Social Networks, Information Acquisition, and Asset Prices

20155149 배상윤

20091530 김현우

Contents

1. Introduction

2. Model Description

3. Analysis

(i) Exogenous information case

(ii) Endogenous information case

4. Empirical prediction

5. Case study

6. Conclusion

1. Introduction

• Financial market consists of two types of asset, which is risk-free asset (bond) and risky asset (stock)

• Market information is important to risk aversion traders to determine investment in risky asset

• When some traders get information about stock market, they exchange it within their group

1. Introduction

• Social network influences the market informativeness, and its ‘Network connectedness’ plays a significant role in the stock market

–Market efficiency

–Cost of capital

–Market liquidity

–Market volume

1. Introduction

• Existing literature argue that increasing network connectedness provide positive effect to financial market

• This paper reveals, when information is expensive, increasing network connectedness can be harmful to financial market. (free-riding problem)

2. Model

In our model there consist of two types of traders:

• Rational traders

– Rational traders makes decision weather to invest in stock market through analysis of market information

• Noise traders

– Noise traders invest regardless to the stock market information, so stock supply of noise trader degrades the value of information

2. Model

N = no. of traders in each

group

μ = fraction of informed

traders

N = 5

μ = 0.4

Groups of rational traders

2. Model

N = no. of traders in each

group

μ = fraction of informed

traders

N = 10

μ = 0.4

Groups of rational traders

2. Model Description

Notations and assumptions

• Uncertain payoff of risky asset

• Stock supplied by noise trader

• Risk-aversion coefficient

2. Model Description

– When Informed traders receive

information about the payoff and noise

2. Model Description

– Uninformed traders also receives signals

and additional noise when they get

information from informed traders

2. Model Description

Price function :

Information contained in the price :

• 𝛼0, 𝛼𝑣, 𝛼𝑥 = Coefficient

• Market efficiency, Liquidity, and Cost of capital can be measured by equations above (Trade volume verified by numeric study)

3. Analysis

Information contained in the price :

• Conditional on 𝑣, 𝜃 is normally distributed with mean 𝑣 and precision 𝜌𝜃

• 𝜌𝜃, or equivalently 𝛼𝑣/𝛼𝑥 reflects the price-informativeness which measure Market efficiency (Ozsoylev and Walden, 2010 and Peress, 2010)

3. Analysis

Ozsoylev, H., and J. Walden. 2010. Asset Pricing in Large Information Networks. Forthcoming at Journal of Economic Theory.

Peress, J. 2010. Product Market Competition, Insider Trading, and Stock Market Efficiency. Journal of Finance 65: 1—43.

Price function :

• 𝛼𝑥 means effect of noise trade on price, and more liquid markets have smaller 𝛼𝑥

• Measure of Market liquidity : 1/𝛼𝑥

3. Analysis

Cost of capital : expected return from holding the risky asset can be defined as following (Easley and O’Hara ,2004)

3. Analysis

Easley, D., and M. O’Hara. 2004. Information and the Cost of Capital. Journal of Finance 59: 1553-1584.

Trade volume can be defined by following equation, but the complexity of term preclude simple analysis. So this paper use intuition and numerical study to investigate

3. Analysis

• When the cost of information is low, the fraction of informed traders (μ) is not sensitive to network connectedness – μ can be regarded to exogenous (fixed)

• When the cost of information is sufficiently high, fraction of informed traders (μ) varies by network connectedness – μ is endogenous(variable)

3. Analysis

Proposition 1

The price function above satisfy market clearing condition (equilibrium) with exogenous μ where

3. Analysis - Exogenous case

• By Proposition 1,

and

• Increasing N -> increasing 𝜌𝜃 -> Market efficiency ↑

• Sharing information among more friends causes more information to be impounded into the price, thereby improving informational efficiency

3. Analysis - Exogenous case

• By Proposition 1,

and

• Increasing N -> decreasing -> Cost of capital ↓

• Less uncertainty makes more demand of stock, so equilibrium price is increased and cost of capital decreased

• Increase of social network empower price informativeness and stock become less risky > cost of capital ↓

