EFA Bergen 2009

The Joint Pricing of Volatility and Liquidity F. Bandi, C. Moise & J. Russell Discussion

Andrea Vedolin [email protected] 22nd August 2009

Discussion EFA, Bandi, Moise & Russell – 1

Summary of the

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Main Idea Comments Suggestions Bibliography

Summary of the Paper

Discussion EFA, Bandi, Moise & Russell – 2

This Paper .... Summary of the Paper Main Idea

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Comments Suggestions

This paper tackles an important question: Are volatility and liquidity systematic risk factors , and if yes, are they jointly priced?

Bibliography

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A vast literature has studied the impact of market volatility on the cross-section of stock returns (see Ang, Hodrick, Xing, and Zhang, 2006 and Adrian and Rosenberg, 2008, among many others).

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Another strand of literature shows that (il)liquidity is a systematic risk factor which affects cross-sectional stock returns (see Pastor and Stambaugh, 2003 and Acharya and Pedersen, 2005, among many others).

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This paper unifies these two strands of the literature by studying jointly market volatility and illiquidity using ETFs on the SPDRs.

Discussion EFA, Bandi, Moise & Russell – 3

Methodological Contribution Summary of the Paper Main Idea

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The paper contributes in a methodological way by introducing two novel proxies for market volatility and illiquidity.

Comments Suggestions

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The optimally sampled “realized variance” is defined as:

Bibliography

★

𝑉ˆ =

𝑀𝑡 ∑

2 𝑟˜𝑗𝛿 ,

where 𝑀 ★ =

𝑗=1

( ∫1

𝜎 4 𝑑𝑠 0 𝑠 2 2

(𝐸(𝜖 ))

)

and 𝑀 ★ is the optimal number of observations per day according to the mean squared error criterion and can be interpreted as a signal-to-noise ratio. 𝛿/𝑀 ★ is the optimal frequency at which intra-daily returns are observed. □

The aggregate illiquidity is computed from the deviation variance: ∑ 𝑀𝑡 2 ˜𝑗𝛿 𝑗=1 𝑟 𝑀𝑡

Discussion EFA, Bandi, Moise & Russell – 4

Methodological Contribution Summary of the Paper Main Idea

⊳

The paper contributes in a methodological way by introducing two novel proxies for market volatility and illiquidity.

Comments Suggestions

□

The optimally sampled “realized variance” is defined as:

Bibliography

★

𝑉ˆ =

𝑀𝑡 ∑

2 𝑟˜𝑗𝛿 ,

where 𝑀 ★ =

𝑗=1

( ∫1

𝜎 4 𝑑𝑠 0 𝑠 2 2

(𝐸(𝜖 ))

)

and 𝑀 ★ is the optimal number of observations per day according to the mean squared error criterion and can be interpreted as a signal-to-noise ratio. 𝛿/𝑀 ★ is the optimal frequency at which intra-daily returns are observed. □

The aggregate illiquidity is computed from the deviation variance: ∑ 𝑀𝑡 2 ˜𝑗𝛿 𝑗=1 𝑟 𝑀𝑡

Discussion EFA, Bandi, Moise & Russell – 4

Methodological Contribution Summary of the Paper Main Idea

⊳

The paper contributes in a methodological way by introducing two novel proxies for market volatility and illiquidity.

Comments Suggestions

□

The optimally sampled “realized variance” is defined as:

Bibliography

★

𝑉ˆ =

𝑀𝑡 ∑

2 𝑟˜𝑗𝛿 ,

where 𝑀 ★ =

𝑗=1

( ∫1

𝜎 4 𝑑𝑠 0 𝑠 2 2

(𝐸(𝜖 ))

)

and 𝑀 ★ is the optimal number of observations per day according to the mean squared error criterion and can be interpreted as a signal-to-noise ratio. 𝛿/𝑀 ★ is the optimal frequency at which intra-daily returns are observed. □

The aggregate illiquidity is computed from the deviation variance: ∑ 𝑀𝑡 2 ˜𝑗𝛿 𝑗=1 𝑟 𝑀𝑡

Discussion EFA, Bandi, Moise & Russell – 4

Findings Summary of the Paper Main Idea

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Comments

Using the two proxies for market volatility and illiquidity, the paper finds that ...

