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Solution Manual For Investments, 12th Edition

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    CHAPTER 1: THE INVESTMENT ENVIRONMENT 1-1 CHAPTER 1: THE INVESTMENT ENVIRONMENT PROBLEM SETS 1. While it is u ltimately true that real assets determine the material well - being of an economy , financial innovation in the form of bundling and unbundling securities creates opportunities for investors to form more efficient portfolios . Both institutional and individual investors can benefit when financial engineering creates new products that allow them to manage their portfolios of financial assets more efficiently . B undling and unbundling create financial products with new properties and sensitivities to various sources of risk that allows investors to reduce volatility by hedg ing 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 t axation/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 . Securitization works well and can benefit many, but only if the market for these securities is highly liquid. As securitization progresses, however, and financial intermediaries lose opportunities, they must increase other revenue - generating activities such as providing short - term liquidity to consumers and small business and financial services. 4. The existence of efficient capital markets and the liquid trading of f inancial assets make it easy for large firms to raise the capital needed to finance their investments in real assets . If Ford , 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.

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    CHAPTER 1: THE INVESTMENT ENVIRONMENT 1-2 5. 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, shares that can be traded in the secondary market are more attractive to initial investors since they know that 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. Remember that stock exchanges like those in New York, London, and Paris are the heart of capitalism, in which firms can raise capital quickly in primary markets because investors know there are liquid secondary markets. 6. a. No . The increase in price did not add to the productive capacity of the economy. b . Yes, the value of the equity held in these assets has increased . c . Future homeowners as a whole are worse off, since mortgage liabilities have also increased . In addition, this housing price bubble will eventually burst and society as a whole (and most likely taxpayers) will suffer the damage. 7 . a . The bank loan is a financial liability for Lanni, and a financial asset for the bank. The cash Lanni receives is a financial asset . The new financial asset created is Lanni's promissory note to repay the loan . b. Lanni transfers financial assets (cash) to the software developers. In return, Lanni receives the completed software package, which is a real asset . No financial assets are created or destroyed; cash is simply transferred from one party to another. c. Lanni exchanges the real asset (the software) for a financial asset, which is 1,250 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. By selling its shares in Microsoft, Lanni exchanges one financial asset ( 1,250 shares of stock) for another ($ 12 5 ,000 in cash ). Lanni uses the financial asset of $50,000 in cash to repay the bank and retire its promissory note. The bank must return its financial asset to Lanni. The loan is "destroyed" in the transaction, since it is retired when paid off and no longer exists.

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    CHAPTER 1: THE INVESTMENT ENVIRONMENT 1-3 8 . a. Assets Liabilities & Shareholders’ E quity 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 = 0.30 b. Assets Liabilities & Shareholders’ E quity 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 = 1.0 c. Assets Liabilities & Shareholders’ E quity Microsoft shares $ 12 5 ,000 Bank loan $ 50,000 Computers 30,000 Shareholders’ equity 10 5 ,000 Total $ 15 5 ,000 Total $ 15 5 ,000 Ratio of real assets to total assets = $30,000/$ 15 5 ,000 = 0. 19 Conclusion: when the firm starts up and rai ses working capital, it is characterized by a low ratio of real assets to total assets . When it is i n 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 . a. For commercial banks, t he ratio is : $ 1 34.3 /$ 17,532.8 = 0. 0 0 77 b. For nonfinancial firms, t he ratio is : $ 2 3 , 678 /$ 45 , 464 = 0. 5 208 c. The difference should be expected primarily be cause the bulk of the business of financial institutions is to make loans and the bulk of the business of non - financial corporations is to invest in equipment, manufacturing plants, and property. The loans are financial assets for financial institutions, but the investments of non - financial corporations are real assets. 10 . a . Primary - market transaction in which gold certificates are being offered to public investors for the first time by an underwriting syndicate led by JW Korth Capital.

