Online Financial Intermediation. Types of Intermediaries Brokers –Match buyers and sellers...

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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
National Income by IndustryIndustry Billions of $
Agriculture, forestry and fishing 121.8Mining 45.2Construction 284.0Manufacturing  Durables 637.0Manufacturing  Nondurables 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
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
ValueAdded Intermediation
• Transformation functions– Continuing role for intermediaries (such as banks) that allow
transformation of asset structures• Changes in maturity (shortterm versus longterm 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
Asset Pricing
• Risk and Return– Stock prices move randomly
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
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
Asset Pricing
NN
N
N
VarN
xN
VarrVar
N
j
N
j
jt
N
j
jtt
2
2
2
1
22
12
1
1
1
1)(
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
Asset Pricing
N
jj
N
jj
N
jj
ijji
j
xN
x
xN
x
xN
x
xx
x
12
1
1
2
var1
var
1varvar
1
,cov
,0
Asset Pricing
jiij
jiijj
NN
N
x
1
1
and
1
Let
var
,correlated are returns Because
N
1j
22
N
1j
2N
1j
Asset Pricing
• Law of large numbers holds when =0– Independent returns
– Uncorrelated returns
– Hedging portfolios
xN
NNx
NNNN
x
var , as Clearly,
11var
11
var
Then
2
22
CAPM
• Capital Asset Pricing Model– Approximation assumption: returns are roughly normally
distributed
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
y
x
y
x
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
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
yx
yz
2222
2
22 yyxyyxyx yx
yz
yx
yzzV
CAPM
• Multiasset 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
CAPM
• As with the two asset case, yields a quadratic relationship between average return to the portfolio and its variance, which is called the meanvariance 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
CAPM
CAPM
• Two fund theorem– Introduce possibility of borrowing or lending without risk
– Example: Tbills
– Let rf denote the riskfree 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 riskfree rate. The portfolio S is called the market portfolio.
CAPM
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
CAPM
• Implications for asset market equilibrium– Riskaverse 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
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
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 rSrf is called the market risk premium since it measures the additional return over the riskfree rate required to get investors to hold the riskier market portfolio.
• Determining rS
• Applications
fSS
f rrrr
fSifi rrrr