Chapter 01 - The Investment Environment CHAPTER 1: THE INVESTMENT ENVIRONMENTPROBLEM SETS1. Ultimately, it is true that real assets determine the material well being of an economy. Nevertheless, individuals can benefit when financial engineering creates new products that allow them to manage their portfolios of financial assets more efficiently. Because bundling and unbundling creates financial products with new properties and sensitivities to various sources of risk, it allows investors to hedge particular sources of risk more efficiently.2. Securitization requires access to a large number of potential investors. To attract these investors, the capital market needs: (1) a safe system of business laws and low probability of confiscatory taxation/regulation; (2) a well-developed investment banking industry; (3) a well-developed system of brokerage and financial transactions, and; (4) well-developed media, particularly financial reporting. These characteristics are found in (indeed make for) a well-developed financial market.3. Securitization leads to disintermediation; that is, securitization provides a means for market participants to bypass intermediaries. For example, mortgage-backed securities channel funds to the housing market without requiring that banks or thrift institutions make loans from their own portfolios. As securitization progresses, financial intermediaries must increase other activities such as providing short-term liquidity to consumers and small business, and financial services.4. Financial assets make it easy for large firms to raise the capital needed to finance their investments in real assets. If General Motors, for example, could not issue stocks or bonds to the general public, it would have a far more difficult time raising capital. Contraction of the supply of financial assets would make financing more difficult, thereby increasing the cost of capital. A higher cost of capital results in less investment and lower real growth. 1-1

Chapter 01 - The Investment Environment5. Even if the firm does not need to issue stock in any particular year, the stock market is still important to the financial manager. The stock price provides important information about how the market values the firm's investment projects. For example, if the stock price rises considerably, managers might conclude that the market believes the firm's future prospects are bright. This might be a useful signal to the firm to proceed with an investment such as an expansion of the firm's business. In addition, the fact that shares can be traded in the secondary market makes the shares more attractive to investors since investors know that, when they wish to, they will be able to sell their shares. This in turn makes investors more willing to buy shares in a primary offering, and thus improves the terms on which firms can raise money in the equity market.6. a. Cash is a financial asset because it is the liability of the federal government. b. No. The cash does not directly add to the productive capacity of the economy. c. Yes. d. Society as a whole is worse off, since taxpayers, as a group will make up for the liability.7. a. The bank loan is a financial liability for Lanni. (Lanni's IOU is the bank's financial asset.) The cash Lanni receives is a financial asset. The new financial asset created is Lanni's promissory note (that is, Lanni’s IOU to the bank). b. Lanni transfers financial assets (cash) to the software developers. In return, Lanni gets a real asset, the completed software. No financial assets are created or destroyed; cash is simply transferred from one party to another. c. Lanni gives the real asset (the software) to Microsoft in exchange for a financial asset, 1,500 shares of Microsoft stock. If Microsoft issues new shares in order to pay Lanni, then this would represent the creation of new financial assets. d. Lanni exchanges one financial asset (1,500 shares of stock) for another ($120,000). Lanni gives a financial asset ($50,000 cash) to the bank and gets back another financial asset (its IOU). The loan is \"destroyed\" in the transaction, since it is retired when paid off and no longer exists. 1-2

Chapter 01 - The Investment Environment8. a. Assets Liabilities & Shareholders’ equity Cash $ 70,000 Bank loan $ 50,000 Computers 30,000 Shareholders’ equity 50,000 Total $100,000 Total $100,000 Ratio of real assets to total assets = $30,000/$100,000 = 0.30b. Assets Liabilities & Shareholders’ equity Software product* $ 70,000 Bank loan $ 50,000 Computers 30,000 Shareholders’ equity 50,000 Total $100,000 Total $100,000 *Valued at cost Ratio of real assets to total assets = $100,000/$100,000 = 1.0c. Assets Liabilities & Shareholders’ equity Microsoft shares $120,000 Bank loan $ 50,000 Computers 30,000 Shareholders’ equity 100,000 Total $150,000 Total $150,000 Ratio of real assets to total assets = $30,000/$150,000 = 0.20 Conclusion: when the firm starts up and raises working capital, it is characterized by a low ratio of real assets to total assets. When it is in full production, it has a high ratio of real assets to total assets. When the project \"shuts down\" and the firm sells it off for cash, financial assets once again replace real assets.9. For commercial banks, the ratio is: $107.5/$10,410.9 = 0.010 For non-financial firms, the ratio is: $13,295/$25,164 = 0.528 The difference should be expected primarily because the bulk of the business of financial institutions is to make loans; which are financial assets for financial institutions.10. a. Primary-market transaction b. Derivative assets c. Investors who wish to hold gold without the complication and cost of physical storage. 1-3

Chapter 01 - The Investment Environment11. a. A fixed salary means that compensation is (at least in the short run) independent of the firm's success. This salary structure does not tie the manager’s immediate compensation to the success of the firm. However, the manager might view this as the safest compensation structure and therefore value it more highly.b. A salary that is paid in the form of stock in the firm means that the manager earns the most when the shareholders’ wealth is maximized. This structure is therefore most likely to align the interests of managers and shareholders. If stock compensation is overdone, however, the manager might view it as overly risky since the manager’s career is already linked to the firm, and this undiversified exposure would be exacerbated with a large stock position in the firm.c. Call options on shares of the firm create great incentives for managers to contribute to the firm’s success. In some cases, however, stock options can lead to other agency problems. For example, a manager with numerous call options might be tempted to take on a very risky investment project, reasoning that if the project succeeds the payoff will be huge, while if it fails, the losses are limited to the lost value of the options. Shareholders, in contrast, bear the losses as well as the gains on the project, and might be less willing to assume that risk.12. Even if an individual shareholder could monitor and improve managers’ performance, and thereby increase the value of the firm, the payoff would be small, since the ownership share in a large corporation would be very small. For example, if you own $10,000 of GM stock and can increase the value of the firm by 5%, a very ambitious goal, you benefit by only: 0.05 × $10,000 = $500 In contrast, a bank that has a multimillion-dollar loan outstanding to the firm has a big stake in making sure that the firm can repay the loan. It is clearly worthwhile for the bank to spend considerable resources to monitor the firm.13. Mutual funds accept funds from small investors and invest, on behalf of these investors, in the national and international securities markets. Pension funds accept funds and then invest, on behalf of current and future retirees, thereby channeling funds from one sector of the economy to another. Venture capital firms pool the funds of private investors and invest in start-up firms. Banks accept deposits from customers and loan those funds to businesses, or use the funds to buy securities of large corporations.14. Treasury bills serve a purpose for investors who prefer a low-risk investment. The lower average rate of return compared to stocks is the price investors pay for predictability of investment performance and portfolio value. 1-4

Chapter 01 - The Investment Environment15. With a “top-down” investing style, you focus on asset allocation or the broad composition of the entire portfolio, which is the major determinant of overall performance. Moreover, top-down management is the natural way to establish a portfolio with a level of risk consistent with your risk tolerance. The disadvantage of an exclusive emphasis on top- down issues is that you may forfeit the potential high returns that could result from identifying and concentrating in undervalued securities or sectors of the market. With a “bottom-up” investing style, you try to benefit from identifying undervalued securities. The disadvantage is that you tend to overlook the overall composition of your portfolio, which may result in a non-diversified portfolio or a portfolio with a risk level inconsistent with your level of risk tolerance. In addition, this technique tends to require more active management, thus generating more transaction costs. Finally, your analysis may be incorrect, in which case you will have fruitlessly expended effort and money attempting to beat a simple buy-and-hold strategy.16. You should be skeptical. If the author actually knows how to achieve such returns, one must question why the author would then be so ready to sell the secret to others. Financial markets are very competitive; one of the implications of this fact is that riches do not come easily. High expected returns require bearing some risk, and obvious bargains are few and far between. Odds are that the only one getting rich from the book is its author.17. a. The SEC website defines the difference between saving and investing in terms of b. the investment alternatives or the financial assets the individual chooses to acquire. According to the SEC website, saving is the process of acquiring a “safe” financial asset and investing is the process of acquiring “risky” financial assets. The economist’s definition of savings is the difference between income and consumption. Investing is the process of allocating one’s savings among available assets, both real assets and financial assets. The SEC definitions actually represent (according the economist’s definition) two kinds of investment alternatives.18. As is the case for the SEC definitions (see Problem 17), the SIA defines saving and investing as acquisition of alternative kinds of financial assets. According to the SIA, saving is the process of acquiring safe assets, generally from a bank, while investing is the acquisition of other financial assets, such as stocks and bonds. On the other hand, the definitions in the chapter indicate that saving means spending less than one’s income. Investing is the process of allocating one’s savings among financial assets, including savings account deposits and money market accounts (“saving” according to the SIA), other financial assets such as stocks and bonds (“investing” according to the SIA), as well as real assets. 1-5