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    CHAPTER 1: THE INVESTMENT ENVIRONMENT 1-4 b . The certificates are d erivative assets because they represent an investment in physical gold, but each investor receives a certificate and no gold. Note that investors can convert the certificate into gold during the four - year period. 11 . 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 , so a manager might not feel too compelled to work hard to maximize firm value. 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 . Five years of vesting helps align the interests of the employee with the long - term performance of the firm. 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 la rge stock position in the firm. c. A profit - linked salary create s great incentives for managers to contribute to the firm’s success . However , a manager whose salary is tied to short - term profits will be risk seeking, especially if these short - term profits determine salary or if the compensation structure does not bear the full cost of the project’s risks . 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 Ford stock and can increase the value of the firm by 5%, a very ambitious goal, you benefit by only : 0.05  $10,000 = $500 . The cost, both personal and financial to an individual investor, is likely to be prohibitive and would typically easily exceed any accrued benefits, in this case $500. In contrast, a creditor, such as 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 domestic and international securities markets. Pension funds accept funds and then invest in a wide range of financial securities , on behalf of current and future retirees, thereby channeling funds from one sector of the economy to another.

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    CHAPTER 1: THE INVESTMENT ENVIRONMENT 1-5 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. 15. 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 over all 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 investors might 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 the appropriate level of risk tolerance . In addition, this technique tends to require more active management, thus generating more transaction costs . Finally, the bottom - up analysis may be incorrect, in which case there will be a 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. Financial a ssets provide for a means to acquire real assets as well as an expansion of these real assets . Financial assets provide a measure of liquidity to real assets and allow for investors to more effectively reduce risk through diversification. 18. Allowing traders to share in the profits increases th e traders’ willingness to assume risk . Traders will share in the upside potential directly in the form of higher compensation but only in the downside indirectly in the form of potential job loss if performance is bad enough. This scenario creates a form of agency conflict known as moral hazard, in which the owners of the financial institution share in both the total profits and losses, while the traders will tend to share more of the gains than the losses.

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    CHAPTER 1: THE INVESTMENT ENVIRONMENT 1-6 19. Answers may vary, however, students should touch on the following: increased transparency, regulations to promote capital adequacy by increasing the frequency of gain or loss settlement, incentives to discourage excessive risk taking, and the promotion of more accurate and unbiased risk assessment .

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    Chapter 2 - Asset Classes a nd Financial Instruments 2-1 CHAPTER 2: ASSET CLASSES AND FINANCIAL INSTRUMENTS PROBLEM SETS 1. 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 high level of 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. Examples of money market securities include Treasury bills, commercial paper, and banker's acceptances, each of which is highly marketable and traded in the secondary market. 3 . (a) A repurchase agreement is an agreement whereby the seller of a security agrees to “repurchase” it from the buyer on an agreed upon date at an agreed upon price . Repos are typically used by securities dealers as a means for obtaining funds to purchase securities. 4 . Spreads between risky commercial paper and risk - free government securities will widen . Deterioration of the economy increases the likelihood of default on commercial paper, making them more risky . Investors will demand a greater premium on all risky debt securities , not just commercial paper . 5. Corp. Bonds Preferred Stock Common Stock Voting r ights ( t ypically) Yes c ontractual o bligation Yes Perpetual p ayments Yes Yes Accumulated d ividends Yes Fixed p ayments ( t ypically) Yes Yes Payment p reference First Second Third

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    Chapter 2 - Asset Classes a nd Financial Instruments 2-2 6. Municipal b ond interest is tax - exempt at the federal level and possibly at the state level as well . When facing hi gher marginal tax rates, a high - income investor would be more inclined to invest in tax - exempt securities. 7 . a. You would have to pay the ask price of: 1 01 . 9297 % of par value of $1,000 = $ 1 ,019.297 b. The coupon rate is 3 . 000 % ; implying coupon payments of $ 30.00 annually or, more precisely $ 15 . 00 ( semiannually ) . c . The yield to maturity on a fixed income security is also known as its required return and is reported by The Wall Street Journal and others in the financial press as the ask yield. In this case, the yield to maturity is 2. 902 %. An investor buying this security today and holding it until it matures will earn an annual return of 2. 902 %. Students will learn in a later chapter how to compute both the price and the yield to maturity with a financial calculator. 8 . Treasury bills are discount securities that mature for $10,000. Therefore, a specific T - bill price is simply the maturity value divided by one plus the semi - annual return: P = $10,000/1.02 = $9,803.92 9 . The total before - tax income is $4 . After the 50 % exclusion for preferred stock dividends, the taxable income is: 0. 5 0  $4 = $ 2 . 0 0 Therefore, taxes are: 0.30  $ 2.0 0 = $0. 60 After - tax income is: $4.00 – $0. 60 = $3. 40 Rate of return is: $3. 40 /$40.00 = 8.50 % 10 . a . You could buy: $5,000/$ 57.94 = 86.30 shares . Since it is not possible to trade in fractions of shares, you could buy 86 shares of Herbalife . b . Your annual dividend income would be: 86  $ 1 . 20 = $ 103. 20 c . The price - to - earnings rati o is 47.75 and the price is $ 57.94 . Therefore: $ 57.94 /Earnings per share = 47.75  Earnings per s hare = $ 1.21 d . Herbalife closed today at $ 57.94 , which was $ 1.39 lower than yesterday’s price of $ 59.33 .

