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

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

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

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

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?

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

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

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

CAPM Return to a portfolio is denoted by z, with Average return to the portfolio is Variance of the portfolio is

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

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

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

CAPM

Two fund theorem –Introduce possibility of borrowing or lending without risk –Example: T-bills –Let r f 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.

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 –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

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

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 r S -r f 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 r S Applications