Suggestions Bibliography

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... in individual regressions, illiquidity and market volatility shocks are negatively correlated with market returns and size and book-to-market sorted portfolios.

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... in joint regressions, shocks to volatility drive out shocks to illiquidity. Shocks to volatility provide a more accurate assessment of risk.

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... the results hold with respect to different illiquidity measures.

Discussion EFA, Bandi, Moise & Russell – 5

Summary of the Paper

⊳ Comments Comments SPDRs RV Joint Reg TS JointReg CS Suggestions Bibliography

Comments

Discussion EFA, Bandi, Moise & Russell – 6

Comments Summary of the Paper Comments Comments SPDRs RV Joint Reg TS JointReg CS

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Suggestions

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Divergence from fundamental value

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Robustness of the Results ...

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What is the economic story behind it?

Bibliography

 The Nature of SPDRs & Dividend Yield  with respect to the market volatility measure  with respect to the assumption of the conditional mean  Sentiment  Uncertainty

Discussion EFA, Bandi, Moise & Russell – 7

Comments Summary of the Paper Comments Comments SPDRs RV Joint Reg TS JointReg CS

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Suggestions

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Divergence from fundamental value

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Robustness of the Results ...

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What is the economic story behind it?

Bibliography

 The Nature of SPDRs & Dividend Yield  with respect to the market volatility measure  with respect to the assumption of the conditional mean  Sentiment  Uncertainty

Discussion EFA, Bandi, Moise & Russell – 7

Comments Summary of the Paper Comments Comments SPDRs RV Joint Reg TS JointReg CS

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Suggestions

□

Divergence from fundamental value

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Robustness of the Results ...

□

What is the economic story behind it?

Bibliography

 The Nature of SPDRs & Dividend Yield  with respect to the market volatility measure  with respect to the assumption of the conditional mean  Sentiment  Uncertainty

Discussion EFA, Bandi, Moise & Russell – 7

Comments Summary of the Paper Comments Comments SPDRs RV Joint Reg TS JointReg CS

⊳

Suggestions

□

Divergence from fundamental value

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Robustness of the Results ...

□

What is the economic story behind it?

Bibliography

 The Nature of SPDRs & Dividend Yield  with respect to the market volatility measure  with respect to the assumption of the conditional mean  Sentiment  Uncertainty

Discussion EFA, Bandi, Moise & Russell – 7

Comments Summary of the Paper Comments Comments SPDRs RV Joint Reg TS JointReg CS

⊳

Suggestions

□

Divergence from fundamental value

□

Robustness of the Results ...

□

What is the economic story behind it?

Bibliography

 The Nature of SPDRs & Dividend Yield  with respect to the market volatility measure  with respect to the assumption of the conditional mean  Sentiment  Uncertainty

Discussion EFA, Bandi, Moise & Russell – 7

SPDRs and Dividend Yield Summary of the Paper Comments Comments SPDRs RV Joint Reg TS JointReg CS

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Suggestions Bibliography

In addition to the level of fundamental risk, a security’s dividend yield affects the magnitude of mispricing. Dividend payments reduce the capital necessary for the arbitrage position and thus, holding costs (see Pontiff, 1996). A dividend is not subject to mispricing even when a security is, because when a dividend is paid, investors receive its full amount. Securities with large dividend yields have less mispricing because holding costs are lower. To appropriately compare the SPDR price with its fundamental, the SPDRs price has to be adjusted by deducting the dividend accumulated since the last ex-dividend date from the SPDR price. 500−𝑆𝑃 𝑌 ) Z If mispricing is (𝑆𝑃 𝑆𝑃 500∗100 , then I find that using an adjusted SPDRs price yields me an almost 20% mispricing (using daily prices and dividend information from CRSP).