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    Chapter 2 - Asset Classes a nd Financial Instruments 2-3 11 . 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: (95+45+ 110 )/3 = 250/3 = 83.333 with a divisor of 3. After the split, s tock C sells for 55 . Therefore, we need to find the divisor (d) such that: 83.333 = (95 + 45 + 55)/d  d = 2.340 . The divisor fell, which is always the case after one of the firms in an index splits its shares. c. The return is zero . The index remains unchanged because the return for each stock separately equals zero. 1 2 . a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000 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% b. The return on each stock is as follows: r A = (95/90) – 1 = 0.0556 r B = (45/50) – 1 = – 0.10 r C = (110/100) – 1 = 0.10 The equally weighted average is: [0.0556 + ( - 0.10) + 0.10]/3 = 0.0185 = 1.85% 1 3 . The after - tax yield on the corporate bonds is: 0.09  (1 – 0.30) = 0.063 = 6.30% Therefore, municipals must offer a yield to maturity of at least 6.30%. 1 4 . Equation (2. 2 ) shows that the equivalent taxable yield is: r = r m /( 1 – t ) , so simply substitute each tax rate in the denominator to obtain the following: a. 4.00% b. 4.44% c. 5.00% d. 5.71%

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    Chapter 2 - Asset Classes a nd Financial Instruments 2-4 15. In an equally weighted index fund, each stock is given equal weight regardless of its market capitalization . Smaller cap stocks will have the same weight as larger cap stocks . The challenges are as follows: • Given equal weights placed to smaller cap and larger cap, equal - weighted indices (EWI) will tend to be more volatile than their market - capitalization counterparts ; • It follows that EWIs are not good reflectors of the broad market that they represent; EWIs underplay the economic importance of larger companies . • Turnover rates will tend to be higher, as an EWI must be rebalanced back to its original target . By design, many of the transactions would be among the smaller, less - liquid stocks. 1 6 . a. The ten - year Treasury bond with the higher coupon rate will sell for a higher price because its bondholder receives higher interest payments. b. The call option with the lower exercise price has more value than one with a higher exercise price . c. The put option written on the lower priced stock has more value than one written on a higher priced stock. 1 7. a. You bought the contract when the futures price was $ 3.96 (see Table 2. 8 ). The contract closes at a price of $ 4.06 , which is $0. 10 more than the original futures price . The contract multiplier is 5000 . Therefore, the gain will be: $0. 08  5 00 0 = $ 400 .00 1 8 . a. T he call option gives you the right, but not the obligation to buy at $ 100; the stock is trading in the secondary market at $ 103 . Since the stock price exceeds the exercise price, you exercise the call. The p ayoff on the option will be: $ 1 03 - $ 1 00 = $ 3 The cost was originally $ 3. 81 , so the profit is: $ 3 - $ 3. 81 = - $ .81 b. Since the stock price is greater than the exercise price, you will exercise the call. The payoff on the option will be: $ 1 03 - $ 95 = $ 8 The option originally cost $ 7.65 , so the profit is $ 8 - $ 7.65 = $. 35 . c. Owning the put option gives you the right, but not the obligation, to sell at $ 105 , but you could sell in the secondary market for $ 03 if you exercise the call the payoff on the option will be: $ 105 - $ 103 = $ 2 . The option originally cost $ 4.79 , so the profit is $ 2.00 - $ 4.79 = - $ 2.79 .

