Risk Management and Financial Institutions. Hull John C.

involves managing risks one by one. Risk aggregation involves relying on the power of diversification to reduce risks. Banks use both approaches to manage market risks. Credit risks have traditionally been managed using risk aggregation, but with the advent of credit derivatives the risk decomposition approach can be used.

      FURTHER READING

      Markowitz, H. “Portfolio Selection.” Journal of Finance 7, no. 1 (March 1952): 77–91.

      Ross, S. “The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory 13, no. 3 (December 1976): 341–360.

      Sharpe, W. “Capital Asset Prices: A Theory of Market Equilibrium.” Journal of Finance 19, no. 3 (September 1964): 425–442.

      Smith, C. W., and R. M. Stulz. “The Determinants of a Firm's Hedging Policy.” Journal of Financial and Quantitative Analysis 20 (1985): 391–406.

      Stulz, R. M. Risk Management and Derivatives. Mason, OH: South-Western, 2003.

      PRACTICE QUESTIONS AND PROBLEMS (ANSWERS AT END OF BOOK)

      1. An investment has probabilities 0.1, 0.2, 0.35, 0.25, and 0.1 of giving returns equal to 40 %, 30 %, 15 %, −5 %, and −15 %. What is the expected return and the standard deviation of returns?

      2. Suppose that there are two investments with the same probability distribution of returns as in Problem 1.1. The correlation between the returns is 0.15. What is the expected return and standard deviation of return from a portfolio where money is divided equally between the investments?

      3. For the two investments considered in Figure 1.2 and Table 1.2, what are the alternative risk-return combinations if the correlation is (a) 0.3, (b) 1.0, and (c) −1.0?

      4. What is the difference between systematic and nonsystematic risk? Which is more important to an equity investor? Which can lead to the bankruptcy of a corporation?

      5. Outline the arguments leading to the conclusion that all investors should choose the same portfolio of risky investments. What are the key assumptions?

      6. The expected return on the market portfolio is 12 % and the risk-free rate is 6 %. What is the expected return on an investment with a beta of (a) 0.2, (b) 0.5, and (c) 1.4?

      7. “Arbitrage pricing theory is an extension of the capital asset pricing model.” Explain this statement.

      8. “The capital structure decision of a company is a trade-off between bankruptcy costs and the tax advantages of debt.” Explain this statement.

      9. What is meant by risk aggregation and risk decomposition? Which requires an in-depth understanding of individual risks? Which requires a detailed knowledge of the correlations between risks?

      10. A bank's operational risk includes the risk of very large losses because of employee fraud, natural disasters, litigation, etc. Do you think operational risk is best handled by risk decomposition or risk aggregation? (Operational risk will be discussed in Chapter 23.)

      11. A bank's profit next year will be normally distributed with a mean of 0.6 % of assets and a standard deviation of 1.5 % of assets. The bank's equity is 4 % of assets. What is the probability that the bank will have a positive equity at the end of the year? Ignore taxes.

      12. Why do you think that banks are regulated to ensure that they do not take too much risk but most other companies (for example, those in manufacturing and retailing) are not?

      13. List the bankruptcy costs incurred by the company in Business Snapshot 1.1.

      14. The return from the market last year was 10 % and the risk-free rate was 5 %. A hedge fund manager with a beta of 0.6 has an alpha of 4 %. What return did the hedge fund manager earn?

      FURTHER QUESTIONS

      15. Suppose that one investment has a mean return of 8 % and a standard deviation of return of 14 %. Another investment has a mean return of 12 % and a standard deviation of return of 20 %. The correlation between the returns is 0.3. Produce a chart similar to Figure 1.2 showing alternative risk-return combinations from the two investments.

      16. The expected return on the market is 12 % and the risk-free rate is 7 %. The standard deviation of the return on the market is 15 %. One investor creates a portfolio on the efficient frontier with an expected return of 10 %. Another creates a portfolio on the efficient frontier with an expected return of 20 %. What is the standard deviation of the return on each of the two portfolios?

      17. A bank estimates that its profit next year is normally distributed with a mean of 0.8 % of assets and the standard deviation of 2 % of assets. How much equity (as a percentage of assets) does the company need to be (a) 99 % sure that it will have a positive equity at the end of the year and (b) 99.9 % sure that it will have positive equity at the end of the year? Ignore taxes.

      18. A portfolio manager has maintained an actively managed portfolio with a beta of 0.2. During the last year, the risk-free rate was 5 % and major equity indices performed very badly, providing returns of about −30 %. The portfolio manager produced a return of −10 % and claims that in the circumstances it was good. Discuss this claim.

      PART One

      Financial Institutions and Their Trading

      CHAPTER 2

      Banks

      The word “bank” originates from the Italian word “banco.” This is a desk or bench, covered by a green tablecloth, that was used several hundred years ago by Florentine bankers. The traditional role of banks has been to take deposits and make loans. The interest charged on the loans is greater than the interest paid on deposits. The difference between the two has to cover administrative costs and loan losses (i.e., losses when borrowers fail to make the agreed payments of interest and principal), while providing a satisfactory return on equity.

      Today, most large banks engage in both commercial and investment banking. Commercial banking involves, among other things, the deposit-taking and lending activities we have just mentioned. Investment banking is concerned with assisting companies in raising debt and equity, and providing advice on mergers and acquisitions, major corporate restructurings, and other corporate finance decisions. Large banks are also often involved in securities trading (e.g., by providing brokerage services).

      Commercial banking can be classified as retail banking or wholesale banking. Retail banking, as its name implies, involves taking relatively small deposits from private individuals or small businesses and making relatively small loans to them. Wholesale banking involves the provision of banking services to medium and large corporate clients, fund managers, and other financial institutions. Both loans and deposits are much larger in wholesale banking than in retail banking. Sometimes banks fund their lending by borrowing in financial markets themselves.

      Typically the spread between the cost of funds and the lending rate is smaller for wholesale banking than for retail banking. However, this tends to be offset by lower costs. (When a certain dollar amount of wholesale lending is compared to the same dollar amount of retail lending, the expected loan losses and administrative costs are usually much less.) Banks that are heavily involved in wholesale banking and may fund their lending by borrowing in financial markets are referred to as money center banks.

      This chapter will review how commercial and investment banking have evolved in the United States over the last hundred years. It will take a first look at the way the banks are regulated, the nature of the risks facing the banks, and the key role of capital in providing a cushion against losses.

      2.1 COMMERCIAL BANKING

      Commercial banking in virtually all countries has been subject to a great deal of regulation. This is because most national governments consider it important that individuals and companies have confidence in the banking system. Among the issues addressed by regulation is the capital that banks must keep, the activities they are allowed to engage in, deposit