FEW THINGS BETTER KNOW BEFORE BUYBACK 2 : RMSE as treasury market liquidity measure

Hu, Grace Xing, Jun Pan, and Jiang Wang. “Noise as Information for Illiquidity.” The Journal of Finance 68, no. 6 (December 2013): 2341–2382. https://doi.org/10.1111/jofi.12083

Intro

The level of liquidity in the aggregate financial market is closely connected to the amount of arbitrage capital available. Price deviations from the fundamental values will be largely eliminated by arbitrage forces. During market crises, however, capital becomes scarce and/or willingness to deploy capital diminishes. Thus, temporary price deviations, or “noise” in prices, being a key symptom of shortage in arbitrage capital, contains important information about the amount of liquidity in the aggregate market.

Why UST

We focus on the U.S. Treasury market for several reasons. First, it is by far the most important asset market in the world. Second, the U.S. Treasury market is one of the safest markets in the world, essentially free of credit risk. More importantly, the fundamental values of Treasuries are determined by a small number of factors. Thus, we can have a more reliable measure of price deviations. Third, the Treasuries market is one of the most active and liquid markets. A shortage of liquidity in this market provides a strong signal about liquidity in the overall market.

Construction

A. data selection

• CRSP Daily Treasury database
• Daily cross-sections of end-of-day bond prices from 1987 through 2009.
• Drop treasury securities with remaining maturities less than 1 month & longer than 10 years
• The cross-section varies over time, with a noticeable dip around late 1990s and early 2000s. This coincided with record surpluses of US government and the reduction of gross issuance of Treasury notes and bonds.

B. curve fitting

• Use a single parsimonious parametric function to describe the entire yield curve. (Svensson)
• Build instantaneous forward rate f

where m denotes the time to maturity, and b = (β1 β2 β3 τ1 τ2) are model parameters to be estimated. β0 represents the forward rate at infinitely long horizon, and β0 + β1 represents the forward rate at maturity zero. In addition, (β2, τ1) and (β3, τ2) control the “humps” of the forward rate curve.

• Using the parameterized forward curve, the zero-coupon yield curve can be derived by

• Use data in A. to back out the model parameters b. We choose the model parameters bt by minimizing the sum of the squared deviations between the actual prices and the model-implied prices:

Nt be the number of bonds and bills available on day t for curving fitting and let Pi,t , i = 1, . . .,Nt be their respective market observed prices. where Pi(b) is the model-implied price for bond i given model parameters b. On each day t, the end product of the curve fitting is therefore the vector of model parameters bt.

C. noise measure

• As a measure of dispersions in yields around the fitted yield curve, construct by calculating the root mean squared distance between the market yields and the model-implied yields.

Suppose that, on date t, there are Nt Treasury bonds with maturity between 1 and 10 years. For each of these Nt bonds, let yi,t denote its market observed yield, and let yi(bt) denote its model-implied yield.

Time-Series Properties

During normal times, the noise measure fluctuates around its time-series average of 3.32 basis points with a standard deviation of 1.65 basis points, and it is highly persistent, with a daily autocorrelation of 94.82%. This level of noise and its fluctuation is in fact comparable to the average spread between bid and ask yields of 2 basis points for the same sample of bonds.

Another interesting aspect captured by our noise measure is that while some liquidity Events are short lived, others take much longer to play out. Take Lehman default on September 15, 2008 as example, Figure 3 provides a closer examination of our noise measure during the period. It is worth emphasizing that our noise measure comes from the US Treasury bond market — the one with the highest credit and liquidity quality and is the number one safe haven during numerous episodes of “flight to quality,” and yet it was able to capture liquidity crises of varying origins and magnitudes. The drastic variation of our illiquidity measure over time, especially during crisis, suggests that it represents substantial market-wide liquidity risk.

One popular measure of liquidity with respect to the Treasury market is the on-the-run and off-the-run premium. Calculating the correlation between daily changes of our noise measure and daily changes of the on-the-run premium, we find that the correlation is 3.95% and 8.85%, respectively, for the five- and ten-year on-the-run premiums. Repeating the same calculation at a month frequency, the correlation increases to 27.73% and 37.49%, respectively. Overall, we see a positive relationship between our noise measure and the on-the-run premium. This accentuates the important fact that the information captured by our noise measure is a collective information over the entire yield curve.

VS. other Measures of Liquidity

Our results also show that factors known to be related to systematic liquidity have a significant relation with our noise measure. This includes the RefCorp spread used as a flight-to-liquidity premium by Longstaff (2004), the systematic liquidity factor in the US equity market by Pastor and Stambaugh (2003), and the CBOE VIX index. By contrast, term structure variables such as the short- and long-term interest rates and interest-rate volatility do not have strong explanatory power for the time-variation for our noise measure.

Others(omitted from abstract HERE)

Moreover, using noise measure as a priced risk factor helps explain cross-sectional returns on hedge funds and currency carry trades, both known to be sensitive to the general liquidity conditions of the market.

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