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Online Financial Intermediation

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  1. Online Financial Intermediation

  2. 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

  3. Size of the Financial Sector

  4. 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

  5. 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

  6. Asset Pricing • Risk and Return • Stock prices move randomly

  7. 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

  8. 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?

  9. Asset Pricing

  10. 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

  11. Asset Pricing

  12. Asset Pricing

  13. Asset Pricing • Law of large numbers holds when =0 • Independent returns • Uncorrelated returns • Hedging portfolios

  14. CAPM • Capital Asset Pricing Model • Approximation assumption: returns are roughly normally distributed

  15. 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

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

  17. 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

  18. 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

  19. 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

  20. CAPM

  21. CAPM • Two fund theorem • Introduce possibility of borrowing or lending without risk • Example: T-bills • Let rfdenote 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.

  22. CAPM

  23. 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

  24. 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

  25. 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

  26. 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-rfis 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