Ackert and Tian (2000) find a miniscule mispricing discount in SPDRs, moreover, it is not economically significant. Whereas, the discount for MidCap SPRDRs is nine times higher. Discussion EFA, Bandi, Moise & Russell – 8

Using Different Measures of RV, I find ... To test the robustness of the results, I employ three different measures of market volatility: □ High Frequency data: 1. Square root of the sum of squared 5 minute log returns on the S&P 500 index over a month (Andersen et al., 2003) 2. TSRV of S&P 500 returns (Corsi, 2009) □ Forward-looking measure of volatility:

1. VIX I run regressions as in equation (21) in the paper using squared 5 min returns: 𝑀 𝐾𝑇 (𝑡) =

0.039 0.225 0.472 𝑉 − 𝑉 (𝑡 − 1) + 𝜖ˆ (𝑡) + 𝑢 ˆ(𝑡), (3.70) (−3.37) (4.97)

using TSRV: 𝑀 𝐾𝑇 (𝑡) =

0.039 0.251 0.768 𝑉𝑇 𝑆𝑅𝑉 − 𝑉𝑇 𝑆𝑅𝑉 (𝑡 − 1) + 𝜖ˆ (𝑡) + 𝑢 ˆ(𝑡). (3.85) (−3.50) (6.38)

using the VIX: 𝑀 𝐾𝑇 (𝑡) =

0.023 0.069 0.838 − 𝑉𝑉 𝐼𝑋 (𝑡 − 1) − 𝜖ˆ𝑉𝑉 𝐼𝑋 (𝑡) + 𝑢 ˆ(𝑡). (2.68) (−1.71) (−11.63) Discussion EFA, Bandi, Moise & Russell – 9

And in the Joint Regressions, I find that ... As a check I also ran equation (22), I obtain the same signs. More importantly using TSRV, the joint regression yields me: 𝑀 𝐾𝑇 (𝑡) =

0.065 0.449 0.011 0.758 𝑉 − 𝑉 (𝑡 − 1) + 𝑃 𝑆(𝑡 − 1) + 𝜖ˆ (𝑡) (5.64) (−5.29) (0.25) (8.18) 0.158 𝑃 𝑆 𝜖ˆ (𝑡) + 𝑢 ˆ(𝑡). + (3.52)

Running the same equation with the VIX and innovations in the VIX, I get: 𝑀 𝐾𝑇 (𝑡) =

0.015 0.028 0.046 0.800 − 𝑉 (𝑡 − 1) + 𝑃 𝑆(𝑡 − 1) − 𝜖ˆ𝑉 (𝑡) (1.72) (−0.63) (1.18) (−10.95) 0.095 𝑃 𝑆 + 𝜖ˆ (𝑡) + 𝑢 ˆ(𝑡). (2.30)

The estimated coefficients of the innovations in liquidity are still highly statistically significant !

Discussion EFA, Bandi, Moise & Russell – 10

And in the Cross-Section? Size-Sorted Portfolios: Squared Returns

BM-Sorted Portfolios: Squared Returns

1

0.5

0.8

0.4

0.6

0.3

0.4

0.2

0.2

0.1

0

0.4

1 2 3 4 5 6 7 8 9 10

Size-Sorted Portfolios: VIX

0.3

0

0.15

1 2 3 4 5 6 7 8 9 10

BM-Sorted Portfolios: VIX

0.1

0.2 0.05 0.1 0

0 −0.1

1 2 3 4 5 6 7 8 9 10

−0.05

1 2 3 4 5 6 7 8 9 10

! Using size-sorted portfolios, I find the “same” pattern. However, ... % the estimated coefficients have a positive sign for almost all portfolios. % more importantly, the estimated coefficients for the liquidity innovations remain statistically significant across all size and book-to-market sorted portfolios.

