PrefBlog

Joseph G. Haubrich, Peter H. Ritchken, George Pennacchi wrote a paper released in March 2009 titled Estimating Real and Nominal Term Structures Using Treasury Yields, Inflation, Inflation Forecasts, and Inflation Swap Rates:

This paper develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The term structures are driven by state variables that include the short term real interest rate, expected inflation, a factor that models the changing level to which inflation is expected to revert, as well as four volatility factors that follow GARCH processes. We derive analytical solutions for the prices of nominal bonds, inflation-indexed bonds that have an indexation lag, the term structure of expected inflation, and inflation swap rates. The model parameters are estimated using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. We find that allowing for GARCH effects is particularly important for real interest rate and expected inflation processes, but that long-horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were underpriced prior to 2004 but subsequently were valued fairly. We find that unexpected increases in both short run and longer run inflation implied by our model have a negative impact on stock market returns.

Of most interest to me is the conclusion on the inflation risk premium:

We can also examine how these risk premia varied over time during our sample period. Figure 8 plots expected inflation, the real risk premium, and the inflation risk premium for a 10-year maturity during the 1982 to 2008 period. Interestingly, while inflation expected over 10 years varied substantially, the levels of the real and inflation risk premia did not. The real risk premium for a 10-year maturity bond varied from 150 to 170 basis points, averaging 157 basis points. This real risk premium is consistent with the substantial slope of the real yield curve discussed earlier. The inflation risk premium for a 10-year maturity bond varied from 38 to 60 basis points and averaged 51 basis points. These estimates of the 10-year inflation risk premium fall within the range of those estimated by other studies.[Footnote]

Footnote: For example, a 10-year inflation risk premium averaging 70 basis points and ranging from 20 to 140 basis points is found by Buraschi and Jiltsov (2005). Using data on TIPS, Adrian and Wu (2008) find a smaller 10-year inflation risk premium varying between -20 and 20 basis points.

and

For example, D’Amico et al. (2008) find a large “liquidity premium” during the early years of TIPS’s existence, especially before 2004. They conclude that until more recently, TIPS yields were difficult to account for within a rational pricing framework. Shen (2006) also finds evidence of a drop in the liquidity premium on TIPS around 2004. He notes that this may have been due to the U.S. Treasury’s greater ssuance of TIPS around this time, as well as the beginning of exchange traded funds that purchased TIPS. Another contemporaneous development that may have led to more fairly priced TIPS was the establishment of the U.S. inflation swap market beginning around 2003. Investors may have arbitraged the underpriced TIPS by purchasing them while simultaneously selling inflation payments via inflation swap contracts.

and additionally:

Our estimated model also suggests that shocks to both short run and longer run inflation coincide with negative stock returns. An implication is that stocks are, at best, an imperfect hedge against inflation. This underscores the importance of inflation-linked securities as a means for safeguarding the real value of investments.

Joseph G. Haubrich of the Cleveland Fed provides a primer on the topic at A New Approach to Gauging Inflation Expectations, together with some charts:

The first chart is the model’s 1-month real interest rate

Click for big

 
Click for big

The methodology is used in the Cleveland Fed Estimates of Inflation Expectations:

The Federal Reserve Bank of Cleveland reports that its latest estimate of 10-year expected inflation is 1.53 percent. In other words, the public currently expects the inflation rate to be less than 2 percent on average over the next decade.

The Cleveland Fed’s estimate of inflation expectations is based on a model that combines information from a number of sources to address the shortcomings of other, commonly used measures, such as the “break-even” rate derived from Treasury inflation protected securities (TIPS) or survey-based estimates. The Cleveland Fed model can produce estimates for many time horizons, and it isolates not only inflation expectations, but several other interesting variables, such as the real interest rate and the inflation risk premium. For more detail, see the links in the See Also box at right.

On October 15, ten-year nominal treasuries yielded 2.50%, while 10-Year TIPS yielded 0.46%, so the Cleveland Fed has decomposed the Break-Even Inflation Rate of 204bp into 1.53% expected inflation and 0.51% Inflation Risk Premium.

I find myself in the uncomfortable position of being deeply suspicious of this decomposition without being able to articulate specific objections to the theory. The paper’s authors claim:

Comparing our model’s implied yields for inflation-indexed bonds to those of TIPS suggests that TIPS were underpriced prior to 2004 but more recently are fairly priced. Hence, the ‘liquidity premium’ in TIPS yields appears to have dissipated. The recent introduction of inflation derivatives, such as zero coupon inflation swaps, may have eliminated this mispricing by creating a more complete market for inflation-linked securities.

but I have great difficulty with the concept that there is no significant liquidity premium in TIPS. The estimation of the 1-month real rate looks way, way too volatile to me. I suspect that the answer to my problems is buried in the estimation methods between the market price of inflation swaps and the forecasts of estimated inflation, but I cannot find it … at least, not yet!

