Investments and Portfolio Management BKM 9th solutions.doc

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. (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.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.5.Corp. BondsPreferred StockCommon StockVoting Rights (Typically)YesContractual ObligationYesPerpetual PaymentsYesYesAccumulated DividendsYesFixed Payments (Typically)YesYesPayment Preference FirstSecondThird6.Municipal Bond interest is tax-exempt. When facing higher marginal tax rates, a high-income investor would be more inclined to pick tax-exempt securities.7.a.You would have to pay the asked price of:86:14 = 86.43750% of par = $864.375b.The coupon rate is 3.5% implying coupon payments of $35.00 annually or, more precisely, $17.50 semiannually.c. Current yield = Annual coupon income/price = $35.00/$864.375 = 0.0405 = 4.05%8.P = $10,000/1.02 = $9,803.929.The total before-tax income is $4. After the 70% exclusion for preferred stock dividends, the taxable income is: 0.30 ´ $4 = $1.20Therefore, taxes are: 0.30 ´ $1.20 = $0.36After-tax income is: $4.00 $0.36 = $3.64Rate of return is: $3.64/$40.00 = 9.10%10.a.You could buy: $5,000/$67.32 = 74.27 sharesb.Your annual dividend income would be: 74.27 ´ $1.52 = $112.89c.The price-to-earnings ratio is 11 and the price is $67.32. Therefore:$67.32/Earnings per share = 11 Þ Earnings per share = $6.12d.General Dynamics closed today at $67.32, which was $0.47 higher than yesterdays price. Yesterdays closing price was: $66.8511.a.At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333The 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 = 83.333After the split, Stock C sells for 55. Therefore, we need to find the divisor (d) such that: 83.333 = (95 + 45 + 55)/d Þ d = 2.340c.The return is zero. The index remains unchanged because the return for each stock separately equals zero.12.a.Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500Rate of return = ($40,500/$39,000) 1 = 3.85%b. The return on each stock is as follows:rA = (95/90) 1 = 0.0556rB = (45/50) 1 = 0.10rC = (110/100) 1 = 0.10The equally-weighted average is:0.0556 + (-0.10) + 0.10/3 = 0.0185 = 1.85%13.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.14.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%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 which 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.16.a.The higher coupon bond.b.The call with the lower exercise price.c.The put on the lower priced stock.17.a. You bought the contract when the futures price was $3.835 (see Figure 2.10). The contract closes at a price of $3.875, which is $0.04 more than the original futures price. The contract multiplier is 5000. Therefore, the gain will be: $0.04 ´ 5000 = $200.00b.Open interest is 177,561 contracts.18.a.Since the stock price exceeds the exercise price, you exercise the call.The payoff on the option will be: $21.75 - $21 = $0.75The cost was originally $0.64, so the profit is: $0.75 - $0.64 = $0.11b.If the call has an exercise price of $22, you would not exercise for any stock price of $22 or less. The loss on the call would be the initial cost: $0.30c.Since the stock price is less than the exercise price, you will exercise the put. The payoff on the option will be: $22 - $21.75 = $0.25The option originally cost $1.63 so the profit is: $0.25 $1.63 = $1.3819.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 call at expirationInitial Cost Profita.04-4b.04-4c.04-4d.541e.1046Value of put at expirationInitial Cost Profita.1064b.56-1c.06-6d.06-6e.06-621.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.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.CFA PROBLEMS 1. (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.4.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%.CHAPTER 3: HOW SECURITIES ARE TRADEDPROBLEM SETS 1. Answers to this problem will vary.2.The dealer sets the bid and asked price. Spreads should be higher on inactively traded stocks and lower on actively traded stocks.3.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, or $800 total. If the price of IBM shares goes above $128, then the stop-buy order would be executed, limiting the losses from the short sale.4. (a) A market order is an order to execute the trade immediately at the best possible price. The emphasis in a market order is the speed of execution (the reduction of execution uncertainty). The disadvantage of a market order is that the price it will be executed at is not known ahead of time; it thus has price uncertainty.5. (a) The advantage of an Electronic Crossing Network (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. 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 = $12,000The 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 = $4,320Therefore, the remaining margin in the investors account is:$9,000 - $4,320 = $4,680The 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%7.a.The initial margin was: 0.50 ´ 1,000 ´ $40 = $20,000As a result of the increase in the stock price Old Economy Traders loses:$10 ´ 1,000 = $10,000Therefore, 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 = $8,000b.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%8.a.The buy order will be filled at the best limit-sell order price: $50.25b.The next market buy order will be filled at the next-best limit-sell order price: $51.50c.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 = $400The rate of return will be: b.The value of the 200 shares is 200P. Equity is (200P $5,000). You will receive a margin call when:= 0.30 Þ when P = $35.71 or lower10.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:= 0.30 Þ when P = $57.69 or higher11.The total cost of the purchase is: $40 ´ 500 = $20,000You 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 = $17,000Percentage 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 = $13,000Percentage 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 ´ = % change in price ´ 1.333For 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% ´ = 13.33%b.The value of the 500 shares is 500P. Equity is (500P $5,000). You will receive a margin call when:= 0.25 Þ when P = $13.33 or lowerc.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:= 0.25 Þ when P = $26.67 or lowerWith 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 = $5,400The 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)= 0.1067 = 10.67%(ii)= 0.0267 = 2.67%(iii) = 0.1600 = 16.00%The relationship between the percentage return and the percentage change in the price of Intel is given by:% return = 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:=10.67%e.The value of the 500 shares is 500P. Equity is (500P $5,400). You will receive a margin call when:= 0.25 Þ when P = $14.40 or lower12.a.The gain or loss on the short position is: (500 ´ P)Invested funds = $15,000Therefore: rate of return = (500 ´ P)/15,000The 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) = $35,000Liabilities are 500P. You will receive a margin call when:= 0.25 Þ when P = $56 or higherc. 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:= 0.25 Þ when P = $55.20 or higher13.The broker is instructed to attempt to sell your Marriott stock as soon as the Marriott stock trades at a bid price of $20 or less. Here, the broker will attempt to execute, but may not be able to sell at $20, since the bid price is now $19.95. The price at which you sell may be more or less than $20 because the stop-loss becomes a market order to sell at current market prices.14.a.$55.50b.$55.25c.The trade will not be executed because the