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    Chapter 2 - Asset Classes a nd Financial Instruments 2-5 19 . 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. 20. Value of C all at E xpiration Initial Cost Profit a. 0 4 - 4 b. 0 4 - 4 c. 0 4 - 4 d. 5 4 1 e. 10 4 6 Value of P ut at E xpiration Initial Cost Profit a. 10 6 4 b. 5 6 - 1 c. 0 6 - 6 d. 0 6 - 6 e. 0 6 - 6 21 . 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. Both positions, however, benefit if the price of the underlying asset falls. 22 . 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. Both positions, however, benefit if the price of the underlying asset rises. CFA PROBLEMS 1. (d) There are tax advantages for corporations that own preferred shares. 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. 4. a. The taxable bond . With a zero tax bracket, the after - tax yield for the

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    Chapter 2 - Asset Classes a nd Financial Instruments 2-6 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 . T he 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%.

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-1 CHAPTER 3: HOW SECURITIES ARE TRADED PROBLEM SETS 1. Limit buy order: an order that purchases stock if the price falls below a predetermined level. Limit sell order : sells stock when the price rises above a predetermined level. Limite orders are not guaranteed to execute since the price may not reach the trigger point. Market order : either a buy or sell order that is executed immediately at the current market price 2 . In response to the potential negative reaction to large [block] trades, trades will be split up into many small trades, effectively hiding the total number of shares bought or sold. 3 . The use of leverage necessarily magnifies returns to investors. Leveraging borrowed money allows for greater return on investment if the stock price increases. However, if the stock price declines, the investor must repay the loan , regardless of how far the stock price drops , and incur a negative rate of return . For example, if an investor buys an asset at $100 and the price rises to $110, the investor earns 10%. If an investor takes out a $40 loan at 5% and buys the same stock, the return will be 13.3%, computed as follows: $10 capital gain minus $2 interest expense divided by the $60 original investment. Of course, if the stock price falls below $100, the negative return will be greater for the leveraged account. 4. a. False: An investor who wishes to sell shares immediately should ask his or her broker to enter a market order. b. False: The ask price is greater than the bid price. (note: the opposite is true for yields) c. False: An issue of additional shares of stock to the public by Microsoft would be called seasoned offering . d. True 5 . (a) A broker market consists of intermediaries who have the discretion to trade for their clients. A large block trade in an illiquid security would most likely trade in this market as the brokers would have the best access to clients interested in this type of security. The advantage of an e lectronic communication n etwork (ECN) is that it can execute large block orders without affecting the public quote . Since this security is illiquid, large block orders are less likely to occur and thus it would not likely trade through an ECN .

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-2 Electronic limit - order markets (ELOM) transact securities with high trading volume . This illiquid security is unlikely to be traded on an ELOM. 6 . 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 c. The percentage margin is now: $4,680/$9,000 = 0.52 , or 52% > 30%. Therefore, the investor will not receive a margin call. d. Using an end price of $30, t he 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 , or − 41.5% Alternatively, divide the initial equity investments into the change in value plus the interest payment: ($3,000 loss + $320 interest)/$8,000 = - 0.415. 7 . 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 , or 16% S o there will be a margin call.

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-3 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 , or − 60% 8 . a. The buy order for FinTrade 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 − = = b. The value of the 200 shares is 200 P . Equity is (200 P – $5,000) . You will receive a margin call when: P P 200 000 , 5 $ 200 − = 0.30  when P = $35.71 or lower 10 . 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 100 P . Therefore, equity is ($7,500 – 100 P ) . A margin call will be issued when: P P 100 100 500 , 7 $ − = 0.30  when P = $57.69 or higher 11. The total cost of the purchase is: $ 2 0  1 , 00 0 = $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 $15,000. a. (i) Equity increases to: ($ 22  1 , 000 ) – $5,000 = $17,000