Chapter 02 - Asset Classes and Financial Instruments CHAPTER 2: ASSET CLASSES AND FINANCIAL INSTRUMENTSPROBLEM SETS1. Preferred stock is like long-term debt in that it typically promises a fixed payment each year. In this way, it is a perpetuity. Preferred stock is also like long-term debt in that it does not give the holder voting rights in the firm. Preferred stock is like equity in that the firm is under no contractual obligation to make the preferred stock dividend payments. Failure to make payments does not set off corporate bankruptcy. With respect to the priority of claims to the assets of the firm in the event of corporate bankruptcy, preferred stock has a higher priority than common equity but a lower priority than bonds.2. Money market securities are called “cash equivalents” because of their great liquidity. The prices of money market securities are very stable, and they can be converted to cash (i.e., sold) on very short notice and with very low transaction costs.3. The spread will widen. Deterioration of the economy increases credit risk, that is, the likelihood of default. Investors will demand a greater premium on debt securities subject to default risk.4. On the day we tried this experiment, 36 of the 50 stocks met this criterion, leading us to conclude that returns on stock investments can be quite volatile.5. a. You would have to pay the asked price of: 118:31 = 118.96875% of par = $1,189.6875 b. The coupon rate is 11.750% implying coupon payments of $117.50 annually or, more precisely, $58.75 semiannually. c. Current yield = Annual coupon income/price = $117.50/$1,189.6875 = 0.0988 = 9.88%6. P = $10,000/1.02 = $9,803.92 2-1

Chapter 02 - Asset Classes and Financial Instruments7. The total before-tax income is $4. After the 70% exclusion for preferred stock dividends, the taxable income is: 0.30 × $4 = $1.20 Therefore, taxes are: 0.30 × $1.20 = $0.36 After-tax income is: $4.00 – $0.36 = $3.64 Rate of return is: $3.64/$40.00 = 9.10%8. a. General Dynamics closed today at $74.59, which was $0.17 higher than yesterday’s price. Yesterday’s closing price was: $74.42 b. You could buy: $5,000/$74.59 = 67.03 shares c. Your annual dividend income would be: 67.03 × $0.92 = $61.67 d. The price-to-earnings ratio is 16 and the price is $74.59. Therefore: $74.59/Earnings per share = 16 Earnings per share = $4.669. a. At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80 At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333 The rate of return is: (83.333/80) − 1 = 4.17% b. In the absence of a split, Stock C would sell for 110, so the value of the index would be: 250/3 = 83.333 After the split, Stock C sells for 55. Therefore, we need to find the divisor (d) such that: 83.333 = (95 + 45 + 55)/d ⇒ d = 2.340 c. The return is zero. The index remains unchanged because the return for each stock separately equals zero.10. a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000 b. Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500 Rate of return = ($40,500/$39,000) – 1 = 3.85% The return on each stock is as follows: rA = (95/90) – 1 = 0.0556 rB = (45/50) – 1 = –0.10 rC = (110/100) – 1 = 0.10 The equally-weighted average is: [0.0556 + (-0.10) + 0.10]/3 = 0.0185 = 1.85% 2-2

Chapter 02 - Asset Classes and Financial Instruments11. The after-tax yield on the corporate bonds is: 0.09 × (1 – 0.30) = 0.0630 = 6.30% Therefore, municipals must offer at least 6.30% yields.12. Equation (2.2) shows that the equivalent taxable yield is: r = rm/(1 – t) a. 4.00% b. 4.44% c. 5.00% d. 5.71%13. a. The higher coupon bond. b. The call with the lower exercise price. c. The put on the lower priced stock.14. a. You bought the contract when the futures price was 1427.50 (see Figure 2.12). The contract closes at a price of 1300, which is 127.50 less than the original futures price. The contract multiplier is $250. Therefore, the loss will be: 127.50 × $250 = $31,875b. Open interest is 601,655 contracts.15. a. Since the stock price exceeds the exercise price, you will exercise the call. The payoff on the option will be: $42 − $40 = $2 The option originally cost $2.14, so the profit is: $2.00 − $2.14 = −$0.14 Rate of return = −$0.14/$2.14 = −0.0654 = −6.54%b. If the call has an exercise price of $42.50, you would not exercise for any stock price of $42.50 or less. The loss on the call would be the initial cost: $0.72c. Since the stock price is less than the exercise price, you will exercise the put. The payoff on the option will be: $42.50 − $42.00 = $0.50 The option originally cost $1.83 so the profit is: $0.50 − $1.83 = −$1.33 Rate of return = −$1.33/$1.83 = −0.7268 = −72.68% 2-3

Chapter 02 - Asset Classes and Financial Instruments16. There is always a possibility that the option will be in-the-money at some time prior to expiration. Investors will pay something for this possibility of a positive payoff.17. Value of call at expiration Initial Cost Profit -4 a. 0 4 -4 -4 b. 0 4 1 6 c. 0 4 Profit d. 5 4 4 -1 e. 10 4 -6 -6 Value of put at expiration Initial Cost -6 a. 10 6 b. 5 6 c. 0 6 d. 0 6 e. 0 618. A put option conveys the right to sell the underlying asset at the exercise price. A short position in a futures contract carries an obligation to sell the underlying asset at the futures price.19. A call option conveys the right to buy the underlying asset at the exercise price. A long position in a futures contract carries an obligation to buy the underlying asset at the futures price.CFA PROBLEMS1. (d)2. The equivalent taxable yield is: 6.75%/(1 − 0.34) = 10.23%3. (a) Writing a call entails unlimited potential losses as the stock price rises. 2-4

Chapter 02 - Asset Classes and Financial Instruments4. a. The taxable bond. With a zero tax bracket, the after-tax yield for the taxable bond is the same as the before-tax yield (5%), which is greater than the yield on the municipal bond. b. The taxable bond. The after-tax yield for the taxable bond is: 0.05 × (1 – 0.10) = 4.5% c. You are indifferent. The after-tax yield for the taxable bond is: 0.05 × (1 – 0.20) = 4.0% The after-tax yield is the same as that of the municipal bond. d. The municipal bond offers the higher after-tax yield for investors in tax brackets above 20%.5. If the after-tax yields are equal, then: 0.056 = 0.08 × (1 – t) This implies that t = 0.30 =30%. 2-5

Chapter 02 - Asset Classes and Financial Instruments CHAPTER 2: ASSET CLASSES AND FINANCIAL INSTRUMENTSPROBLEM SETS1. Preferred stock is like long-term debt in that it typically promises a fixed payment each year. In this way, it is a perpetuity. Preferred stock is also like long-term debt in that it does not give the holder voting rights in the firm. Preferred stock is like equity in that the firm is under no contractual obligation to make the preferred stock dividend payments. Failure to make payments does not set off corporate bankruptcy. With respect to the priority of claims to the assets of the firm in the event of corporate bankruptcy, preferred stock has a higher priority than common equity but a lower priority than bonds.2. Money market securities are called “cash equivalents” because of their great liquidity. The prices of money market securities are very stable, and they can be converted to cash (i.e., sold) on very short notice and with very low transaction costs.3. The spread will widen. Deterioration of the economy increases credit risk, that is, the likelihood of default. Investors will demand a greater premium on debt securities subject to default risk.4. On the day we tried this experiment, 36 of the 50 stocks met this criterion, leading us to conclude that returns on stock investments can be quite volatile.5. a. You would have to pay the asked price of: 118:31 = 118.96875% of par = $1,189.6875 b. The coupon rate is 11.750% implying coupon payments of $117.50 annually or, more precisely, $58.75 semiannually. c. Current yield = Annual coupon income/price = $117.50/$1,189.6875 = 0.0988 = 9.88%6. P = $10,000/1.02 = $9,803.92 2-1

Chapter 02 - Asset Classes and Financial Instruments7. The total before-tax income is $4. After the 70% exclusion for preferred stock dividends, the taxable income is: 0.30 × $4 = $1.20 Therefore, taxes are: 0.30 × $1.20 = $0.36 After-tax income is: $4.00 – $0.36 = $3.64 Rate of return is: $3.64/$40.00 = 9.10%8. a. General Dynamics closed today at $74.59, which was $0.17 higher than yesterday’s price. Yesterday’s closing price was: $74.42 b. You could buy: $5,000/$74.59 = 67.03 shares c. Your annual dividend income would be: 67.03 × $0.92 = $61.67 d. The price-to-earnings ratio is 16 and the price is $74.59. Therefore: $74.59/Earnings per share = 16 Earnings per share = $4.669. a. At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80 At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333 The rate of return is: (83.333/80) − 1 = 4.17% b. In the absence of a split, Stock C would sell for 110, so the value of the index would be: 250/3 = 83.333 After the split, Stock C sells for 55. Therefore, we need to find the divisor (d) such that: 83.333 = (95 + 45 + 55)/d ⇒ d = 2.340 c. The return is zero. The index remains unchanged because the return for each stock separately equals zero.10. a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000 b. Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500 Rate of return = ($40,500/$39,000) – 1 = 3.85% The return on each stock is as follows: rA = (95/90) – 1 = 0.0556 rB = (45/50) – 1 = –0.10 rC = (110/100) – 1 = 0.10 The equally-weighted average is: [0.0556 + (-0.10) + 0.10]/3 = 0.0185 = 1.85% 2-2