Discussion EFA, Bandi, Moise & Russell – 11

And in the Cross-Section? Size-Sorted Portfolios: Squared Returns

BM-Sorted Portfolios: Squared Returns

1

0.5

0.8

0.4

0.6

0.3

0.4

0.2

0.2

0.1

0

0.4

1 2 3 4 5 6 7 8 9 10

Size-Sorted Portfolios: VIX

0.3

0

0.15

1 2 3 4 5 6 7 8 9 10

BM-Sorted Portfolios: VIX

0.1

0.2 0.05 0.1 0

0 −0.1

1 2 3 4 5 6 7 8 9 10

−0.05

1 2 3 4 5 6 7 8 9 10

! Using size-sorted portfolios, I find the “same” pattern. However, ... % the estimated coefficients have a positive sign for almost all portfolios. % more importantly, the estimated coefficients for the liquidity innovations remain statistically significant across all size and book-to-market sorted portfolios.

Discussion EFA, Bandi, Moise & Russell – 11

And in the Cross-Section? Size-Sorted Portfolios: Squared Returns

BM-Sorted Portfolios: Squared Returns

1

0.5

0.8

0.4

0.6

0.3

0.4

0.2

0.2

0.1

0

0.4

1 2 3 4 5 6 7 8 9 10

Size-Sorted Portfolios: VIX

0.3

0

0.15

1 2 3 4 5 6 7 8 9 10

BM-Sorted Portfolios: VIX

0.1

0.2 0.05 0.1 0

0 −0.1

1 2 3 4 5 6 7 8 9 10

−0.05

1 2 3 4 5 6 7 8 9 10

! Using size-sorted portfolios, I find the “same” pattern. However, ... % the estimated coefficients have a positive sign for almost all portfolios. % more importantly, the estimated coefficients for the liquidity innovations remain statistically significant across all size and book-to-market sorted portfolios.

Discussion EFA, Bandi, Moise & Russell – 11

Summary of the Paper Comments

⊳ Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions Bibliography

Suggestions

Discussion EFA, Bandi, Moise & Russell – 12

Suggestions Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Robustness with respect to different measures of market volatility: Z An alternative way to construct a factor that mimics volatility risk is to directly construct a traded asset that reflects only volatility risk. Coval and Shumway (2001) construct market-neutral straddle positions using index options. Z Using ...

! High-frequency data: TSRV (Corsi, 2009) ! Forward-looking measure: VIX (Ang et. al., 2006).

Z Distinguish between long-run and short-run components of volatility (see, e.g., Adrian and Rosenberg, 2008).

Discussion EFA, Bandi, Moise & Russell – 13

Suggestions Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Robustness with respect to different measures of market volatility: Z An alternative way to construct a factor that mimics volatility risk is to directly construct a traded asset that reflects only volatility risk. Coval and Shumway (2001) construct market-neutral straddle positions using index options. Z Using ...

! High-frequency data: TSRV (Corsi, 2009) ! Forward-looking measure: VIX (Ang et. al., 2006).

Z Distinguish between long-run and short-run components of volatility (see, e.g., Adrian and Rosenberg, 2008).

Discussion EFA, Bandi, Moise & Russell – 13

Suggestions Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Robustness with respect to different measures of market volatility: Z An alternative way to construct a factor that mimics volatility risk is to directly construct a traded asset that reflects only volatility risk. Coval and Shumway (2001) construct market-neutral straddle positions using index options. Z Using ...

! High-frequency data: TSRV (Corsi, 2009) ! Forward-looking measure: VIX (Ang et. al., 2006).

Z Distinguish between long-run and short-run components of volatility (see, e.g., Adrian and Rosenberg, 2008).

Discussion EFA, Bandi, Moise & Russell – 13

Suggestions Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Robustness with respect to different measures of market volatility: Z An alternative way to construct a factor that mimics volatility risk is to directly construct a traded asset that reflects only volatility risk. Coval and Shumway (2001) construct market-neutral straddle positions using index options. Z Using ...

! High-frequency data: TSRV (Corsi, 2009) ! Forward-looking measure: VIX (Ang et. al., 2006).

Z Distinguish between long-run and short-run components of volatility (see, e.g., Adrian and Rosenberg, 2008).

