The Research Library of Newfound Research

Month: January 2023

The Hidden Cost in Costless Put-Spread Collars: Rebalance Timing Luck

We have published a new paper on the topic of rebalance timing luck in option strategies: The Hidden Cost in Costless Put-Spread Collars: Rebalance Timing Luck.

Prior research and empirical investment results demonstrate that strategy performance can be highly sensitive to rebalance schedules, an effect called rebalance timing luck (“RTL”). In this paper we extend the empirical analysis to option-based strategies. As a case study, we replicate a popular strategy – the self-financing, three-month put-spread collar – with three implementations that vary only in their rebalance schedule. We find that the annualized tracking error between any two implementations is in excess of 400 basis points. We also decompose the empirically-derived rebalance timing luck for this strategy into its linear and non-linear components. Finally, we provide intuition for the driving causes of rebalance timing luck in option-based strategies.

Return Stacking in an Inverted Yield Curve Environment


When we first started publicly writing and talking about capital efficiency in 2017 – the predecessor conversation to return stackingTM – the 13-week U.S. Treasury Bill rate sat around 1.30%.

The prototypical example at the time was a 1.5x levered 60% stock / 40% bond portfolio (also referred to as a “90/60”).  Such a portfolio would allow investors to achieve the exposure of a 60/40 using just two-thirds of their capital, freeing up valuable portfolio real estate for diversifying alternatives.

Implementing such a portfolio in practice was also trivial: for every $1 invested, $0.9 could be invested in stocks and $0.1 held aside as cash collateral for a $0.6 notional position in U.S. Treasury futures.

Figure 1: One Possible Implementation of a 90/60 Portfolio

Today, the 13-week Treasury Bill rate hovers near 4.5% and the yield curve is severely inverted, causing many to ask, “does return stackingTM still make sense, particularly if we use Treasury futures to achieve our leverage?”

We believe the answer is a resounding “yes,” with four key points to consider.

It’s the portfolio, not the asset

With the yield curve severely inverted, paying short-term financing costs to invest in long-term Treasuries to achieve our leverage may seem like a losing prospect.  We believe this line of thinking is misguided, however; it misses the forest for the trees.

Using U.S. Treasury futures is simply a means to an end.  Sticking with our 90/60 example, what we actually care about is achieving 1.5x levered 60/40 exposure and the flexibility that creates for us in portfolio construction.

Would we have the same concern about an inverted yield curve if for every $1 invested we purchased $0.6 of U.S. Treasuries and held $0.4 in cash as collateral for $0.9 in S&P 500 futures exposure?  What if we simply borrowed money to lever an entire 60/40 portfolio up 1.5x?

Figure 2 plots that the annual returns of these three different approaches.  We can see that they are nearly identical to one another.

Figure 2: Annual Returns for Varying Approaches to Implementing a Levered 60/40 Portfolio

Source: Tiingo, Bloomberg, Barcharts.  Calculations by Newfound Research.  Past performance is backtested and hypothetical.  Returns are gross of all fees, costs, and taxes except for underlying expense ratios.  Returns assume the reinvestment of all distributions.  Past performance is not indicative of future results.  Starting date based upon the availability of pricing data.

To draw this point out further, consider the case of explicitly borrowing money to lever the 60/40 portfolio up 1.5x and the following ways we could implement this portfolio:

  • Hold 90% in stocks, 10% in U.S. Treasuries, and borrow to buy another 50% in U.S. Treasuries;
  • Hold 60% in U.S. Treasuries, 40% in stocks, and borrow to buy another 50% in stocks;
  • Hold 60% in stocks, 40% in U.S. Treasuries, and borrow to buy another 30% in stocks and 20% in U.S. Treasuries.

Figure 3: Different Approaches to Creating a 90/60 Portfolio

Does it matter which we choose?  Does an inverted yield curve make the first choice less attractive than the second?

In theory, we should be indifferent to these choices.  If we are concerned about using U.S. Treasury futures to achieve a levered 60/40, we should be equally concerned about using equity futures (“invert, always invert!”),

Sourcing cheap leverage.

In practice, we do care how we implement a return stackedTM portfolio.  Not because the yield curve is inverted, but because explicitly borrowing at the short-term Treasury Bill rate is difficult for all but the largest institutions.

Treasury futures have historically allowed us to do just that, giving us a very cost-effective source of leverage.  Figure 4 plots the embedded cost of leverage in 10-Year U.S. Treasury Futures relative to 3-Month U.S. Treasury Bill rates. By contrast, at the time of this writing, the current base margin rate is 10.75% at Schwab, 11.33% at Fidelity, and 12.50% at TD Ameritrade.

Figure 4: Embedded Financing Cost in 10-Year U.S. Treasury Futures versus 3-Month U.S. Treasury Bill Rate

Source: Bloomberg.