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-4 Percentage gain = $2,000/$15,000 = 0.1333 , or 13.33% (ii) With price unchanged, equity is unchanged. Percentage gain = zero (iii) Equity falls to ($ 18  1 , 000 ) – $5,000 = $13,000 Percentage gain = ( – $2,000/$15,000) = – 0.1333 , or – 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  equity initial s Investor' investment Total = % change in price  1.333 For example, when the stock price rises from $ 20 to $ 22 , the percentage change in price is 10%, while the percentage gain for the investor is: % return = 10%  000 , 15 $ 000 , 20 $ = 13.33% b. The value of the 1 , 00 0 shares is 1 , 000 P . Equity is ( 1 , 000 P – $5,000) . You will receive a margin call when: P P 000 , 1 000 , 5 $ 000 , 1 − = 0.25  when P = $ 6.67 or lower c. The value of the 1,0 00 shares is 1,0 00 P . But now you have borrowed $10,000 instead of $5,000 . Therefore, equity is ( 1,0 00 P – $10,000) . You will receive a margin call when: P P 000 , 1 000 , 10 $ 000 , 1 − = 0.25  when P = $ 13.33 or lower With less equity in the account, you are far more vulnerable to a margin call. e. 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 ( 1 , 000 P – $5,400) . Initial equity was $15,000 . Therefore, your rate of return after one year is as follows: (i) 000 , 15 $ 000 , 15 $ 400 , 5 $ ) 22 $ 000 , 1 ( − −  = 0.1067 , or 10.67% (ii) 000 , 15 $ 000 , 15 $ 400 , 5 $ ) 20 $ 000 , 1 ( − −  = – 0.0267 , or – 2.67% (iii) 000 , 15 $ 000 , 15 $ 400 , 5 $ ) 18 $ 000 , 1 ( − −  = – 0.1600 , or – 16.00%

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-5 The relationship between the percentage return and the percentage change in the price of Xtel is given by: % return =          equity initial s Investor' investment Total price in change %          − equity initial s Investor' borrowed Funds % 8 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:        000 , 15 $ 000 , 20 $ % 10        − 000 , 15 $ 000 , 5 $ % 8 =10.67% e. The value of the 1000 shares is 1 , 000 P . Equity is ( 1 , 000 P – $5,400) . You will receive a margin call when: P P 000 , 1 400 , 5 $ 000 , 1 − = 0.25  when P = $ 7.20 or lower 12. a. The gain or loss on the short position is: ( – 1 , 000  Δ P ) Invested funds = $15,000 Therefore: rate of return = ( – 1 , 000  Δ P )/15,000 The rate of return in each of the three scenarios is: (i) R ate of return = ( – 1 , 000  $ 2 )/$15,000 = – 0.1333 , or – 13.33% (ii) R ate of return = ( – 1 , 000  $0 )/$15,000 = 0% (iii) R ate of return = [ – 1 , 000  ( – $ 2 )]/$15,000 = +0.1333 , or +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 500 P . You will receive a margin call when: P P 000 , 1 000 , 1 000 , 35 $ − = 0.25  when P = $ 28 or higher c. With a $1 dividend, the short position must now pay on the borrowed shares: ($1/share  1000 shares) = $ 10 00 . Rate of return is now: [( – 1 , 000  Δ P ) – 1 , 000 ]/15,000 (i) R ate of return = [( – 1 , 000  $ 2 ) – $ 1 , 000 ]/$15,000 = – 0. 2000 , or – 20.00 % (ii) R ate of return = [( – 1 , 000  $0) – $ 1 , 000 ]/$15,000 = – 0.0 667 , or – 6.67 %

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-6 (iii) R ate of return = [( – 1 , 000 )  ( – $ 2 ) – $ 1 , 000 ]/$15,000 = +0. 067 , or + 6.67 % Total assets are $35,000, and liabilities are ( 1 , 000 P + 1 , 000 ) . A margin call will be issued when: P P 000 , 1 000 , 1 000 , 1 000 , 35 − − = 0.25  when P = $ 27.2 or higher 13. The broker is instructed to attempt to sell your Marabel, Inc. stock as soon as the Marabel, Inc. stock trades at a bid price of $ 70 or less . Here, the broker will attempt to execute but may not be able to sell at $ 70 , since the bid price is now $ 6 9 .95 . The price at which you sell may be more or less than $ 70 because the stop - loss becomes a market order to sell at current market prices. 1 4 . 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. 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 Ixnay 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: P P 000 , 1 000 , 20 $ 000 , 1 − = 0.35  when P = $30.77 or lower 16. The proceeds from the short sale (net of commission) were: ($ 21  100) – $50 = $ 2 , 0 50 A dividend payment of $200 was withdrawn from the account . Cover ing the short sale at $15 per share cost s ( with commission): $ 1,5 00 + $50 = $ 1,5 50 Therefore, the value of your account is equal to the net profit on the transaction: $2,0 50 – $200 – $ 1,5 50 = $ 3 00

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    CHAPTER 3: HOW SECURITIES ARE TRADED 3-7 te that your profit ($300) equals (100 shares  profit per share of $3). Your net proceeds per share were: $21 selling price of stock – $15 repurchase price of stock – $ 2 dividend per share – $ 1 2 trades  $0.50 commission per share $ 3 CFA PROBLEMS 1. 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.