Chapter 02 - Asset Classes and Financial Instruments11. The after-tax yield on the corporate bonds is: 0.09 × (1 – 0.30) = 0.0630 = 6.30% Therefore, municipals must offer at least 6.30% yields.12. Equation (2.2) shows that the equivalent taxable yield is: r = rm/(1 – t) a. 4.00% b. 4.44% c. 5.00% d. 5.71%13. a. The higher coupon bond. b. The call with the lower exercise price. c. The put on the lower priced stock.14. a. You bought the contract when the futures price was 1427.50 (see Figure 2.12). The contract closes at a price of 1300, which is 127.50 less than the original futures price. The contract multiplier is $250. Therefore, the loss will be: 127.50 × $250 = $31,875b. Open interest is 601,655 contracts.15. a. Since the stock price exceeds the exercise price, you will exercise the call. The payoff on the option will be: $42 − $40 = $2 The option originally cost $2.14, so the profit is: $2.00 − $2.14 = −$0.14 Rate of return = −$0.14/$2.14 = −0.0654 = −6.54%b. If the call has an exercise price of $42.50, you would not exercise for any stock price of $42.50 or less. The loss on the call would be the initial cost: $0.72c. Since the stock price is less than the exercise price, you will exercise the put. The payoff on the option will be: $42.50 − $42.00 = $0.50 The option originally cost $1.83 so the profit is: $0.50 − $1.83 = −$1.33 Rate of return = −$1.33/$1.83 = −0.7268 = −72.68% 2-3

Chapter 02 - Asset Classes and Financial Instruments16. There is always a possibility that the option will be in-the-money at some time prior to expiration. Investors will pay something for this possibility of a positive payoff.17. Value of call at expiration Initial Cost Profit -4 a. 0 4 -4 -4 b. 0 4 1 6 c. 0 4 Profit d. 5 4 4 -1 e. 10 4 -6 -6 Value of put at expiration Initial Cost -6 a. 10 6 b. 5 6 c. 0 6 d. 0 6 e. 0 618. A put option conveys the right to sell the underlying asset at the exercise price. A short position in a futures contract carries an obligation to sell the underlying asset at the futures price.19. A call option conveys the right to buy the underlying asset at the exercise price. A long position in a futures contract carries an obligation to buy the underlying asset at the futures price.CFA PROBLEMS1. (d)2. The equivalent taxable yield is: 6.75%/(1 − 0.34) = 10.23%3. (a) Writing a call entails unlimited potential losses as the stock price rises. 2-4

Chapter 02 - Asset Classes and Financial Instruments4. a. The taxable bond. With a zero tax bracket, the after-tax yield for the taxable bond is the same as the before-tax yield (5%), which is greater than the yield on the municipal bond. b. The taxable bond. The after-tax yield for the taxable bond is: 0.05 × (1 – 0.10) = 4.5% c. You are indifferent. The after-tax yield for the taxable bond is: 0.05 × (1 – 0.20) = 4.0% The after-tax yield is the same as that of the municipal bond. d. The municipal bond offers the higher after-tax yield for investors in tax brackets above 20%.5. If the after-tax yields are equal, then: 0.056 = 0.08 × (1 – t) This implies that t = 0.30 =30%. 2-5

Chapter 03 - How Securities are Traded CHAPTER 3: HOW SECURITIES ARE TRADEDPROBLEM SETS1. Answers to this problem will vary.2. The SuperDot system expedites the flow of orders from exchange members to the specialists. It allows members to send computerized orders directly to the floor of the exchange, which allows the nearly simultaneous sale of each stock in a large portfolio. This capability is necessary for program trading.3. The dealer sets the bid and asked price. Spreads should be higher on inactively traded stocks and lower on actively traded stocks.4. a. In principle, potential losses are unbounded, growing directly with increases in the price of IBM. b. If the stop-buy order can be filled at $128, the maximum possible loss per share is $8. If the price of IBM shares goes above $128, then the stop-buy order would be executed, limiting the losses from the short sale.5. a. The stock is purchased for: 300 × $40 = $12,000 The amount borrowed is $4,000. Therefore, the investor put up equity, or margin, of $8,000. b. If the share price falls to $30, then the value of the stock falls to $9,000. By the end of the year, the amount of the loan owed to the broker grows to: $4,000 × 1.08 = $4,320 Therefore, the remaining margin in the investor’s account is: $9,000 − $4,320 = $4,680 The percentage margin is now: $4,680/$9,000 = 0.52 = 52% Therefore, the investor will not receive a margin call. c. The rate of return on the investment over the year is: (Ending equity in the account − Initial equity)/Initial equity = ($4,680 − $8,000)/$8,000 = −0.415 = −41.5% 3-1

Chapter 03 - How Securities are Traded6. a. The initial margin was: 0.50 × 1,000 × $40 = $20,000 As a result of the increase in the stock price Old Economy Traders loses: $10 × 1,000 = $10,000 Therefore, margin decreases by $10,000. Moreover, Old Economy Traders must pay the dividend of $2 per share to the lender of the shares, so that the margin in the account decreases by an additional $2,000. Therefore, the remaining margin is: $20,000 – $10,000 – $2,000 = $8,000 b. The percentage margin is: $8,000/$50,000 = 0.16 = 16% So there will be a margin call. c. The equity in the account decreased from $20,000 to $8,000 in one year, for a rate of return of: (−$12,000/$20,000) = −0.60 = −60%7. Much of what the specialist does (e.g., crossing orders and maintaining the limit order book) can be accomplished by a computerized system. In fact, some exchanges use an automated system for night trading. A more difficult issue to resolve is whether the more discretionary activities of specialists involving trading for their own accounts (e.g., maintaining an orderly market) can be replicated by a computer system.8. a. The buy order will be filled at the best limit-sell order price: $50.25 b. The next market buy order will be filled at the next-best limit-sell order price: $51.50 c. You would want to increase your inventory. There is considerable buying demand at prices just below $50, indicating that downside risk is limited. In contrast, limit sell orders are sparse, indicating that a moderate buy order could result in a substantial price increase.9. a. You buy 200 shares of Telecom for $10,000. These shares increase in value by 10%, or $1,000. You pay interest of: 0.08 × $5,000 = $400 The rate of return will be: $1,000 − $400 = 0.12 = 12% $5,000 3-2

Chapter 03 - How Securities are Traded b. The value of the 200 shares is 200P. Equity is (200P – $5,000). You will receive a margin call when: 200P − $5,000 = 0.30 ⇒ when P = $35.71 or lower 200P10. a. Initial margin is 50% of $5,000 or $2,500. b. Total assets are $7,500 ($5,000 from the sale of the stock and $2,500 put up for margin). Liabilities are 100P. Therefore, equity is ($7,500 – 100P). A margin call will be issued when: $7,500 −100P = 0.30 ⇒ when P = $57.69 or higher 100P11. The total cost of the purchase is: $40 × 500 = $20,000 You borrow $5,000 from your broker, and invest $15,000 of your own funds. Your margin account starts out with equity of $15,000. a. (i) Equity increases to: ($44 × 500) – $5,000 = $17,000 Percentage gain = $2,000/$15,000 = 0.1333 = 13.33% (ii) With price unchanged, equity is unchanged. Percentage gain = zero (iii) Equity falls to ($36 × 500) – $5,000 = $13,000 Percentage gain = (–$2,000/$15,000) = –0.1333 = –13.33% The relationship between the percentage return and the percentage change in the price of the stock is given by: % return = % change in price × Total investment = % change in price × 1.333 Investor's initial equity For example, when the stock price rises from $40 to $44, the percentage change in price is 10%, while the percentage gain for the investor is: % return = 10% × $20,000 = 13.33% $15,000 b. The value of the 500 shares is 500P. Equity is (500P – $5,000). You will receive a margin call when: 500P − $5,000 = 0.25 ⇒ when P = $13.33 or lower 500P 3-3

Chapter 03 - How Securities are Traded c. The value of the 500 shares is 500P. But now you have borrowed $10,000 instead of $5,000. Therefore, equity is (500P – $10,000). You will receive a margin call when: 500P − $10,000 = 0.25 ⇒ when P = $26.67 500P With less equity in the account, you are far more vulnerable to a margin call. d. By the end of the year, the amount of the loan owed to the broker grows to: $5,000 × 1.08 = $5,400 The equity in your account is (500P – $5,400). Initial equity was $15,000. Therefore, your rate of return after one year is as follows: (i) (500 × $44) − $5,400 − $15,000 = 0.1067 = 10.67% $15,000 (ii) (500 × $40) − $5,400 − $15,000 = –0.0267 = –2.67% $15,000 (iii) (500 × $36) − $5,400 − $15,000 = –0.1600 = –16.00% $15,000 The relationship between the percentage return and the percentage change in the price of Intel is given by:% return = % change in price × Total investment − 8% × Funds borrowed Investor's initial equity Investor's initial equity For example, when the stock price rises from $40 to $44, the percentage change in price is 10%, while the percentage gain for the investor is: 10% × $20,000 − 8% × $5,000 =10.67% $15,000 $15,000 e. The value of the 500 shares is 500P. Equity is (500P – $5,400). You will receive a margin call when: 500P − $5,400 = 0.25 ⇒ when P = $14.40 or lower 500P 3-4