It’s the excess returns that matter.

But what about the fact that short-term rates have climbed from near-zero to north of 4%.  Is leverage now unattractive because the cost of financing is so high?

Let us return, for a moment, back to basic portfolio theory which says the expected return of an asset can be decomposed into two parts: the risk-free rate and the asset’s risk premium.  For example, the expected return of stocks should be equal to the risk-free rate plus the equity risk premium (“ERP”).  Similarly, the expected return of bonds should be equal to the risk-free rate plus the bond risk premium (“BRP”).

Figure 5: Decomposing Expected Returns into the Risk-Free Rate and Risk Premia

The expected return of a portfolio, then, can simply be thought of as the risk-free rate plus the blended return of risk premia.  For example, the expected return of a 60/40 is:

60% ERStocks + 40% ERBonds

Which can be decomposed as:

60% (Risk-Free Rate + ERP) + 40% (Risk-Free Rate + BRP)

Which equals:

60% ERP + 40% BRP + 100% Risk-Free Rate

Similarly, the 90/60 portfolio becomes:

90% ERP + 60% BRP + 100% Risk-Free Rate

= 1.5x (60% ERP + 40% BRP) + 100% Risk-Free Rate

What about a 45% Stock / 30% Bond / 25% Cash portfolio?  No surprise:

30% ERP + 20% BRP + 100% Risk-Free Rate

= 0.5x (60% ERP + 40% BRP) + 100% Risk-Free Rate

Whether we’re holding cash, fully invested, or levered, all we are doing is scaling the risk premium exposure!  It is the returns in excess of the risk-free rate that matter.

The important implication here is that if we believe the levered portfolio is unattractive to invest in, it must also mean we believe the unlevered portfolio is unattractive to invest in.1  If 60% ERP + 40% BRP is negative, no amount of scaling up or down will change it; we’d be better off just holding cash.

The null hypothesis is that markets are efficient.

None of this negates the fact that an investor may hold the active view that intermediate- to long-term U.S. Treasuries are unattractive to hold relative to cash today.  Such a view, however, is not unique to a levered portfolio: it would affect levered and unlevered portfolios alike.  To remain consistent with such a view, an investor should sell down their long-duration bonds in preference for short-duration exposure, regardless of leverage.

The only point we will stress here is that we believe the prudent approach is to assume, as a null hypothesis, that markets are generally efficient.  After all, if everyone held the same active view that long duration bonds are currently unattractive, they would sell those bonds, driving up the yield until the point they are attractive.  If we believe markets are generally in equilibrium, the current long-term yield should be equally attractive as the short yield when appropriately adjusted for their risks.

How can that be the case when the short-term rate is higher than the long-term rate?  The pure expectations hypothesis states that the yield curve embeds the expected path of short rates.  It is important to remember that the expected return of a longer-dated Treasury should be compared to the expected return of a constantly rolled shorter-dated Treasury.  An inverted yield curve, then, expresses the aggregate view that short rates should be lower in the future, which would bring down the return of the constantly rolled short-rate series.

Nevertheless, if an investor does have an active view about the relative expected returns of short- versus longer-dated Treasuries, that view would be expressed regardless of whether the portfolio is levered or not.


In this note we have attempted to address the question as to whether return stackingTM still makes sense when the cost of financing goes up, particularly if we’re accessing that financing through longer-dated Treasury futures during an inverted yield curve environment.

We believe the answer is ‘yes’, and four key points help illustrate this fact.  First, philosophically, we care less about the specific asset we are levering than the make-up of the levered portfolio.  Second, in practice we want to choose an asset to lever that provides us with a cost of financing as close to the risk-free rate as possible.  Third, it is the return in excess of the risk-free rate that ultimately matters.  Finally, an active view about the relative attractiveness of Treasuries applies regardless of whether the portfolio is levered or not.

As a final point, we want to zoom out once more to emphasize the portfolio view.  Consider the investor who uses a 90/60 portfolio to free up capital, and that freed up capital is invested for alpha exposure.  Very frequently, alpha exposures are packaged in a way they provide cash plus alpha returns.  For example, a managed futures fund is effectively U.S. T-Bills plus the return of an active futures trading strategy.

Which means the cash positions effectively net out.  Assume we put 66.6% of our portfolio in a 90/60 and 33.3% of our portfolio in a managed futures fund.  If we x-ray the former position, we effectively have 60% stocks plus 40% bonds minus 33.3% U.S. T-Bills.  If we x-ray the latter, we effectively have 33.3% T-Bills plus 33.3% of the active futures strategy.  Taken together, we’re left with 60% stocks plus 40% bonds plus 33.3% of the active futures strategy.

More than anything, it’s the net portfolio allocation that matters.



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