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    CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES 4-1 CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES PROBLEM SETS 1. 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 : D iversification 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 : D iversification 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 ; ability to coordinate realization of capital gains or losses with investor s ’ personal tax situation s ; capability of designing portfolio to investor’s specific risk and return 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.

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    CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES 4-2 5 . Unlike an open - end fund, in which underlying shares are redeemed when the fund is redeemed, a closed - end fund trades as a security in the market . Thus, their prices may differ from the NAV. 6 . Advantages of an ETF over a mutual fund: • ETFs are continuously traded and can be sold or purchased on margin . • There are no c apital g ains t ax triggers when an ETF is sold (shares are just sold from one investor to another) . • Investors buy from b rokers, thus eliminating the cost of dire c t marketing to individual small investors . This implies lower management fees . Disadvantages of an ET F over a mutual fund: • Prices can depart from NAV (unlike an open - end fund) . • There is a b roker fee when buying and selling (unlike a no - load fund) . 7 . 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 = 06 . 0 1 70 . 10 $ Load 1 NAV − = − = $11.38 8 . NAV = O ffering price  (1 – L oad) = $12.30  .95 = $11.69 9 . Stock Value H eld by F und A $ 7,000,000 B 12,000,000 C 8,000,000 D 15,000,000 Total $42,000,000 Net asset value = 000 , 000 , 4 000 , 30 $ 000 , 000 , 42 $ − = $10.49 10 . Value of stocks sold and replaced = $15,000,000 Turnover rate = 000 , 000 , 42 $ 000 , 000 , 15 $ = 0.357 , or 35.7%

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    CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES 4-3 11 . a. 40 . 39 $ 000 , 000 , 5 000 , 000 , 3 $ 000 , 000 , 200 $ NAV = − = b. Premium (or discount) = NAV NAV ice Pr − = 40 . 39 $ 40 . 39 $ 36 $ − = – 0.086 , or - 8.6% The fund sells at an 8.6% discount from NAV . 1 2 . 1 0 0 NAV NAV Distributions $12.10 $12.50 $1.50 0.088, or 8.8% NAV $12.50 − + − + = = 1 3 . a. Start - of - year price: P 0 = $12.00 × 1.02 = $12.24 End - of - year price: P 1 = $12.10 × 0.93 = $11.25 Although NAV increased by $0.10, the price of the fund decreased by $0.99 . Rate of return = 1 0 0 Distributions $11.25 $12.24 $1.50 0.042, or 4.2% $12.24 P P P − + − + = = b. 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: 1 0 0 NAV NAV Distributions $12.10 $12.00 $1.50 0.133, or 13.3% NAV $12.00 − + − + = = 1 4 . 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 sh ould be concerned that the poor performance will persist. 1 5 . NAV 0 = $200,000,000/10,000,000 = $20 Dividends per share = $2,000,000/10,000,000 = $0.20 NAV 1 is based on the 8% price gain, less the 1% 12b - 1 fee: NAV 1 = $20  1.08  (1 – 0.01) = $21.384 Rate of return = 20 $ 20 . 0 $ 20 $ 384 . 21 $ + − = 0.0792 , or 7.92%

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    CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES 4-4 1 6 . 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 , or 18.2% . 17. 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 . 18. A s 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% . 19. Assume $1 , 000 investment Loaded - Up Fund Economy Fund Yearly g rowth ( r is 6%) (1 .01 .0075) r + − − (.98) (1 .0025) r  + − t = 1 y ear $1,042.50 $1,036.35 t = 3 y ears $1,133.00 $1,158.96 t = 10 y ears $1,516.21 $1,714.08 20. a. $450,000,000 $10,000000 $10 44,000,000 − = b. The redemption of 1 million shares will most likely trigger capital gains taxes which will lower the remaining portfolio by an amount greater than $10,000,000 (implying a remaining total value less than $440,000,000) . The outstandin g shares fall to 43 million and the NAV drops to below $10. 2 1 . Suppose you have $1,000 to invest . The initial investment in Class A shares is $940 ( = $1000 × [1 - .06]) 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