Chapter 03 - How Securities are Traded12. a. The gain or loss on the short position is: (–500 × ∆P) Invested funds = $15,000 Therefore: rate of return = (–500 × ∆P)/15,000 The rate of return in each of the three scenarios is: (i) rate of return = (–500 × $4)/$15,000 = –0.1333 = –13.33% (ii) rate of return = (–500 × $0)/$15,000 = 0% (iii) rate of return = [–500 × (–$4)]/$15,000 = +0.1333 = +13.33%b. Total assets in the margin account equal: $20,000 (from the sale of the stock) + $15,000 (the initial margin) = $35,000 Liabilities are 500P. You will receive a margin call when: $35,000 − 500P = 0.25 ⇒ when P = $56 or higher 500Pc. With a $1 dividend, the short position must now pay on the borrowed shares: ($1/share × 500 shares) = $500. Rate of return is now: [(–500 × ∆P) – 500]/15,000 (i) rate of return = [(–500 × $4) – $500]/$15,000 = –0.1667 = –16.67% (ii) rate of return = [(–500 × $0) – $500]/$15,000 = –0.0333 = –3.33% (iii) rate of return = [(–500) × (–$4) – $500]/$15,000 = +0.1000 = +10.00% Total assets are $35,000, and liabilities are (500P + 500). A margin call will be issued when: 35,000 − 500P − 500 = 0.25 ⇒ when P = $55.20 or higher 500P13. The broker is instructed to attempt to sell your Marriott stock as soon as the Marriott stock trades at a bid price of $38 or less. Here, the broker will attempt to execute, but may not be able to sell at $38, since the bid price is now $37.95. The price at which you sell may be more or less than $38 because the stop-loss becomes a market order to sell at current market prices. 3-5

Chapter 03 - How Securities are Traded14. a. $55.50 b. $55.25 c. The trade will not be executed because the bid price is lower than the price specified in the limit sell order. d. The trade will not be executed because the asked price is greater than the price specified in the limit buy order.15. a. In an exchange market, there can be price improvement in the two market orders. Brokers for each of the market orders (i.e., the buy order and the sell order) can agree to execute a trade inside the quoted spread. For example, they can trade at $55.37, thus improving the price for both customers by $0.12 or $0.13 relative to the quoted bid and asked prices. The buyer gets the stock for $0.13 less than the quoted asked price, and the seller receives $0.12 more for the stock than the quoted bid price.b. Whereas the limit order to buy at $55.37 would not be executed in a dealer market (since the asked price is $55.50), it could be executed in an exchange market. A broker for another customer with an order to sell at market would view the limit buy order as the best bid price; the two brokers could agree to the trade and bring it to the specialist, who would then execute the trade.16. a. You will not receive a margin call. You borrowed $20,000 and with another $20,000 of your own equity you bought 1,000 shares of Disney at $40 per share. At $35 per share, the market value of the stock is $35,000, your equity is $15,000, and the percentage margin is: $15,000/$35,000 = 42.9% Your percentage margin exceeds the required maintenance margin.b. You will receive a margin call when: 1,000P − $20,000 = 0.35 ⇒ when P = $30.77 or lower 1,000P 3-6

Chapter 03 - How Securities are Traded17. The proceeds from the short sale (net of commission) were: ($14 × 100) – $50 = $1,350 A dividend payment of $200 was withdrawn from the account. Covering the short sale at $9 per share cost you (including commission): $900 + $50 = $950 Therefore, the value of your account is equal to the net profit on the transaction: $1350 – $200 – $950 = $200 Note that your profit ($200) equals (100 shares × profit per share of $2). Your net proceeds per share was: $14 selling price of stock –$9 repurchase price of stock –$2 dividend per share –$1 2 trades × $0.50 commission per share $2CFA PROBLEMS1. a. In addition to the explicit fees of $70,000, FBN appears to have paid an implicit price in underpricing of the IPO. The underpricing is $3 per share, or a total of $300,000, implying total costs of $370,000. b. No. The underwriters do not capture the part of the costs corresponding to the underpricing. The underpricing may be a rational marketing strategy. Without it, the underwriters would need to spend more resources in order to place the issue with the public. The underwriters would then need to charge higher explicit fees to the issuing firm. The issuing firm may be just as well off paying the implicit issuance cost represented by the underpricing.2. (d) The broker will sell, at current market price, after the first transaction at $55 or less.3. (d) 3-7

Chapter 04 - Mutual Funds and Other Investment Companies CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIESPROBLEM SETS1. The unit investment trust should have lower operating expenses. Because the investment trust portfolio is fixed once the trust is established, it does not have to pay portfolio managers to constantly monitor and rebalance the portfolio as perceived needs or opportunities change. Because the portfolio is fixed, the unit investment trust also incurs virtually no trading costs.2. a. Unit investment trusts: diversification from large-scale investing, lower transaction costs associated with large-scale trading, low management fees, predictable portfolio composition, guaranteed low portfolio turnover rate. b. Open-end mutual funds: diversification from large-scale investing, lower transaction costs associated with large-scale trading, professional management that may be able to take advantage of buy or sell opportunities as they arise, record keeping. c. Individual stocks and bonds: No management fee, realization of capital gains or losses can be coordinated with investors’ personal tax situations, portfolio can be designed to investor’s specific risk profile.3. Open-end funds are obligated to redeem investor's shares at net asset value, and thus must keep cash or cash-equivalent securities on hand in order to meet potential redemptions. Closed-end funds do not need the cash reserves because there are no redemptions for closed-end funds. Investors in closed-end funds sell their shares when they wish to cash out.4. Balanced funds keep relatively stable proportions of funds invested in each asset class. They are meant as convenient instruments to provide participation in a range of asset classes. Life-cycle funds are balanced funds whose asset mix generally depends on the age of the investor. Aggressive life-cycle funds, with larger investments in equities, are marketed to younger investors, while conservative life-cycle funds, with larger investments in fixed-income securities, are designed for older investors. Asset allocation funds, in contrast, may vary the proportions invested in each asset class by large amounts as predictions of relative performance across classes vary. Asset allocation funds therefore engage in more aggressive market timing. 4-1

Chapter 04 - Mutual Funds and Other Investment Companies5. The offering price includes a 6% front-end load, or sales commission, meaning that every dollar paid results in only $0.94 going toward purchase of shares. Therefore: Offering price = NAV = $10.70 = $11.38 1 − load 1 − 0.066. NAV = offering price × (1 – load) = $12.30 × 0.95 = $11.697. Stock Value held by fund A $ 7,000,000 B 12,000,000 C 8,000,000 D 15,000,000Total $42,000,000Net asset value = $42,000,000 − $30,000 = $10.49 4,000,0008. Value of stocks sold and replaced = $15,000,000 Turnover rate = $15,000,000 = 0.357 = 35.7% $42,000,0009. a. NAV = $200,000,000 − $3,000,000 = $39.40 5,000,000b. Premium (or discount) = Pr ice − NAV = $36 − $39.40 = –0.086 = -8.6% NAV $39.40 The fund sells at an 8.6% discount from NAV.10. Rate of return = NAV1 − NAV0 + distributions = $12.10 − $12.50 + $1.50 = 0.088 = 8.8% NAV0 $12.50 4-2

Chapter 04 - Mutual Funds and Other Investment Companies11. a. Start-of-year price: P0 = $12.00 × 1.02 = $12.24 End-of-year price: P1 = $12.10 × 0.93 = $11.25 Although NAV increased by $0.10, the price of the fund decreased by: $0.99 Rate of return = P1 − P0 + Distributions = $11.25 − $12.24 + $1.50 = 0.042 = 4.2% P0 $12.24b. An investor holding the same securities as the fund manager would have earned a rate of return based on the increase in the NAV of the portfolio: Rate of return = NAV1 − NAV0 + distributions = $12.10 − $12.00 + $1.50 = 0.133 = 13.3% NAV0 $12.0012. a. Empirical research indicates that past performance of mutual funds is not highly predictive of future performance, especially for better-performing funds. While there may be some tendency for the fund to be an above average performer next year, it is unlikely to once again be a top 10% performer.b. On the other hand, the evidence is more suggestive of a tendency for poor performance to persist. This tendency is probably related to fund costs and turnover rates. Thus if the fund is among the poorest performers, investors would be concerned that the poor performance will persist.13. NAV0 = $200,000,000/10,000,000 = $20 Dividends per share = $2,000,000/10,000,000 = $0.20 NAV1 is based on the 8% price gain, less the 1% 12b-1 fee: NAV1 = $20 × 1.08 × (1 – 0.01) = $21.384 Rate of return = $21.384 − $20 + $0.20 = 0.0792 = 7.92% $2014. The excess of purchases over sales must be due to new inflows into the fund. Therefore, $400 million of stock previously held by the fund was replaced by new holdings. So turnover is: $400/$2,200 = 0.182 = 18.2%15. Fees paid to investment managers were: 0.007 × $2.2 billion = $15.4 million Since the total expense ratio was 1.1% and the management fee was 0.7%, we conclude that 0.4% must be for other expenses. Therefore, other administrative expenses were: 0.004 × $2.2 billion = $8.8 million 4-3