3. Analysis - Exogenous case

• By Proposition 1,

and

• where

• where , increasing N -> Market liquidity ↑

3. Analysis - Exogenous case

Proposition 2

When the information structure is exogenous, increasing connectedness

of networks will improve market efficiency, and lower cost of capital.

and also improve market liquidity if and only if satisfying following

condition:

3. Analysis - Exogenous case

• When network connectedness (N ) is increased, direct information

sharing among friends and the market efficiency are improved, and

risk faced by rational traders is decreased. So that they will trade stock

more aggressively and average Trade volume will be increased

3. Analysis - Exogenous case

Numerical result

Market measuring factors

with various N

(Exogenous case)

3. Analysis - Exogenous case

• When μ fraction of traders have already purchased the private signal, uninformed traders consider whether purchase information with price c and it’s expected benefit can be expressed to following equation (Grossman and Stiglitz ,1980)

And it can be approximated to

3. Analysis – Endogenous case

Grossman, S., and J. Stiglitz. 1980. On the Impossibility of Informationally Efficient Markets. American Economic Review 70: 393-408.

Proposition 3 : when , there is a unique

equilibrium fraction ( : ) of informed traders given by

and 𝜇∗ is decreased when network connectedness (N) increased

3. Analysis – Endogenous case

• Condition from Proposition 3 ( ) is

equivalent to , otherwise, expected benefit of

purchasing information is positive value when no one is informed and

negative value when everyone is informed

3. Analysis – Endogenous case

• When equilibrium ( ), and it can be

derived to

• By the expression of 𝜇∗ in proposition 3, when N increased, will be

increased and will decreased to hold above equation

• Increasing N -> decreasing -> Market efficiency ↓

3. Analysis – Endogenous case

• By the same reason with exogenous case,

if and only if

• However, in endogenous condition, will be decreased when N is increased

• Where , increasing N -> Market liquidity ↓ ( )

3. Analysis – Endogenous case

• By the Proposition 3, and it is

denominator of (measure of Cost of capital)

• When N increase, 𝜇∗ will be decreased by proposition 3 and also

will be decreased

• Increasing network connectedness will decrease 𝜇∗ and it leads to higher average

risk to trader -> Cost of capital ↑

3. Analysis – Endogenous case

Proposition 4 : when , increasing the

connectedness N of social network will harm market efficiency and

raise the cost of capital. And also reduce liquidity when

3. Analysis – Endogenous case

• According to proposition 4, increasing network connectedness will

cause traders to trade stock less aggressively, so the average Trade

volume will be decreased

3. Analysis – Endogenous case

3. Analysis – Endogenous case

Numerical result

(a) Expected benefit of

additional information

with various μ

(Endogenous case)

(b) 𝜇∗ with various N

(Endogenous case)

3. Analysis – Endogenous case

Numerical result

Market measuring factors

with various N

(Endogenous case)

• Two cases:

–When the cost of acquiring information is low (Exogenous case)

Increasing N

-> (Market efficiency ↑, Cost of Capital ↓, Liquidity ↑, Volume ↑)

–When the cost of acquiring information is sufficiently high (Endogenous case)

Increasing N

-> (Market efficiency ↓, Cost of Capital ↑, Liquidity ↓, Volume ↓)

4. Empirical prediction

4. Empirical prediction

• Prediction 1

(a) For firms with low information acquisition cost, the cost of capital is significantly negatively related to network connectedness.

(b) For firms with high information acquisition cost, the cost of capital is significantly positively related to network connectedness.

4. Empirical prediction

• Case for (b)

‒ stocks in regions with low population density tend to have higher prices.

Low population density = N ↓ 𝜇∗ ↑

(Market efficiency ↑, Cost of Capital ↓, Liquidity ↑, Volume ↑)

4. Empirical prediction

• Prediction 2

(a) For firms with low information acquisition cost, market efficiency is higher when there are more social communications among their investors.

(b) For firms with high information acquisition cost, market efficiency is lower when there are more social communications among their investors.

5. Case study : Why Korean stock market is so unstable?

• High population density N ↑

• High usage of social network services N ↑

• How to measure cost of information?

