One common use of currency swaps is to combine them with bonds denominated in foreign currencies, effectively changing the foreign currency cash flows into domestic currency cash flows (i.e., they can be a tool to hedge currency exchange rate risk). Depending on the scope allowed by the IPS and the manager’s view on exchange rates, the manager may choose to overhedge or underhedge the foreign currency payments; i.e., use the swap as tool to engage in active currency management.