Chapter 04 - Mutual Funds and Other Investment Companies16. As an initial approximation, your return equals the return on the shares minus the total of the expense ratio and purchase costs: 12% − 1.2% − 4% = 6.8% But the precise return is less than this because the 4% load is paid up front, not at the end of the year. To purchase the shares, you would have had to invest: $20,000/(1 − 0.04) = $20,833 The shares increase in value from $20,000 to: $20,000 × (1.12 − 0.012) = $22,160 The rate of return is: ($22,160 − $20,833)/$20,833 = 6.37%17. Suppose you have $1,000 to invest. The initial investment in Class A shares is $940 net of the front-end load. After four years, your portfolio will be worth: $940 × (1.10)4 = $1,376.25 Class B shares allow you to invest the full $1,000, but your investment performance net of 12b-1 fees will be only 9.5%, and you will pay a 1% back-end load fee if you sell after four years. Your portfolio value after four years will be: $1,000 × (1.095)4 = $1,437.66 After paying the back-end load fee, your portfolio value will be: $1,437.66 × 0.99 = $1,423.28 Class B shares are the better choice if your horizon is four years. With a fifteen-year horizon, the Class A shares will be worth: $940 × (1.10)15 = $3,926.61 For the Class B shares, there is no back-end load in this case since the horizon is greater than five years. Therefore, the value of the Class B shares will be: $1,000 × (1.095)15 = $3,901.32 At this longer horizon, Class B shares are no longer the better choice. The effect of Class B's 0.5% 12b-1 fees accumulates over time and finally overwhelms the 6% load charged to Class A investors.18. a. After two years, each dollar invested in a fund with a 4% load and a portfolio return equal to r will grow to: $0.96 × (1 + r – 0.005)2 Each dollar invested in the bank CD will grow to: $1 × 1.062 If the mutual fund is to be the better investment, then the portfolio return (r) must satisfy: 0.96 × (1 + r – 0.005)2 > 1.062 0.96 × (1 + r – 0.005)2 > 1.1236 (1 + r – 0.005)2 > 1.1704 1 + r – 0.005 > 1.0819 1 + r > 1.0869 Therefore: r > 0.0869 = 8.69% 4-4

Chapter 04 - Mutual Funds and Other Investment Companies b. If you invest for six years, then the portfolio return must satisfy: 0.96 × (1 + r – 0.005)6 > 1.066 = 1.4185 (1 + r – 0.005)6 > 1.4776 1 + r – 0.005 > 1.0672 1 + r > 1.0722 r > 7.22% The cutoff rate of return is lower for the six-year investment because the “fixed cost” (i.e., the one-time front-end load) is spread out over a greater number of years. c. With a 12b-1 fee instead of a front-end load, the portfolio must earn a rate of return (r) that satisfies: 1 + r – 0.005 – 0.0075 > 1.06 In this case, r must exceed 7.25% regardless of the investment horizon.19. The turnover rate is 50%. This means that, on average, 50% of the portfolio is sold and replaced with other securities each year. Trading costs on the sell orders are 0.4% and the buy orders to replace those securities entail another 0.4% in trading costs. Total trading costs will reduce portfolio returns by: 2 × 0.4% × 0.50 = 0.4%20. For the bond fund, the fraction of portfolio income given up to fees is: 0.6% = 0.150 = 15.0% 4.0% For the equity fund, the fraction of investment earnings given up to fees is: 0.6% = 0.050 = 5.0% 12.0% Fees are a much higher fraction of expected earnings for the bond fund, and therefore may be a more important factor in selecting the bond fund. This may help to explain why unmanaged unit investment trusts are concentrated in the fixed income market. The advantages of unit investment trusts are low turnover, low trading costs and low management fees. This is a more important concern to bond- market investors. 4-5

Chapter 04 - Mutual Funds and Other Investment Companies21. Suppose that finishing in the top half of all portfolio managers is purely luck, and that the probability of doing so in any year is exactly ½. Then the probability that any particular manager would finish in the top half of the sample five years in a row is (½)5 = 1/32. We would then expect to find that [350 × (1/32)] = 11 managers finish in the top half for each of the five consecutive years. This is precisely what we found. Thus, we should not conclude that the consistent performance after five years is proof of skill. We would expect to find eleven managers exhibiting precisely this level of \"consistency\" even if performance is due solely to luck. 4-6

Chapter 05 - Learning About Return and Risk from the Historical Record CHAPTER 5: LEARNING ABOUT RETURN AND RISK FROM THE HISTORICAL RECORDPROBLEM SETS1. The Fisher equation predicts that the nominal rate will equal the equilibrium real rate plus the expected inflation rate. Hence, if the inflation rate increases from 3% to 5% while there is no change in the real rate, then the nominal rate will increase by 2%. On the other hand, it is possible that an increase in the expected inflation rate would be accompanied by a change in the real rate of interest. While it is conceivable that the nominal interest rate could remain constant as the inflation rate increased, implying that the real rate decreased as inflation increased, this is not a likely scenario.2. If we assume that the distribution of returns remains reasonably stable over the entire history, then a longer sample period (i.e., a larger sample) increases the precision of the estimate of the expected rate of return; this is a consequence of the fact that the standard error decreases as the sample size increases. However, if we assume that the mean of the distribution of returns is changing over time but we are not in a position to determine the nature of this change, then the expected return must be estimated from a more recent part of the historical period. In this scenario, we must determine how far back, historically, to go in selecting the relevant sample. Here, it is likely to be disadvantageous to use the entire dataset back to 1880.3. The true statements are (c) and (e). The explanations follow. Statement (c): Let σ = the annual standard deviation of the risky investments and σ1 = the standard deviation of the first investment alternative over the two-year period. Then: σ1 = 2 ×σ Therefore, the annualized standard deviation for the first investment alternative is equal to: σ1 = σ <σ 22 5-1

Chapter 05 - Learning About Return and Risk from the Historical Record Statement (e): The first investment alternative is more attractive to investors with lower degrees of risk aversion. The first alternative (entailing a sequence of two identically distributed and uncorrelated risky investments) is riskier than the second alternative (the risky investment followed by a risk-free investment). Therefore, the first alternative is more attractive to investors with lower degrees of risk aversion. Notice, however, that if you mistakenly believed that ‘time diversification’ can reduce the total risk of a sequence of risky investments, you would have been tempted to conclude that the first alternative is less risky and therefore more attractive to more risk-averse investors. This is clearly not the case; the two-year standard deviation of the first alternative is greater than the two-year standard deviation of the second alternative.4. For the money market fund, your holding period return for the next year depends on the level of 30-day interest rates each month when the fund rolls over maturing securities. The one-year savings deposit offers a 7.5% holding period return for the year. If you forecast that the rate on money market instruments will increase significantly above the current 6% yield, then the money market fund might result in a higher HPR than the savings deposit. The 20-year Treasury bond offers a yield to maturity of 9% per year, which is 150 basis points higher than the rate on the one-year savings deposit; however, you could earn a one-year HPR much less than 7.5% on the bond if long-term interest rates increase during the year. If Treasury bond yields rise above 9%, then the price of the bond will fall, and the resulting capital loss will wipe out some or all of the 9% return you would have earned if bond yields had remained unchanged over the course of the year.5. a. If businesses reduce their capital spending, then they are likely to decrease their demand for funds. This will shift the demand curve in Figure 5.1 to the left and reduce the equilibrium real rate of interest. b. Increased household saving will shift the supply of funds curve to the right and cause real interest rates to fall. c. Open market purchases of U.S. Treasury securities by the Federal Reserve Board is equivalent to an increase in the supply of funds (a shift of the supply curve to the right). The equilibrium real rate of interest will fall. 5-2