Discussion EFA, Bandi, Moise & Russell – 13

Suggestions cont’d Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Robustness with respect to different conditional means of 𝑉 : 𝑉 is highly serially correlated in your series but seems stationary. Ang et al. (2006) use difference in volatility. Z My findings indicate that the signs of estimated coefficients depend crucially on the number of lags included in the estimation. Z Use an information criterion such as BIC or AIC to determine the optimal number of lags in the AR specification.

Discussion EFA, Bandi, Moise & Russell – 14

Suggestions cont’d Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Robustness with respect to different conditional means of 𝑉 : 𝑉 is highly serially correlated in your series but seems stationary. Ang et al. (2006) use difference in volatility. Z My findings indicate that the signs of estimated coefficients depend crucially on the number of lags included in the estimation. Z Use an information criterion such as BIC or AIC to determine the optimal number of lags in the AR specification. Robustness with respect to time period: Harvey (1989), Whitelaw (1994), and Lettau and Ludvigson (2004) among many more, show that the risk-return relation may be time-varying. Z Run rolling regressions.

Discussion EFA, Bandi, Moise & Russell – 14

Suggestions cont’d Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

Better disentangle the exposure of liquidity risk to volatility risk: The unconditional correlation between 𝐼𝑉 and 𝐼𝐹 𝑉 is almost 60%. This is huge! The unconditional correlation in my data, depending on the volatility measure is between 9% (sum squared returns) and 19% (VIX). To better disentangle the effect in the cross-section, rather measure the exposure to risk than a regression on the risk attributes themselves: ① Sort stocks into five quintiles based on historical 𝑉 betas. ② Within each quintile, sort stocks into five quintiles based on their past 𝛽𝑉 coefficient loading. These portfolios are rebalanced monthly and value weighted. These portfolios will account for the spreads in average returns of high 𝛽𝐿𝑖𝑞 portfolios. ZIf the spread (high size or book-to-market portfolio return minus low) of this portfolio sorting yields a similar pattern as in a sorting without sorting, then one could argue that liquidity does not account for the difference in the returns. Discussion EFA, Bandi, Moise & Russell – 15

What’s the Economic Story behind it? Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

“ [...] it would seem relevant to ask whether their individual explanatory power is subsumed in a model which allows for the other proxy to be present.” p. 2, Bandi, Moise, and Russell I suggest two different paths: ① PDR Services Corporation, 1996: “since SPDRs trade in an open auction market on the floor of the American Stock Exchange, prices are affected by supply and demand as well as market volatility, sentiment and other factors ”. Z Use consumer sentiment data from University of Michigan webpage. ② Routledge and Zin (2004) propose a model to study the impact of Knightian uncertainty on liquidity risk in times of economic crises. Uncertainty also impacts on the market volatility. Z Use mean absolute difference of forecasts about future GDP standardized by consensus estimate available from BlueChip Economic Indicators. Discussion EFA, Bandi, Moise & Russell – 16

What’s the Economic Story behind it? Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

⊳

Bibliography

“ [...] it would seem relevant to ask whether their individual explanatory power is subsumed in a model which allows for the other proxy to be present.” p. 2, Bandi, Moise, and Russell I suggest two different paths: ① PDR Services Corporation, 1996: “since SPDRs trade in an open auction market on the floor of the American Stock Exchange, prices are affected by supply and demand as well as market volatility, sentiment and other factors ”. Z Use consumer sentiment data from University of Michigan webpage. ② Routledge and Zin (2004) propose a model to study the impact of Knightian uncertainty on liquidity risk in times of economic crises. Uncertainty also impacts on the market volatility. Z Use mean absolute difference of forecasts about future GDP standardized by consensus estimate available from BlueChip Economic Indicators. Discussion EFA, Bandi, Moise & Russell – 16

What’s the Economic Story behind it? Summary of the Paper Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

⊳

Bibliography

“ [...] it would seem relevant to ask whether their individual explanatory power is subsumed in a model which allows for the other proxy to be present.” p. 2, Bandi, Moise, and Russell I suggest two different paths: ① PDR Services Corporation, 1996: “since SPDRs trade in an open auction market on the floor of the American Stock Exchange, prices are affected by supply and demand as well as market volatility, sentiment and other factors ”. Z Use consumer sentiment data from University of Michigan webpage. ② Routledge and Zin (2004) propose a model to study the impact of Knightian uncertainty on liquidity risk in times of economic crises. Uncertainty also impacts on the market volatility. Z Use mean absolute difference of forecasts about future GDP standardized by consensus estimate available from BlueChip Economic Indicators. Discussion EFA, Bandi, Moise & Russell – 16

The Joint Pricing of Volatility, Liquidity and Uncertainty?

