Understanding the "warp" in long-term Treasuries

A common point of confusion for many investors is the distinction between average maturity and effective duration, two metrics that are often used interchangeably but serve very different roles in a portfolio. Average maturity represents the weighted average of the time remaining until the bonds in a fund reach their final payment date. Effective duration, however, measures the fund's actual price sensitivity to interest rate changes. For a fund like the Vanguard Long-Term Treasury ETF (VGLT), this gap is significant. As of early 2026, VGLT carries a weighted average maturity of approximately 21.90 years, yet its effective duration sits lower at roughly 14.10 years. (See figure below. Data source: Vanguard.) This occurs because the semi-annual coupon payments "shorten" the economic life of the investment, meaning you recover your capital faster than the final maturity date suggests.

The primary reason to understand the difference between these measures is to predict how your principal will react to a changing rate environment. The mathematical relationship is inverse: when interest rates go down, the principal value of the bond fund goes up. Using VGLT’s current effective duration of 14.10 as a guide, we can quantify this "warp" in value. If the 10-year and 30-year Treasury yields were to drop by 1% (100 basis points), the share price of VGLT would be expected to rise by approximately 14.10%. This leveraged-like sensitivity is exactly why long-term Treasuries are favored by those looking to hedge against economic slowdowns, as the price appreciation can be substantial during a "flight to safety."

This distinction is the cornerstone of sophisticated bond investing and the reason why this post is important. If an investor looks only at the 21.9-year maturity of VGLT, they might overestimate the time their capital is locked away or the immediate volatility of the fund. Conversely, failing to account for the 14.10 duration means ignoring the precise tool used to calculate risk. By understanding that effective duration is the "speedometer" of one’s bond portfolio’s price movement, one can better position their assets to benefit from shifting yields rather than being caught off guard by them. (Disclosure: the author owns VGLT shares at the time of this writing.)

How much do long Treasuries increase with each 1% decrease in the 10-year Treasury yield?

The figure below shows five values of the TLT exchange-traded fund, which tracks the value of Treasury bonds with maturities of 20 years or more (i.e., long Treasuries), and of the corresponding 10-year Treasury yields. The latter, 10-year Treasury yields, are highly correlated, in a lagged way, with the Federal Funds rate. This rate is set by the Fed.

As you can see from the best fitting line equation, there is an increase of approximately 19 points in the value of the TLT for each 1% decrease in the 10-year Treasury yields. So, if the Federal Funds rate us expected to go down, the gain likely to be obtained by investing in long Treasuries in quite attractive. The video linked below provides a brief discussion on this a few other related issues.

Understanding the price of bitcoin: Data from early 2019 to mid-2020

Summary

- We conducted a multivariate analysis of the price of bitcoin with financial data from early 2019 to mid-2020.

- Our main conclusion is that bitcoin should do well in what we could call a “nervous bull market”.

- In this scenario, we would see the market generally going up, with some expectation of inflation in the future, all of this against a bearish backdrop.

The analysis

We used WarpPLS () to create several second-order indices (as composites of first-order index funds) and link them in an exploratory model to help us understand what has been driving the price of bitcoin from early 2019 to mid-2020.

The period from early 2019 to mid-2020 was used because prior to it bitcoin was generally perceived as a cash-like currency that could be used for day-to-day transactions among individuals and organizations. From early 2019 onwards, the perception shifted to one of a store of value; something akin to “digital gold”.

We collected and analyzed daily data from various funds. More specifically, the price of one share of each fund at each day’s close was used. In terms of WarpPLS settings, the outer model analysis algorithm used was “PLS Regression”, and the default inner model analysis algorithm was “Linear”. The composite variables were made up of the following funds.

- FIN, reflecting a bullish view of financial institutions, was made up of the iShares U.S. Regional Banks ETF (IAT), and the Financial Select Sector SPDR Fund (XLF).

- HDG, reflecting a bearish view of the market (intention to hedge), was made up of the iShares Silver Trust (SLV), the SPDR Gold Shares (GLD), and the iShares 20+ Year Treasury Bond ETF (TLT).

- MKT, reflecting a bullish view of the market, was made up of the SPDR S&P 500 ETF Trust (SPY), and the Invesco QQQ Trust (QQQ).

- GBTC, reflecting the price of bitcoin, was measured through a single indicator, namely the Grayscale Bitcoin Trust (GBTC).

The Grayscale Bitcoin Trust (GBTC) provides one of the most straightforward ways for investors to own bitcoin. It is generally available to retail investors through various online brokers.

The results

The figure below shows our model with the main results. The iGBTC variable is an instrumental variable that controls for the effect of “time” on the results; to account for autoregression, or the fact that the variable GBTC is influenced by its own values back in time. The instrument used was a numeric variable generated based on the date associated with each data point. In a previous analysis published on this blog, based on the same data, we did not employ this type of control, which led to slightly different results.

The path coefficients (indicated as beta coefficients) reflect the strength of the relationships; they are a bit like standard univariate (or Pearson) correlation coefficients, except that they take into consideration multivariate relationships (they control for competing effects). A positive beta means that an increase in a variable is associated with an increase in the variable that it points to.

The P values indicate the statistical significance of the relationship; a P lower than 0.05 means a significant relationship (95 percent or higher likelihood that the relationship is “real”). The R-squared value reflects the percentage of explained variance for the variable in question; the higher it is, the better the model fit with the data.

I should note that the P values have been calculated using a nonparametric technique, which does not require the assumption that the data is normally distributed to be met. This is good, because I checked the data, and it does not look like it is normally distributed. 

So, what does the model above tell us? It tells us that: 

- As a bullish view of financial institutions (FIN) increases, the price of bitcoin (GBTC) also increases, in a statistically significant way (beta=0.13; P below .01). This is not normally what one would expect, if we assume that bitcoin’s success means the failure of financial institutions.

- As a bearish view of the market (HDG) increases, the price of bitcoin (GBTC) also increases, in a statistically significant way (beta=0.42; P below .01). This is what one would expect, if we assume that bitcoin is used as a hedge against a drop in the market. Note that this effect is the strongest in the model, by far.

- As a bullish view of the market (MKT) increases, the price of bitcoin (GBTC) also increases, in a statistically significant way (beta=0.17; P below .01). Again, this is not normally what one would expect, if we assume that bitcoin’s success means that a bear market is under way.

The three predictors above (i.e., FIN, HDG, and MKT) explain 33 percent of the variance in the variable GBTC (R-squared=0.33). This essentially means that the model is incomplete, although it does explain enough of the variance in GBTC to be useful in an exploration of major influences on the price of bitcoin.

Main conclusion

While the results above may look contradictory, they in fact suggest that bitcoin should do well in what we could call a “nervous bull market”. Here we would see the market generally going up, with some expectation of inflation in the future (which tends to be good for financials), all of this against a generally bearish backdrop.

Disclosure

The author does not own bitcoin at the time of this writing.