Chapter 05 - Learning About Return and Risk from the Historical Record6. a. The “Inflation-Plus” CD is the safer investment because it guarantees the purchasing power of the investment. Using the approximation that the real rate equals the nominal rate minus the inflation rate, the CD provides a real rate of 1.5% regardless of the inflation rate. b. The expected return depends on the expected rate of inflation over the next year. If the expected rate of inflation is less than 3.5% then the conventional CD offers a higher real return than the Inflation-Plus CD; if the expected rate of inflation is greater than 3.5%, then the opposite is true. c. If you expect the rate of inflation to be 3% over the next year, then the conventional CD offers you an expected real rate of return of 2%, which is 0.5% higher than the real rate on the inflation-protected CD. But unless you know that inflation will be 3% with certainty, the conventional CD is also riskier. The question of which is the better investment then depends on your attitude towards risk versus return. You might choose to diversify and invest part of your funds in each. d. No. We cannot assume that the entire difference between the risk-free nominal rate (on conventional CDs) of 5% and the real risk-free rate (on inflation-protected CDs) of 1.5% is the expected rate of inflation. Part of the difference is probably a risk premium associated with the uncertainty surrounding the real rate of return on the conventional CDs. This implies that the expected rate of inflation is less than 3.5% per year.7. E(r) = [0.35 × 44.5%] + [0.30 × 14.0%] + [0.35 × (–16.5%)] = 14% σ2 = [0.35 × (44.5 – 14)2] + [0.30 × (14 – 14)2] + [0.35 × (–16.5 – 14)2] = 651.175 σ = 25.52% The mean is unchanged, but the standard deviation has increased, as the probabilities of the high and low returns have increased.8. Probability distribution of price and one-year holding period return for a 30-year U.S. Treasury bond (which will have 29 years to maturity at year’s end):Economy Probability YTM Price Capital Coupon HPR Gain Interest 11.0% $74.05Boom 0.20 8.0% $100.00 −$25.95 $8.00 −17.95%Normal Growth 0.50 7.0% $112.28 $0.00Recession 0.30 $12.28 $8.00 8.00% $8.00 20.28% 5-3

Chapter 05 - Learning About Return and Risk from the Historical Record9. E(q) = (0 × 0.25) + (1 × 0.25) + (2 × 0.50) = 1.25 σq = [0.25 × (0 – 1.25)2 + 0.25 × (1 – 1.25)2 + 0.50 × (2 – 1.25)2]1/2 = 0.829210. (a) With probability 0.9544, the value of a normally distributed variable will fall within two standard deviations of the mean; that is, between –40% and 80%.11. From Table 5.3, the average risk premium for large-capitalization U.S. stocks for the period 1926-2005 was: (12.15% − 3.75%) = 8.40% per year Adding 8.40% to the 6% risk-free interest rate, the expected annual HPR for the S&P 500 stock portfolio is: 6.00% + 8.40% = 14.40%12. The average rates of return and standard deviations are quite different in the sub periods: STOCKS Mean Standard Skewness Kurtosis Deviation1926 – 2005 12.15% 20.26% -0.3605 -0.06731976 – 2005 13.85% 15.68% -0.4575 -0.64891926 – 1941 6.39% 30.33% -0.0022 -1.0716 BONDS Mean Standard Skewness Kurtosis Deviation 5.68% 1.63141926 – 2005 9.57% 8.09% 0.9903 -0.03291976 – 2005 4.42% 0.50341926 – 1941 10.32% 0.3772 4.32% -0.5036The most relevant statistics to use for projecting into the future would seem to be thestatistics estimated over the period 1976-2005, because this later period seems to havebeen a different economic regime. After 1955, the U.S. economy entered the Keynesianera, when the Federal government actively attempted to stabilize the economy and toprevent extremes in boom and bust cycles. Note that the standard deviation of stockreturns has decreased substantially in the later period while the standard deviation ofbond returns has increased.13. a r = 1 + R −1 = R − i = 0.80 − 0.70 = 0.0588 = 5.88% b. 1 + i 1 + i 1.70 r ≈ R − i = 80% − 70% = 10% Clearly, the approximation gives a real HPR that is too high. 5-4

Chapter 05 - Learning About Return and Risk from the Historical Record14. From Table 5.2, the average real rate on T-bills has been: 0.72% a. T-bills: 0.72% real rate + 3% inflation = 3.72% b. Expected return on large stocks: 3.72% T-bill rate + 8.40% historical risk premium = 12.12% c. The risk premium on stocks remains unchanged. A premium, the difference between two rates, is a real value, unaffected by inflation.15. Real interest rates are expected to rise. The investment activity will shift the demand for funds curve (in Figure 5.1) to the right. Therefore the equilibrium real interest rate will increase.16. a. Probability Distribution of the HPR on the Stock Market and Put: STOCK PUTState of the Probability Ending Price + HPR Ending Value HPREconomy DividendBoom 0.30Normal Growth 0.50 $134 34% $0.00 −100%Recession 0.20 $0.00 −100% $114 14% $29.50 146% $84 −16%Remember that the cost of the index fund is $100 per share, and the cost of the putoption is $12.b. The cost of one share of the index fund plus a put option is $112. The probability distribution of the HPR on the portfolio is:State of the Probability Ending Price + HPR = (134 − 112)/112Economy Put + = (114 − 112)/112 0.30 19.6% = (113.50 − 112)/112Boom 0.50 $4 Dividend 1.8%Normal Growth 0.20 $134.00 1.3%Recession $114.00 $113.50c. Buying the put option guarantees the investor a minimum HPR of 1.3% regardless of what happens to the stock's price. Thus, it offers insurance against a price decline. 5-5

Chapter 05 - Learning About Return and Risk from the Historical Record17. The probability distribution of the dollar return on CD plus call option is:State of the Probability Ending Value Ending Value CombinedEconomy of CD of Call ValueBoom 0.30 $114.00 $19.50 $133.50Normal Growth 0.50 $114.00 $0.00 $114.00Recession 0.20 $114.00 $0.00 $114.00CFA PROBLEMS1. The expected dollar return on the investment in equities is $18,000 compared to the $5,000 expected return for T-bills. Therefore, the expected risk premium is $13,000.2. E(r) = [0.2 × (−25%)] + [0.3 × 10%] + [0.5 × 24%] =10%3. E(rX) = [0.2 × (−20%)] + [0.5 × 18%] + [0.3 × 50%] =20% E(rY) = [0.2 × (−15%)] + [0.5 × 20%] + [0.3 × 10%] =10%4. σX 2 = [0.2 × (– 20 – 20)2] + [0.5 × (18 – 20)2] + [0.3 × (50 – 20)2] = 592 σX = 24.33% σY 2 = [0.2 × (– 15 – 10)2] + [0.5 × (20 – 10)2] + [0.3 × (10 – 10)2] = 175 σX = 13.23%5. E(r) = (0.9 × 20%) + (0.1 × 10%) =19%6. The probability that the economy will be neutral is 0.50, or 50%. Given a neutral economy, the stock will experience poor performance 30% of the time. The probability of both poor stock performance and a neutral economy is therefore: 0.30 × 0.50 = 0.15 = 15%7. E(r) = (0.1 × 15%) + (0.6 × 13%) + (0.3 × 7%) = 11.4% 5-6

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets CHAPTER 6: RISK AVERSION AND CAPITAL ALLOCATION TO RISKY ASSETSPROBLEM SETS1. (e)2. (b) A higher borrowing is a consequence of the risk of the borrowers’ default. In perfect markets with no additional cost of default, this increment would equal the value of the borrower’s option to default, and the Sharpe measure, with appropriate treatment of the default option, would be the same. However, in reality there are costs to default so that this part of the increment lowers the Sharpe ratio. Also, notice that answer (c) is not correct because doubling the expected return with a fixed risk-free rate will more than double the risk premium and the Sharpe ratio.3. Assuming no change in risk tolerance, that is, an unchanged risk aversion coefficient (A), then higher perceived volatility increases the denominator of the equation for the optimal investment in the risky portfolio (Equation 6.12). The proportion invested in the risky portfolio will therefore decrease.4. a. The expected cash flow is: (0.5 × $70,000) + (0.5 × 200,000) = $135,000 With a risk premium of 8% over the risk-free rate of 6%, the required rate of return is 14%. Therefore, the present value of the portfolio is: $135,000/1.14 = $118,421 b. If the portfolio is purchased for $118,421, and provides an expected cash inflow of $135,000, then the expected rate of return [E(r)] is derived as follows: $118,421 × [1 + E(r)] = $135,000 Therefore, E(r) = 14%. The portfolio price is set to equate the expected rate or return with the required rate of return. c. If the risk premium over T-bills is now 12%, then the required return is: 6% + 12% = 18% The present value of the portfolio is now: $135,000/1.18 = $114,407 6-1

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets d. For a given expected cash flow, portfolios that command greater risk premia must sell at lower prices. The extra discount from expected value is a penalty for risk.5. When we specify utility by U = E(r) – 0.5Aσ 2, the utility level for T-bills is: 0.07 The utility level for the risky portfolio is: U = 0.12 – 0.5A(0.18)2 = 0.12 – 0.0162A In order for the risky portfolio to be preferred to bills, the following inequality must hold: 0.12 – 0.0162A > 0.07 ⇒ A < 0.05/0.0162 = 3.09 A must be less than 3.09 for the risky portfolio to be preferred to bills.6. Points on the curve are derived by solving for E(r) in the following equation: U = 0.05 = E(r) – 0.5Aσ 2 = E(r) – 1.5σ 2 The values of E(r), given the values of σ 2, are therefore: σ σ 2 E(r) 0.00 0.0000 0.05000 0.05 0.0025 0.05375 0.10 0.0100 0.06500 0.15 0.0225 0.08375 0.20 0.0400 0.11000 0.25 0.0625 0.14375 The bold line in the following graph (labeled Q6, for Question 6) depicts the indifference curve. 6-2

