A forecasting analysis of risk‐neutral equity and Treasury volatilities

• DOI: http://doi.org/10.1002/for.2591
• Author: Ana González‐Urteaga,Belén Nieto,Gonzalo Rubio
• Published date: 01 November 2019
• Date: 01 November 2019

RESEARCH ARTICLE

A forecasting analysis of risk‐neutral equity and Treasury

volatilities

Ana González‐Urteaga

1

| Belén Nieto

2

| Gonzalo Rubio

3

1

Department of Business Management,

Universidad Pública de Navarra and

Institute for Advanced Research in

Business and Economics, INARBE

Campus Arrosadía, 31006 Pamplona,

Spain

2

Department of Financial Economics and

Accounting, Universidad de Alicante, San

Vicente del Raspeig, 03690 Alicante, Spain

3

Department of Economics and Business,

Universidad CEU Cardenal Herrera,

Reyes Católicos 19, 03204 Elche, Alicante,

Spain

Correspondence

Gonzalo Rubio, Department of Economics

and Business, Universidad CEU Cardenal

Herrera, Reyes Católicos 19, 03204 Elche,

Alicante, Spain.

Email: gonzalo.rubio@uch.ceu.es

Funding information

Generalitat Valenciana, Grant/Award

Number: Prometeo/2017/158; UPNA

Research Grant for Young Researchers,

Edition 2018, Grant/Award Number:

UPNA 2018; Bank of Spain, Grant/Award

Number: 2016‐18; Ministry of Economics

and Competitiveness, Grant/Award Num-

bers: ECO2015‐67035‐P and ECO2016‐

77631‐R

Abstract

This paper employs equity (VIX) and Treasury (MOVE) risk‐neutral volatilities

to assess their relative forecasting performance with respect to future real activ-

ity, stock and Treasury excess returns, and aggregate risk factors. The in‐

sample evidence suggests that the square of VIX tends to dominate the square

of MOVE. Out‐of‐sample predictive analysis, performed as a horse race

between equity and Treasury risk‐neutral volatilities, shows that, contrary to

earlier results, the square of VIX and MOVE tend to complement each other.

KEYWORDS

forecasting real activity, predictability of asset returns, risk‐neutral equity volatility, risk‐neutral

treasury volatility

JEL CLASSIFICATION

C53; G12; G13

1|INTRODUCTION

The VIX index is the risk‐neutral one‐month expected

stock market volatility for the S&P 500 Index. It is com-

puted by averaging the weighted prices of puts and calls

on the S&P 500 Index over a wide range of strike prices.

It has become an extremely popular and useful measure

of near‐term market volatility. It is surprising that the

large extant literature on implied volatility focuses almost

exclusively on equity markets.

1

Indeed, by noting the lack of evidence on the relative

importance of risk‐neutral equity and Treasury

volatilities, the main contribution of this paper is to par-

tially fill this gap by analyzing the forecasting perfor-

mance of both types of risk‐neutral volatility.

Specifically, we perform an in‐sample, and a competing

out‐of‐sample forecasting analysis between VIX and the

Treasury risk‐neutral volatility regarding future real

1

Notable exceptions are Choi et al. (2017) and Mueller et al. (2016), who

analyze market variance risk premium in both equity and Treasury mar-

kets, and Mele, Obayashi, and Shalen (2015), who study the information

contained in the VIX and the interest rate swap rate volatility index

known as SRVX.

Received: 15 October 2018 Revised: 22 February 2019 Accepted: 8 March 2019

DOI: 10.1002/for.2591

Journal of Forecasting. 2019; :681–698. © 2019 John Wiley & Sons, Ltd.wileyonlinelibrary.com/journal/for

681

38

activity, as well as future financial returns. This may be

especially informative given the recent findings of

González‐Urteaga, Nieto, and Rubio (2018). These

authors study the connectedness dynamics between both

types of risk‐neutral volatility, and show that most of the

time, but especially during bad economic times, the Trea-

sury risk‐neutral volatility is a net sender of volatility to

VIX. They also detect that both monetary policy and eco-

nomic drivers explain the spillover dynamics between the

two risk‐neutral volatilities.

We use the Merrill Lynch Option Volatility

Estimate Index (MOVE), as Treasury implied volatility.