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    CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES 4-5 After paying the back - end load fee, your portfolio value will be: $1,437.66  .99 = $1,423.28 Class B shares are the better choice if your horizon is four years. With a 15 - 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. 2 2 . 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  1.06 2 . If the mutual fund is to be the better investment, then the portfolio return ( r ) must satisfy: 0.96  (1 + r – 0.005) 2 > 1.06 2 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% b. If you invest for six years, then the portfolio return must satisfy: 0.96  (1 + r – 0.005) 6 > 1.06 6 = 1.4185 (1 + r – 0.005) 6 > 1.4776 1 + r – 0.005 > 1.0672 r > 7.22% The cutoff rate of return is lower for the six - year investment because the “fixed cost” (the one - time front - end load) is spread over a greater number of years.

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    CHAPTER 4: MUTUAL FUNDS AND OTHER INVESTMENT COMPANIES 4-6 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. 2 3 . 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% 2 4 . For the bond fund, the fraction of portfolio income given up to fees is: % 0 . 4 % 6 . 0 = 0.150 , or 15.0% For the equity fund, the fraction of investment earnings given up to fees is: % 0 . 12 % 6 . 0 = 0.050 , or 5.0% 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 investm ent trusts are low turnover, low trading costs , and low management fees . This is a more important concern to bond - market investors. 2 5 . 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 11 managers exhibiting precisely this level of "consistency" even if performance is due solely to luck.

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    CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD 5-1 CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD PROBLEM SETS 1. 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, i t is possible that a n increase in the expected inflation rate w ould be accompanied by a change in the r eal 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. I f 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 data set back to 1880 . 3. Nominal Real Real 1 1 .45 1 1.1154 11.54% 1 1 .30 r r r i + + + = = = → = + + 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 5 % holding period return for the year . If you forecast that the rate on money market instruments will increase significantly above the current 3 % 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 5 % per year, which is 1 0 0 basis points higher than the rate on the one - year savings deposit; however, you could earn a one - year HPR much less than 4 % on the bond if long - term interest rates increase during the year . If Treasury bond yields rise above 5 %, then the price of the bond will fall, and the resulting capital loss will wipe out some or all of the 5 % return you would have earned if bond yields had remained unchanged over the course of the year.

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    CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD 5-2 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 are equivalent to an increase in the supply of funds (a shift of the supply curve to the right) . The FED buys treasuries with cash from its own account or it issues certificates which trade like cash. As a result, there is an increase in the money supply, and the equilibrium real rate of interest will fall. 6 . 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 - p lus 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%  2 = [0.35 × (44 .5 – 14) 2 ] + [0.30 × (14 – 14) 2 ] + [0.35 × ( – 16 .5 – 14) 2 ] = 6 51.175  = 25. 52 % The mean is unchanged, but the standard deviation has increased, as the probabilities of the high and low returns have increased.

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    CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD 5-3 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 - end): Economy Probability YTM Price Capital Gain Coupon Interest HPR Boom 0.20 11.0% $ 74.05 − $25.95 $8.00 − 17.95% Normal g rowth 0.50 8.0 100.00 0.00 8.00 8.00 Recession 0.30 7.0 112.28 12.28 8.00 20.28 9. E ( q ) = (0 × 0.25) + ( 1 × 0.25) + (2 × 0.50) = 1.25 σ q = [0.25 × (0 – 1.25) 2 + 0.25 × (1 – 1.25) 2 + 0.50 × (2 – 1.25) 2 ] 1/2 = 0.8292 10. (a) With probability 0.9544 , the value of a normally distributed variable will fall within 2 standard deviations of the mean; that is, between – 40% and 80%. Simply add a nd subtract 2 standard deviations to and from the mean. 11. From Table 5 . 4 , the average risk premium Big/Value for the period 192 7 - 20 1 8 was: 11.69 % per year . Adding 11. 69 % to the 3% risk - free interest rate, the expected annual HPR for the Big/Value portfolio is: 3.00% + 11.69 % = 14. 69 % . 12 . (01/ 19 30 - 6 / 197 4 ) Small Big Low 2 High Low 2 High Average 0.99% 1.17% 1.48% 0.76% 0.81% 1.19% SD 8.29% 8.38% 10.17% 5.70% 6.72% 8.89% Skew 1.30 1.63 2.35 0.17 1.75 1.77 Kurtosis 9.74 13.10 17.69 7.06 17.80 14.64 ( 0 7 / 197 4 - 12/ 201 8 ) Small Big Low 2 High Low 2 High Average 1.00% 1.35% 1.45% 0.99% 1.05% 1.13% SD 6.69% 5.28% 5.49% 4.70% 4.35% 4.90% Skew - 0.43 - 0.55 - 0.47 - 0.33 - 0.43 - 0.54 Kurtosis 2.08 3.60 4.30 1.99 2.57 2.96