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets E(r) U(Q7,A=4) U(Q6,A=3) 5 4 U(Q8,A=0) U(Q9,A<0)7. Repeating the analysis in Problem 6, utility is now: U = E(r) – 0.5Aσ 2 = E(r) – 2.0σ 2 = 0.04 The equal-utility combinations of expected return and standard deviation are presented in the table below. The indifference curve is the upward sloping line in the graph above, labeled Q7 (for Question 7). σ σ 2 E(r) 0.00 0.0000 0.0400 0.05 0.0025 0.0450 0.10 0.0100 0.0600 0.15 0.0225 0.0850 0.20 0.0400 0.1200 0.25 0.0625 0.1650 The indifference curve in Problem 7 differs from that in Problem 6 in both slope and intercept. When A increases from 3 to 4, the increased risk aversion results in a greater slope for the indifference curve since more expected return is needed in order to compensate for additional σ. The lower level of utility assumed for Problem 7 (0.04 rather than 0.05) shifts the vertical intercept down by 1%.8. The coefficient of risk aversion for a risk neutral investor is zero. Therefore, the corresponding utility is equal to the portfolio’s expected return. The corresponding indifference curve in the expected return-standard deviation plane is a horizontal line, labeled Q8 in the graph above (see Problem 6). 6-3

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets9. A risk lover, rather than penalizing portfolio utility to account for risk, derives greater utility as variance increases. This amounts to a negative coefficient of risk aversion. The corresponding indifference curve is downward sloping in the graph above (see Problem 6), and is labeled Q9.10. The portfolio expected return and variance are computed as follows: (1) (2) (3) (4) rPortfolio σPortfolio σ 2 PortfolioW Bills (3) × 20% rBills WIndex rIndex (1)×(2)+(3)×(4)0.0 5% 1.0 13.5% 13.5% = 0.135 20% = 0.20 0.04000.2 5% 0.8 13.5% 11.8% = 0.118 16% = 0.16 0.02560.4 5% 0.6 13.5% 10.1% = 0.101 12% = 0.12 0.01440.6 5% 0.4 13.5% 8.4% = 0.084 8% = 0.08 0.00640.8 5% 0.2 13.5% 6.7% = 0.067 4% = 0.04 0.00161.0 5% 0.0 13.5% 5.0% = 0.050 0% = 0.00 0.000011. Computing utility from U = E(r) – 0.5 × Aσ 2 = E(r) – 1.5σ 2 , we arrive at the values in the column labeled U(A = 3) in the following table:W Bills W Index rPortfolio σPortfolio σ2 Portfolio U(A = 3) U(A = 5) 0.20 0.0400 0.0 1.0 0.135 0.16 0.0256 0.0750 0.0350 0.2 0.8 0.118 0.12 0.0144 0.0796 0.0540 0.4 0.6 0.101 0.08 0.0064 0.0794 0.0650 0.6 0.4 0.084 0.04 0.0016 0.0744 0.0680 0.8 0.2 0.067 0.00 0.0000 0.0646 0.0630 1.0 0.0 0.050 0.0500 0.0500The column labeled U(A = 3) implies that investors with A = 3 prefer a portfolio that isinvested 80% in the market index and 20% in T-bills to any of the other portfolios in thetable.12. The column labeled U(A = 5) in the table above is computed from: U = E(r) – 0.5Aσ 2 = E(r) – 2.5σ 2 The more risk averse investors prefer the portfolio that is invested 40% in the market index, rather than the 80% market weight preferred by investors with A = 3.13. Expected return = (0.7 × 18%) + (0.3 × 8%) = 15% Standard deviation = 0.7 × 28% = 19.6% 6-4

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets14. Investment proportions: 30.0% in T-bills 0.7 × 25% = 17.5% in Stock A 0.7 × 32% = 22.4% in Stock B 0.7 × 43% = 30.1% in Stock C15. Your reward-to-volatility ratio: S = 18 − 8 = 0.3571 28 Client's reward-to-volatility ratio: S = 15 − 8 = 0.3571 19.616. 30 25 CAL (Slope = 0.3571) P 20 Client E(r) 15 10 20 30 40 % σ (%) 10 5 0 017. a. E(rC) = rf + y[E(rP) – rf] = 8 + y(18 − 8) If the expected return for the portfolio is 16%, then: 16 = 8 + 10 y ⇒ y = 16 − 8 = 0.8 10 Therefore, in order to have a portfolio with expected rate of return equal to 16%, the client must invest 80% of total funds in the risky portfolio and 20% in T-bills. 6-5

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assetsb. Client’s investment proportions: 20.0% in T-bills 0.8 × 25% = 20.0% in Stock A 0.8 × 32% = 25.6% in Stock B 0.8 × 43% = 34.4% in Stock Cc. σC = 0.8 × σP = 0.8 × 28% = 22.4%18. a. σC = y × 28% b. If your client prefers a standard deviation of at most 18%, then: y = 18/28 = 0.6429 = 64.29% invested in the risky portfolio E(rC) = 8 + 10y = 8 + (0.6429 × 10) = 8 + 6.429 = 14.429%19. a. y* = E(rP ) − rf = 0.18 − 0.08 = 0.10 = 0.3644 3.5 × 0.282 0.2744 Aσ 2 P Therefore, the client’s optimal proportions are: 36.44% invested in the risky portfolio and 63.56% invested in T-bills.b. E(rC) = 8 + 10y* = 8 + (0.3644 × 10) = 11.644% σC = 0.3644 × 28 = 10.203%20. a. If the period 1926 - 2005 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(rM) − rf = 8.39%, σM = 20.54% (we use the standard deviation of the risk premium from Table 6.8). Then y* is given by: y* = E(rM ) − rf = 0.0839 = 0.4972 4 × 0.20542 Aσ 2 M That is, 49.72% of the portfolio should be allocated to equity and 50.28% should be allocated to T-bills.b. If the period 1986 - 2005 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(rM) − rf = 8.60%, σM = 16.24% and y* is given by: y* = E(rM ) − rf = 0.0860 = 0.8152 Aσ 2 4 × 0.16242 M Therefore, 81.52% of the complete portfolio should be allocated to equity and 18.48% should be allocated to T-bills. 6-6

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assetsc. In part (b), the market risk premium is expected to be higher than in part (a) and market risk is lower. Therefore, the reward-to-volatility ratio is expected to be higher in part (b), which explains the greater proportion invested in equity.21. a. E(rC) = 8% = 5% + y(11% – 5%) ⇒ y = 8−5 = 0.5 11 − 5b. σC = yσP = 0.50 × 15% = 7.5%c. The first client is more risk averse, allowing a smaller standard deviation.22. Data: rf = 5%, E(rM) = 13%, σM = 25%, and rfB = 9% The CML and indifference curves are as follows: E(r) lend borrow13 P CCAMLL9 5 σ 25 6-7

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets23. For y to be less than 1.0 (so that the investor is a lender), risk aversion (A) must be large enough such that:y = E(rM ) − rf < 1 ⇒ A > 0.13 − 0.05 = 1.28 Aσ 2 0.252 MFor y to be greater than 1.0 (so that the investor is a borrower), risk aversion must besmall enough such that:y = E(rM ) − rf > 1 ⇒ A < 0.13 − 0.09 = 0.64 Aσ 2 0.252 MFor values of risk aversion within this range, the client will neither borrow nor lend,but instead will hold a complete portfolio comprised only of the optimal riskyportfolio:y = 1 for 0.64 ≤ Α ≤ 1.2824. a. The graph for Problem 22 has to be redrawn here, with: E(rP) = 11% and σP = 15%b. For a lending position: A > 0.11 − 0.05 = 2.67 0.152For a borrowing position: A < 0.11 − 0.09 = 0.89 0.152Therefore, y = 1 for 0.89 ≤ A ≤ 2.67 6-8

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets E(r ) M CM L13 F CAL11 9 5 σ15 2525. The maximum feasible fee, denoted f, depends on the reward-to-variability ratio. For y < 1, the lending rate, 5%, is viewed as the relevant risk-free rate, and we solve for f as follows:11 − 5 − f = 13 − 5 ⇒ f = 6 − 15 × 8 = 1.2%15 25 25For y > 1, the borrowing rate, 9%, is the relevant risk-free rate. Then we notice that,even without a fee, the active fund is inferior to the passive fund because:11 − 9 = 0.13 < 13 − 9 = 0.16 15 25More risk tolerant investors (who are more inclined to borrow) will not be clients of thefund even without a fee. (If you solved for the fee that would make investors whoborrow indifferent between the active and passive portfolio, as we did above for lendinginvestors, you would find that f is negative: that is, you would need to pay investors tochoose your active fund.) These investors desire higher risk-higher return completeportfolios and thus are in the borrowing range of the relevant CAL. In this range, thereward-to-variability ratio of the index (the passive fund) is better than that of themanaged fund. 6-9