This is a term structure index of the normalized implied

volatility on one‐month Treasury options that are

weighted on 2‐,5‐,10‐, and 30‐year contracts. It is

therefore the equivalent of the VIX for Treasury bond

returns and reflects a market‐based measure of uncer-

tainty about the composite future behavior of interest

rates across different maturities of the yield curve.

Current increases in MOVE suggests that the market is

willing to pay more to hedge against unexpected

movements in interest rates.

Given the evidence reported by Adrian, Crump, and

Vogt (2017) on the importance of nonlinearities, our

analysis of forecasting employs the square of VIX

and MOVE rather than the volatilities themselves.

The in‐sample relative forecasting ability of VIX

2

and

MOVE

2

suggests that VIX

2

tends to dominate MOVE

2

in

both real activity and financial returns. However, it is

important to recall that González‐Urteaga et al. (2018)

show that MOVE is a net contributor of volatility to

VIX. This transmitted information may help VIX improve

its forecasting capacity for future output and financial

returns.

On the other hand, the out‐of‐sample forecasting

improvement of VIX

2

over MOVE

2

and vice versa is

mixed when predicting real activity, the stock market,

or Treasury bond returns. Both VIX

2

and MOVE

2

complement each other in our forecasting exercises.

However, VIX

2

tends to outperform MOVE

2

when

forecasting aggregate risk factors on an out‐of‐

sample basis.

This paper proceeds as follows. Section 2 presents a

brief discussion of the behavior of VIX and MOVE

and describes the data employed in the analysis.

Section 3 describes the decomposition of VIX and MOVE

into their uncertainty and risk aversion components.

Section 4 describes the in‐sample predictive ability of

equity and Treasury risk‐neutral volatilities, while

Section 5 contains the out‐of‐sample forecasting analysis.

Finally, Section 6 presents our conclusions. The online

Appendix contains detailed out‐of‐sample forecasting

results.

2|DATA AND A PRELIMINARY

ANALYSIS OF VIX AND MOVE

We collect daily and monthly data for VIX and MOVE

from April 4, 1988 to October 5, 2017, where monthly

data refer to the last trading day of each month through-

out the sample period.

2

Figure 1 shows annualized daily behavior of VIX and

MOVE. As expected, risk‐neutral volatilities are counter-

cyclical, and spikes during economic crises are much

larger in equity than in Treasury volatilities. On a daily

basis, the minimum (9.2%) and maximum (80.9%) levels

for VIX were reached on October 5, 2017 and November

20, 2008, respectively, whereas for MOVE the minimum

(4.7%) and maximum (26.5%) were observed on August

7, 2017 and October 10, 2008, respectively. Figure 2

displays monthly volatility of both risk‐neutral volatilities

estimated with daily data within each month in our

sample. This is a measure of financial uncertainty in the

equity and Treasury bond markets, respectively. As

expected, VIX seems to be much more volatile than

MOVE with much larger spikes during times of bad

economic news.

Table 1 contains summary statistics for VIX and

MOVE obtained from monthly data from April 1988 to

September 2017 using observations on the last day of

each month. Over the full sample period, average risk‐

neutral volatility for the stock market is 19.5%, whereas

the risk‐neutral volatility for Treasuries is much lower

at 9.7%. VIX is also much more volatile than MOVE,

and accordingly, the range between the minimum and

maximum values is from 9.5% to 59.9% for VIX and

4.8% to 21.4% for MOVE.

3

VIX presents much higher pos-

itive skewness and kurtosis than MOVE. Finally, both

implied volatilities are highly persistent with autocorrela-

tion coefficients of 0.84 and 0.85 for VIX and MOVE,

respectively.

We next describe the data used in our forecasting anal-

ysis. All the competing or control variables that we employ

together with VIX and MOVE have been shown to be

2

VIX was downloaded from www.cboe.com and MOVE from

Bloomberg. Since MOVE is available from April 1988, we employ VXO

(risk‐neutral market volatility for the U.S. S&P 100 Index) from April

1988 to December 1989. Starting January 2003, the CBOE launched

the 10‐year Treasury Note Volatility Index (TYVIX), which measures a

constant 30‐day risk‐neutral expected volatility on 10‐year Treasury

Note futures prices. Given that MOVE is available for a much longer

sample period, this research employs MOVE rather than TYVIX. The

correlation between both series using monthly data (quoted at the last

day of each month) from January 2003 to September 2017 is 0.953.

3

To be precise, the coefficients of variation are 0.38 and 0.27 for VIX and

MOVE, respectively.

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