Constant Dib GDP

Volatility

Volatility

Liq

Liq

MrkExret

MrkExret

MrkExret

0.092★★★ (3.52) 0.212★★★ (4.23)

0.018 (0.30)

−0.081★★★ (-2.77) 0.104★★ (2.37)

0.008 (0.12)

−0.001 (-0.08) -0.081 (-0.09)

0.024 (1.20) -0.719 (-0.91)

0.001★ (1.67)

Sentiment

0.001★★★ (2.99)

-0.004 (-0.53)

Volatility

0.053 (0.83)

Liquidity 𝜖DiB

−3.502★★ (-2.28) 0.076 (0.75)

𝜖Vol 𝜖Liq Adjusted 𝑅2

0.11

0.05

0.02

-0.00

0.03

0.015 (0.29) −2.871★ (-1.91)

0.161★★★ (2.93) 0.07

−2.555★ (-1.75) -0.002 (-0.02) 0.155★★★ (2.79) 0.06

□

Sentiment is not statistically significant for liquidity and market excess returns.

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Innovations in volatility are not statistically significant in the presence of market uncertainty.

Discussion EFA, Bandi, Moise & Russell – 17

Conclusions Summary of the Paper

The paper ...

Comments Suggestions Choice of RV Conditional Mean Vol & Liq Economics Conclusions

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Bibliography

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ask an important question

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is well executed and ...

However, □

Since you are claiming that these are general results, convince the reader that this is the case

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Give more economic content.

Discussion EFA, Bandi, Moise & Russell – 18

Summary of the Paper Comments Suggestions

⊳ Bibliography Bibliography

Bibliography

Discussion EFA, Bandi, Moise & Russell – 19

Bibliography Summary of the Paper Comments Suggestions Bibliography Bibliography

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Ackert, L. F., and Y. S. Tian (2000): “Arbitrage and Valuation in the Market for Standard and Poor’s Depository Receipts,” Financial Management, 29, p. 71 – 88. Adrian, T., and J. Rosenberg (2008): “Stock Returns and Volatility: Pricing the Short-Run and Long-Run Components of Market Risk,” Journal of Finance, 63, p. 2997 – 3030. Amihud, Y., and H. Mendelson (1991): “Liquidity, Maturity, and the Yields on the U.S. Treasury Securities,” Journal of Finance, 4, p. 1411 – 1425. Ang, A., R. J. Hodrick, Y. Xing, and X. Zhang (2006): “The Cross-Section of Volatility and Expected Returns,” Journal of Finance, 61, p. 259 – 299. Bali, T., and L. Peng (2006): “Is There a Risk-Return Tradeoff? Evidence from High-Frequency Data,” Journal of Applied Econometrics, 21, p. 1169–1198. Basu, D., and L. Martellini (2008): “Total Volatility and the Cross Section of Expected Stock Returns,” Working Paper, EDHEC. Chua, C. T., J. Goh, and Z. Zhang (2008): “Expected Volatility, Unexpected Volatility, and the Cross-section of Stock Returns,” forthcoming, Journal of Financial Research. Corsi, F. (2009): “A Simple Approximate Long-Memory Model of Realized Volatility,” Journal of Financial Econometrics, 9, p. 174 – 196. Coval, J., and T. Shumway (2001): “Expected Option Returns,” Journal of Finance, 56, p. 983–1009. Ghysels, E., P. Santa-Clara, and R. Valkanov (2005): “There Discussion EFA, Bandi, Moiseis&aRussell – 20 Risk-Return Tradeoff After All,” Journal of Financial Economics, 76, p. 509 –