online financial intermediation

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Online Financial Intermediation

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Online Financial Intermediation. Types of Intermediaries. Brokers Match buyers and sellers Retailers Buy products from sellers and resell to buyers Transformers Buy products and resell them after modifications Information brokers Sell information only. Size of the Financial Sector. - PowerPoint PPT Presentation

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Page 1: Online Financial Intermediation

Online Financial Intermediation

Page 2: Online Financial Intermediation

Types of Intermediaries

• Brokers– Match buyers and sellers

• Retailers– Buy products from sellers and resell to buyers

• Transformers– Buy products and resell them after modifications

• Information brokers– Sell information only

Page 3: Online Financial Intermediation

Size of the Financial Sector

National Income by IndustryIndustry Billions of $

Agriculture, forestry and fishing 121.8Mining 45.2Construction 284.0Manufacturing - Durables 637.0Manufacturing - Non-durables 444.4Transportation and Public Utilities 477.6Wholesale Trade 351.4Retail Trade 510.7Finance, insurance and real estate 1047.5Services 1458.3Government 846.8Total Domestic 6224.7Source: Survey of Current Business, Feb. 1997

Page 4: Online Financial Intermediation

Transactional Efficiencies

• Phases of Transaction– Search

• Automation efficiencies• Fewer constraints on search with wider scope

– Negotiation• Online price discovery

– Settlement• Efficiencies associated with electronic clearing of transactions

• Automation and expansion will increase competition among intermediaries, reducing the impact of existing gatekeepers

Page 5: Online Financial Intermediation

Value-Added Intermediation

• Transformation functions– Continuing role for intermediaries (such as banks) that allow

transformation of asset structures• Changes in maturity (short-term versus long-term borrowing and lending

activities)• Volume transformation (aggregation of savings for provision of large loans)

• Information Brokerage– Importance of information in evaluation of risk and uncertainty– Enhancements on the internet: EDGAR (Electronic Data Gathering,

Analysis and Retrieval)• Online database with all SEC filings and analysis of publicly available

information

Page 6: Online Financial Intermediation

Asset Pricing

• Risk and Return– Stock prices move randomly

Page 7: Online Financial Intermediation

Asset Pricing

• Diversification and the law of large number– Model returns as a stochastic process– N assets, j=1,2,…,N– Simple model with AR(1) returns:

– Special case with =0: IID returns

10

1,,,0 2

1

ttj

xxj

t

jt

jt

jt

Page 8: Online Financial Intermediation

Asset Pricing

• Construct a portfolio consisting of 1/N shares of each stock– Payoff to the portfolio is the average return

– We measure the risk associated with the portfolio as simply the variance (or standard deviation of the returns).

• Risk of any given asset will be 2

• What is the risk of the average portfolio?

N

j

jt

N

j

jtt N

xN

r11

11

Page 9: Online Financial Intermediation

Asset Pricing

NNN

N

VarN

xN

VarrVar

N

j

N

j

jt

N

j

jtt

2

2

2

1

22

12

1

1

1

1)(

Page 10: Online Financial Intermediation

Asset Pricing

• It now follows that for independent random processes, the variance of the average goes to zero as the number of stocks in the portfolio goes to infinity

• Law of Large Numbers• Result depends critically on the independence assumption

– Example with correlated returns – Extreme case occurs when all returns are identical ex ante as well

as ex post

Page 11: Online Financial Intermediation

Asset Pricing

N

jj

N

jj

N

jj

ijji

j

xN

x

xN

x

xN

x

xx

x

12

1

1

2

var1var

1varvar

1

,cov

,0

Page 12: Online Financial Intermediation

Asset Pricing

jiij

jiijj

NN

N

x

11

and

1Let

var

,correlated are returns Because

N

1j

22

N

1j

2N

1j

Page 13: Online Financial Intermediation

Asset Pricing

• Law of large numbers holds when =0– Independent returns– Uncorrelated returns– Hedging portfolios

xNNN

x

NNNN

x

var , as Clearly,

11var

11var

Then

2

22

Page 14: Online Financial Intermediation

CAPM

• Capital Asset Pricing Model– Approximation assumption: returns are roughly normally

distributed

Page 15: Online Financial Intermediation

CAPM

• Normal distribution characterized by two parameters: mean and variance (i.e. return and risk)

• Holding different combinations (portfolios) of assets affects the possible combinations of return and risk an investor can obtain

• 2 asset model =proportion of stock 1 held in portfolio– 1-=proportion of stock 2 held in portfolio– Joint distribution of the returns on the two stocks

2

2

,yxy

xyx

yx

yx

Page 16: Online Financial Intermediation

CAPM

• Return to a portfolio is denoted by z, with

• Average return to the portfolio is

• Variance of the portfolio is

yxz 1

yxEz 1

xyyxzV 121 2222

Page 17: Online Financial Intermediation

CAPM

• We can derive the relationship between the mean of the portfolio and its variance by noting that

• Substituting for in the expression for the variance of the portfolio, we find

• To portfolio spreadsheet

yxyz

22222

22 yyxyyxyx yxyz

yxyzzV

Page 18: Online Financial Intermediation

CAPM

• Multi-asset specification– Choose portfolio which minimizes the variance of the portfolio

subject to generating a specified average return– Have to perform the optimization since you can no longer solve

for the weights from the specification of the relationship between the averages

N

jj

N

jjj xz

1

1

1

where

Page 19: Online Financial Intermediation

CAPM

• As with the two asset case, yields a quadratic relationship between average return to the portfolio and its variance, which is called the mean-variance frontier– Frontier indicates possible combinations of risk and return

available to investors when they hold efficient portfolios (i.e. those that minimize the risk associated with getting a specific return

– Optimal portfolio choice can be determined by confronting investor preferences for risk versus return with possibilities

Page 20: Online Financial Intermediation

CAPM

Page 21: Online Financial Intermediation

CAPM

• Two fund theorem– Introduce possibility of borrowing or lending without risk– Example: T-bills– Let rf denote the risk-free rate of return

• Historically, around 1.5%– The two fund theorem then states that there exists a portfolio of

risky assets (which we will denote by S) such that all efficient combinations or risk and return (i.e. those which minimize risk for a given rate of return) can be obtained by putting some fraction of wealth in S while borrowing or lending at the risk-free rate. The portfolio S is called the market portfolio.

Page 22: Online Financial Intermediation

CAPM

Page 23: Online Financial Intermediation

CAPM

• Implications of the two fund theorem for asset prices– In equilibrium, asset prices will adjust until all portfolios lie on the

security market line

Page 24: Online Financial Intermediation

CAPM

• Implications for asset market equilibrium– Risk-averse investors require higher returns to compensate for

bearing increased risk– Idiosyncratic risk versus market risk– Equilibrium risk vs. return relationships

• Market risk of asset i is defined as the ratio of the covariance between asset i and the market portfolio to the variance of the market portfolio

2S

iSi

Page 25: Online Financial Intermediation

CAPM

• Since iS=iS i S (where iS is the correlation coefficient between asset i and the market portfolio S), we can write

• Finally, since the returns on all assets must be perfectly correlated with those on the market portfolio (in equilibrium), we know that iS=1, so that

S

iiS

S

ii

S

ii

Page 26: Online Financial Intermediation

CAPM

• Since the equation for the market line is

it follows that the predicted equilibrium return on a given asset i will be

• The term rS-rf is called the market risk premium since it measures the additional return over the risk-free rate required to get investors to hold the riskier market portfolio.

• Determining rS

• Applications

fSS

f rrrr

fSifi rrrr