- Number of analysts following the firm

- Dispersion of analyst forecasts

- Analyst forecast error

• Another relevant measure of the cost for investors to be informed is the amount of media coverage

5. Case study : Why Korean stock market is so unstable?

• By Thompson Reuter, information correctness about profit of company from Korea analyst was 81% which is 36th

place in 45 countries

• This rate is lower than average of 45 countries (91%)

• this result suggest that information cost in Korea is very high

5. Case study : Why Korean stock market is so unstable?

3) http://www.newsis.com/ar_detail/view.html?ar_id=NISX20140205_0012702256&cID=10104&pID=10100, last accessed at 2015.05.27

2) http://www.mt.co.kr/view/mtview.php?type=1&no=2014012418105330075&outlink=1, last accessed at 2015.05.27

1) http://www.businesspost.co.kr/news/articleView.html?idxno=3316 , last accessed at 2015.05.27

1)

2)

3)

• Korean stock market matches our endogenous case (c↑)

• In this environment, high connectedness of Korea can be harmful

5. Case study : Why Korean stock market is so unstable?

4) http://news.kbs.co.kr/news/NewsView.do?SEARCH_NEWS_CODE=3085783, last accessed at 2015.05.27

3) http://daily.hankooki.com/lpage/column/201410/dh20141022140821141170.htm, last accessed at 2015.05.27

2) http://article.joins.com/news/article/article.asp?total_id=17168172, last accessed at 2015.05.27

1) http://lady.khan.co.kr/khlady.html?mode=view&code=10&artid=201502031108491, last accessed at 2015.05.27

1)

2)

3)

4)

1)

5. Conclusion

• Existing literatures have been argued that network connectedness is helpful for stock market

• However, network connectedness is harmful for stock market in specific condition (high information cost)

• Information cost reflect correctness, stability, availability of information. If they can be improved, well-connected network environment will significantly improve stock market performance.

5. Conclusion

Candidates of further research topic

• In financial market, elapsed time of information is very critical problem

• In this research, information does not be depreciated by time

• If elapsed time factor added on this model, the result can be significantly closer to real financial market

5. Conclusion

Candidates of further research topic

• Social network do not have single-connection only

• When someone give second information providing, their noise will be exponentially increase and model will be changed

• Expanding research to this reliable social network condition can significantly derive it to real industry implication

5. Conclusion

Candidates of further research topic

• In this model, noise from user identically distributed

• However, in networks, level of noise can be vary depending on nodes

• Like information transmission study, smart-user (the node reducing noise) also can be applied to this model

References

• Han, Bing, and Liyan Yang. "Social networks, information acquisition, and asset prices." Management Science 59.6 (2013): 1444-1457.

• Ozsoylev, H., and J. Walden. 2010. Asset Pricing in Large Information Networks. Forthcoming at Journal of Economic Theory.

• Peress, J. 2010. Product Market Competition, Insider Trading, and Stock Market Efficiency. Journal of Finance 65: 1-43.

• Easley, D., and M. O’Hara. 2004. Information and the Cost of Capital. Journal of Finance 59: 1553-1584.

• Grossman, S., and J. Stiglitz. 1980. On the Impossibility of Informationally Efficient Markets. American Economic Review 70: 393-408.

• http://www.businesspost.co.kr/news/articleView.html?idxno=3316 , last accessed at 2015.05.27

• http://www.mt.co.kr/view/mtview.php?type=1&no=2014012418105330075&outlink=1, last accessed at 2015.05.27

• http://www.newsis.com/ar_detail/view.html?ar_id=NISX20140205_0012702256&cID=10104&pID=10100, last accessed at 2015.05.27

• http://lady.khan.co.kr/khlady.html?mode=view&code=10&artid=201502031108491, last accessed at 2015.05.27

• http://article.joins.com/news/article/article.asp?total_id=17168172, last accessed at 2015.05.27

• http://daily.hankooki.com/lpage/column/201410/dh20141022140821141170.htm, last accessed at 2015.05.27

• http://news.kbs.co.kr/news/NewsView.do?SEARCH_NEWS_CODE=3085783, last accessed at 2015.05.27