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    CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD 5-4 . The distributions from (01/1930 – 06/1974) and (07/1974 – 12/2018) periods have distinct characteristics due to systematic shocks to the economy and subsequent government intervention. While the returns from the two periods do not differ greatly, their respective distributions tell a different story. The standard deviation for all six portfolios is larger in the first period. Skew is also positive, but negative in the second, showing a greater likelihood of higher-than-normal returns in the right tail. Kurtosis is also markedly larger in the first period. 13 . a nominal nominal real 1 0.80 0.70 1 0.0588, 5.88% 1 1 1.70 r r i r or i i + − − = − = = = + + b. nominal .80 .70 .10 real r i r − = − =  Clearly, the approximation gives a real HPR that is too high. 14 . From Table 5. 3 , the average real rate on T - bills has been 0. 46 % . a. T - bills: 0. 46 % real rate + 3% inflation = 3. 46 % b. Expected return on Big/Value : 3. 46 % T - bill rate + 11. 69 % historical risk premium = 15. 15 % 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 d istribution of the HPR on the s toc k m arket and p ut: STOCK PUT State of the Economy Probability Ending Price + Dividend HPR Ending Value HPR Excellent 0.25 $ 131 .00 31 .00 % $ 0.00 − 100% Good 0.45 114 .00 14 .00 $ 0.00 − 100 Poor 0.25 93.25 − 6.75 $ 20.25 68.75 Crash 0. 0 5 48 . 00 − 52 .00 $ 64.00 433.33 Remember that the cost of the index fund is $100 per share, and the cost of the put option is $12.

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    CHAPTER 5: INTRODUCTION TO RISK, RETURN, AND THE HISTORICAL RECORD 5-5 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 Economy Probability Ending Price + Put + Dividend HPR Excellent 0.25 $ 131 .00 17.0 % = (13 1 − 112)/112 Good 0.45 114.00 1.8 = (114 − 112)/112 Poor 0.25 113.50 1.3 = (113.50 − 112)/112 Crash 0. 0 5 112.00 0.0 = ( 112 − 112)/112 c. Buying the put option guarantees the investor a minimum HPR of 0.0 % regardless of what happens to the stock's price . Thus, it offers insurance against a price decline. 17. The probability distribution of the dollar return on CD plus call option is: State of the Economy Probability Ending Value of CD Ending Value of Call Combined Value Excellent 0.25 $ 114.00 $1 6 .50 $13 0 .50 Good 0.45 114.00 0.00 114.00 Poor 0.2 5 114.00 0.00 114.00 Crash 0.05 114.00 0.00 114.00 18. a. Total return of the bond is (100/84.49) - 1 = 0.1836. With t = 10, the annual rate on the real bond is (1 + EAR) = = 1.69%. b. With a per quarter yield of 2%, the annual yield is = 1.0824 , or 8.24%. The equivalent continuously compounding (cc) rate is ln(1+.0824) = .0792 , or 7.92% . The risk - free rate is 3.55 % with a cc rate of ln(1+.0355) = .0349 , or 3.49% . The cc risk premium will equal .0792 - .0349 = .0443 , or 4.433%. c. T he appropriate formula is , where . Using solver or goal seek, setting the target cell to the known effective cc rate by changing the unknown variance ( cc ) rate, the equivalent standard deviation (cc) is 18.03% (excel may yield slightly different solutions) . d. The expected value of the excess return will grow by 120 months (12 months over a 10 - year horizon). Therefore the excess return will be 120 × 4.433% = 531.9%. The expected SD grows by the square root of time

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