As reported by Bloomberg, David Easley, Marcos Mailoc Lopez de Prado and Maureen O’Hara have published a paper titled The Microstructure of the ‘Flash Crash’: Flow Toxicity, Liquidity Crashes and the Probability of Informed Trading:

The ‘flash crash’ of May 6th 2010 was the second largest point swing (1,010.14 points) and the biggest one-day point decline (998.5 points) in the history of the Dow Jones Industrial Average. For a few minutes, $1 trillion in market value vanished. In this paper, we argue that the ‘flash crash’ is the result of the new dynamics at play in the current market structure, not conjunctural factors, and therefore similar episodes are likely to occur again. We highlight the role played by order toxicity in affecting liquidity provision, and we provide compelling evidence that the collapse could have been anticipated with some degree of confidence given the increasing toxicity of the order flow in the hours and days prior to collapse. We also show that a measure of this toxicity, the Volume-Synchronized Probability of Informed Trading (the VPIN* informed trading metric), Granger-causes volatility, while the reciprocal is less likely, and that it takes on average 1/10 of a session’s volume for volatility to adjust to changes in the VPIN metric. We attribute this cause-effect relationship to the impact that flow toxicity has on market makers’ willingness to provide liquidity. Since the ‘flash crash’ might have been avoided had liquidity providers remained in the marketplace, a solution is proposed in the form of a ‘VPIN contract’, which would allow them to dynamically monitor and manage their risks.

They make the point:

Providing liquidity in a high frequency environment introduces new risks for market makers. When order flows are essentially balanced, high frequency market makers have the potential to earn razor thin margins on massive numbers of trades. When order flows become unbalanced, however, market makers face the prospect of losses due to adverse selection. The market makers’ estimate of the toxicity (the expected loss from trading with position takers) of the flow directed to them by position takers now becomes a crucial factor in determining their participation. If they believe that this toxicity is too high, they will liquidate their positions and leave the market.

In summary, we see three forces at play in the recent market structure:

• Concentration of liquidity provision into a small number of highly specialized firms.
• Reduced participation of retail investors resulting in increased toxicity of the flow received by market makers.
• High sensitivity of liquidity providers to intraday losses, as a result of the liquidity providers low capitalization, high turnover, increased competition and small profit target.

Quick! Sign up the big banks to provide liquidity through proprietary trading! Oh … wait ….

Further, they make the point about market-making:

To understand why toxicity of order flow can induce such behavior from market makers, let us return to the role that information plays in affecting liquidity in the market. Easley and O’Hara (1992) sets out the mechanism by which informed traders extract wealth from liquidity providers. For example, if a liquidity provider trades against a buy order he loses the difference between the ask price and the expected value of the contract if the buy is from an informed trader. On the other hand, he gains the difference between the ask price and the expected value of the contract if the buy is from an uninformed trader. This loss and gain, weighted by the probabilities of the trade arising from an informed trader or an uninformed trader just balance due to the intense competition between liquidity providers.

[Formula]

If flow toxicity unexpectedly rises (a greater than expected fraction of trades arises from informed traders), market makers face losses. Their inventory may grow beyond their risk limits, in which case they are forced to withdraw from the side of the market that is being adversely selected. Their withdrawal generates further weakness on that side of the market and their inventories keep accumulating additional losses. At some point they capitulate, dumping their inventory and taking the loss. In other words, extreme toxicity has the ability of transforming liquidity providers into liquidity consumers.

The earlier paper by these authors, detailing the calculation of VPIN, was titled Measuring Flow Toxicity in a High Frequency World:

Order flow is regarded as toxic when it adversely selects market makers, who are unaware that they are providing liquidity at their own loss. Flow toxicity can be expressed in terms of Probability of Informed Trading (PIN). We present a new procedure to estimate the Probability of Informed Trading based on volume imbalance (the VPIN* informed trading metric). An important advantage of the VPIN metric over previous estimation procedures comes from being a direct analytic procedure which does not require the intermediate estimation of non-observable parameters describing the order flow or the application of numerical methods. It also renders intraday updates mutually comparable in a frequency that matches the speed of information arrival (stochastic time clock). Monte Carlo experiments show this estimate to be accurate for all theoretically possible combinations of parameters, even for statistics computed on small samples. Finally, the VPIN metric is computed on a wide range of products to show that this measure anticipated the ‘flash crash’ several hours before the markets collapsed

Although the calibration is interesting and perhaps valuable, the underlying theory is pretty simple:

classify each transaction as buy or sell initiated:[Footnote]
a. A transaction i is a buy if either:
i. [Price increases], or
ii. [Price unchanged] and the [previous transaction] was also a buy.
b. Otherwise, the transaction is a sell.

Footnote: According to Lee and Ready (1991), 92.1% of all buys at the ask and 90.0% of all sells at the bid are correctly classified by this simple procedure. See Lee, C.M.C. and M.J. Ready (1991): “Inferring trade direction from intraday data”, The Journal of Finance, 46, 733-746. Alternative trade classification algorithms could be used.

and VPIN is simply the absolute value of the difference between buy-volume and sell-volume, expressed as a fraction of total volume. Yawn.

The VPIN indicator is very similar to Joe Granville’s Technical Analysis indicator On-Balance Volume. While Easley, Lopez de Prado and O’Hara have dressed it up with a little math and illustrated it in the glorious TA tradition of anecdotal cherry picking, they have neither provided anything particularly new nor proved their case.