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets26. a. Slope of the CML = 13 − 8 = 0.20 25 The diagram follows.b. My fund allows an investor to achieve a higher mean for any given standard deviation than would a passive strategy, i.e., a higher expected return for any given level of risk. Expected Retrun 18 CML and CAL 16 14 CAL: Slope = 0.3571 12 10 CML: Slope = 0.20 8 10 20 30 6 Standard Deviation 4 2 0 027. a. With 70% of his money invested in my fund’s portfolio, the client’s expected return is 15% per year and standard deviation is 19.6% per year. If he shifts that money to the passive portfolio (which has an expected return of 13% and standard deviation of 25%), his overall expected return becomes: E(rC) = rf + 0.7[E(rM) − rf] = 8 + [0.7 × (13 – 8)] = 11.5% The standard deviation of the complete portfolio using the passive portfolio would be: σC = 0.7 × σM = 0.7 × 25% = 17.5% Therefore, the shift entails a decrease in mean from 14% to 11.5% and a decrease in standard deviation from 19.6% to 17.5%. Since both mean return and standard deviation decrease, it is not yet clear whether the move is beneficial. The disadvantage of the shift is that, if the client is willing to accept a mean return on his total portfolio of 11.5%, he can achieve it with a lower standard deviation using my fund rather than the passive portfolio. 6-10

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets To achieve a target mean of 11.5%, we first write the mean of the complete portfolio as a function of the proportion invested in my fund (y): E(rC) = 8 + y(18 − 8) = 8 + 10y Our target is: E(rC) = 11.5%. Therefore, the proportion that must be invested in my fund is determined as follows: 11.5 = 8 + 10y ⇒ y = 11.5 − 8 = 0.35 10 The standard deviation of this portfolio would be: σC = y × 28% = 0.35 × 28% = 9.8% Thus, by using my portfolio, the same 11.5% expected return can be achieved with a standard deviation of only 9.8% as opposed to the standard deviation of 17.5% using the passive portfolio. b. The fee would reduce the reward-to-volatility ratio, i.e., the slope of the CAL. The client will be indifferent between my fund and the passive portfolio if the slope of the after-fee CAL and the CML are equal. Let f denote the fee: Slope of CAL with fee = 18 − 8 − f = 10 − f 28 28 Slope of CML (which requires no fee) = 13 − 8 = 0.20 25 Setting these slopes equal we have: 10 − f = 0.20 ⇒ 10 − f = 28 × 0.20 = 5.6 ⇒ f = 10 − 5.6 = 4.4% per year 2828. a. The formula for the optimal proportion to invest in the passive portfolio is: y* = E(rM ) − rf Aσ 2 M Substitute the following: E(rM) = 13%; rf = 8%; σM = 25%; A = 3.5: y* = 0.13 − 0.08 = 0.2286 3.5 × 0.252b. The answer here is the same as the answer to Problem 27(b). The fee that you can charge a client is the same regardless of the asset allocation mix of the client’s portfolio. You can charge a fee that will equate the reward-to-volatility ratio of your portfolio to that of your competition. 6-11

Chapter 06 - Risk Aversion and Capital Allocation to Risky AssetsCFA PROBLEMS1. Utility for each investment = E(r) – 0.5 × 4 × σ 2We choose the investment with the highest utility value. Expected Standard UtilityInvestment return deviation U E(r) σ -0.0600 0.30 -0.3500 1 0.12 0.50 0.1588 2 0.15 0.16 0.1518 3 0.21 0.21 4 0.242. When investors are risk neutral, then A = 0; the investment with the highest utility is Investment 4 because it has the highest expected return.3. (b)4. Indifference curve 25. Point E6. (0.6 × $50,000) + [0.4 × (−$30,000)] − $5,000 = $13,0007. (b)8. Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16% Expected return of client’s overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Standard deviation of client’s overall portfolio = 0.6 × 14% = 8.4%9. Reward-to-volatility ratio = 10 = 0.71 14 6-12

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assets CHAPTER 6: APPENDIX1. By year end, the $50,000 investment will grow to: $50,000 × 1.06 = $53,000 Without insurance, the probability distribution of end-of-year wealth is: Probability WealthNo fire 0.999 $253,000Fire 0.001 $ 53,000For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(253,000)] + [0.001 × ln(53,000)] = 12.439582The certainty equivalent is: WCE = e 12.439582 = $252,604.85With fire insurance, at a cost of $P, the investment in the risk-free asset is:$(50,000 – P)Year-end wealth will be certain (since you are fully insured) and equal to:[$(50,000 – P) × 1.06] + $200,000Solve for P in the following equation:[$(50,000 – P) × 1.06] + $200,000 = $252,604.85 ⇒ P = $372.78This is the most you are willing to pay for insurance. Note that the expected loss is“only” $200, so you are willing to pay a substantial risk premium over the expectedvalue of losses. The primary reason is that the value of the house is a large proportion ofyour wealth.2. a. With insurance coverage for one-half the value of the house, the premium is $100, and the investment in the safe asset is $49,900. By year end, the investment of $49,900 will grow to: $49,900 × 1.06 = $52,894 If there is a fire, your insurance proceeds will be $100,000, and the probability distribution of end-of-year wealth is:No fire Probability WealthFire 0.999 $252,894 0.001 $152,894For this distribution, expected utility is computed as follows: E[U(W)] = [0.999 × ln(252,894)] + [0.001 × ln(152,894)] = 12.4402225The certainty equivalent is: WCE = e 12.4402225 = $252,766.77 6-13

Chapter 06 - Risk Aversion and Capital Allocation to Risky Assetsb. With insurance coverage for the full value of the house, costing $200, end-of-year wealth is certain, and equal to: [($50,000 – $200) × 1.06] + $200,000 = $252,788 Since wealth is certain, this is also the certainty equivalent wealth of the fully insured position.c. With insurance coverage for 1½ times the value of the house, the premium is $300, and the insurance pays off $300,000 in the event of a fire. The investment in the safe asset is $49,700. By year end, the investment of $49,700 will grow to: $49,700 × 1.06 = $52,682 The probability distribution of end-of-year wealth is:No fire Probability WealthFire 0.999 $252,682 0.001 $352,682For this distribution, expected utility is computed as follows:E[U(W)] = [0.999 × ln(252,682)] + [0.001 × ln(352,682)] = 12.4402205The certainty equivalent is: WCE = e 12.440222 = $252,766.27Therefore, full insurance dominates both over- and under-insurance. Over-insuringcreates a gamble (you actually gain when the house burns down). Risk isminimized when you insure exactly the value of the house. 6-14

Chapter 07 - Optimal Risky Portfolios CHAPTER 7: OPTIMAL RISKY PORTFOLIOSPROBLEM SETS1. (a) and (e).2. (a) and (c). After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash and real estate. Portfolio variance now includes a variance term for real estate returns and a covariance term for real estate returns with returns for each of the other three asset classes. Therefore, portfolio risk is affected by the variance (or standard deviation) of real estate returns and the correlation between real estate returns and returns for each of the other asset classes. (Note that the correlation between real estate returns and returns for cash is most likely zero.)3. (a) Answer (a) is valid because it provides the definition of the minimum variance portfolio.4. The parameters of the opportunity set are:E(rS) = 20%, E(rB) = 12%, σS = 30%, σB = 15%, ρ = 0.10From the standard deviations and the correlation coefficient we generate the covariancematrix [note that Cov(rS, rB) = ρσSσB]:Bonds Bonds StocksStocks 225 45 45 900The minimum-variance portfolio is computed as follows:wMin(S) = σ 2 − Cov(rS , rB ) = 225 − 45 = 0.1739 B − 2Cov(rS , rB ) + 225 − (2 × σ 2 + σ 2 900 45) S B wMin(B) = 1 − 0.1739 = 0.8261The minimum variance portfolio mean and standard deviation are:E(rMin) = (0.1739 × 20) + (0.8261 × 12) = 13.39%σMin = [w 2 σ 2 + w 2 σ 2 + 2w Sw BCov(rS , rB )]1/ 2 S S B B = [(0.17392 × 900) + (0.82612 × 225) + (2 × 0.1739 × 0.8261 × 45)]1/2 = 13.92% 7-1

Chapter 07 - Optimal Risky Portfolios5. Proportion Proportion Expected Standard return Deviation in stock fund in bond fund 12.00% 15.00% 0.00% 100.00% 13.39% 13.92% 13.60% 13.94% 17.39% 82.61% 15.20% 15.70% minimum variance 15.61% 16.54% tangency portfolio 20.00% 80.00% 16.80% 19.53% 18.40% 24.48% 40.00% 60.00% 20.00% 30.00% 45.16% 54.84% 60.00% 40.00% 80.00% 20.00% 100.00% 0.00% Graph shown below.6. The graph indicates that the optimal portfolio is the tangency portfolio with expected return approximately 15.6% and standard deviation approximately 16.5%. 7-2

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