INVESTMENT ECONOMICS
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Economics 494 INVESTMENT ECONOMICS |
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Answers to Recommended Problems III
16. a. Price today = $1052.42 (found using spreadsheet) Price in six months = $1044.52 (found using spreadsheet) b. HPR =
20.
. 22. Accrued interest = (Annual coupon payment / 2) * (Days since last coupon payment / Days between coupon payments) = (70 / 2) * (15 / 182) = $2.88 Invoice price = Bond price + Accrued interest = $1001.25 + $2.88 = $1004.13 . 27. From Excel, the stated YTM is 16.07% and the expected YTM is 8.53%. . 30 ABC has a shorter maturity, which reduces the coupon rate. ABC has collateral backing the bond, which reduces the risk and thus the coupon rate. ABC bonds are not callable, and non-callable bonds usually have a lower coupon rate. ABC bonds don't have a sinking fund. A sinking fund allows the firm to buy back bonds if interest rates decrease, which hurts investors. Therefore, XYZ bondholders need to be compensated with a higher coupon to take into account that the bonds may be bought back by the sinking fund. .
A = Zero coupon bond
B =
C = 10% coupon bond
CFA 3. Market conversion value = Conversion ratio * Price of stock = 20.83 * $28.00 = $583.24 Conversion premium = Price of bond - Market conversion value = $775.00 - $583.24 = $191.76 . Chapter 11 8. Duration (YTM = 6%) = 2.83 years (found with spreadsheet) Duration (YTM = 10%) = 2.82 years (found with spreadsheet) . 9. % Change in price = -D * [change in (1 + y) / (1 + y)] = -7.194 * [0.0050 / (1 + 0.10)] = -0.0327 or -3.27% . 10. w1 = 0.27, w2 = 0.50, w3 = 0.23 D = 1 * 0.27 + 2 * 0.50 + 3 * 0.23 = 1.95 . 11. DZero = 1 year DPerp = (1 + 0.10) / 0.10 = 11 years Asset duration = WZero * 1 + WPerp * 11 = 1.95 => WZero * 1 + (1 - WZero) * 11 = 1.95 => WZero + 11 - 11 WZero = 1.95 => -10 WZero = -9.05 => WZero = 0.905, WPerp = 1 - 0.905 = 0.095 PVLiab = $3.31 million Amount in zero coupon bond = $3.00 million Amount in perpetuity = $0.31 million . 13. Skip . 14. a. The return will be higher with higher risk, so the Baa-rated bonds will have a higher holding period return. b. The price change will be higher with a lower coupon, so the 3% coupon bond will have a higher holding period return. c. The price change will be higher with a lower coupon, so the 4% coupon bond will have a higher holding period return. . 16. a. DLiab = (1 + 0.16) / 0.16 = 7.25 years W * 4 + (1 - W) * 11 = 7.25 => 4 W + 11 - 11 W = 7.25 => -7 W = -3.75 => W = 0.5357 => 1 - W = 0.4643 PVPerp = Amount / r = $2 million / 0.16 = $12.5 million Amount in 5-year maturity bonds = 0.5357 * $12.5 million = $6.70 million Amount in 20-year maturity bonds = 0.4643 * $12.5 million = $5.80 million b. Skip . 19. a. DZero = 5 years DPerp = (1 + 0.05) / 0.05 = 21 years W * 5 + (1 - W) * 21 = 10 => 5 W + 21 - 21 W = 10 => -16 W = -11 => W = 0.6875 => 1 - W = 0.3125 PV = $1,000,000 / (1 + 0.05)10 = $613,913 Amount in zero coupon bond = 0.6875 * $613,913 = $422,065 Amount in 5% perpetuity = 0.3125 * $613,913 = $191,848 b. DZero = 4 years DPerp = (1 + 0.05) / 0.05 = 21 years W * 4 + (1 - W) * 21 = 9 => 4 W + 21 - 21 W = 9 => -17 W = -12 => 0.7059 => 1 - W = 0.2941 PV = $1,000,000 / (1 + 0.05)9 = $644,609 Amount in zero coupon bond = 0.7059 * $644,609 = $455,029 Amount in 5% perpetuity = 0.3125 * $644,609 = $189,579 . 27.
. Chapter 15 4. a. Payoff = 100 * (165 - 160) = $500 Profit = $500 - (15.00 * 100) = -$1,000 b. Payoff = $0 (out of the money) Profit = 0 - (9.40 * 100) = -$940 c. Payoff = $0 (out of the money) Profit = 0 - (11.70 * 100) = -$1,170 d. Payoff = $0 (out of the money) Profit = 0 - (10.85 * 100) = -$1,085 e. Payoff = $0 (out of the money) Profit = 0 - (8.93 * 100) = -$893 f. Payoff = 100 * (170 - 165) = $500 Profit = $500 - (13.00 * 100) = -$800 . 10. The option premiums offset one another. The maximum profit is $2 per share if the price hits $40 or more (call strike price of $40 - share price of $38). The maximum loss is $3 per share if the price hits $35 or less (put strike price of $35 - share price of $38). . 11. The collar involves buying 5,000 $35 puts for $15,000 and selling 5,000 $45 calls for $10,000 for a net premium of -$5,000.
. 12.
. 15. a. Writing covered calls at $45 would bring in $30,000 in premiums. If the price rises to above $45, the total received would be $480,000 ($450,000 + $30,000). The price could drop to $32 a share and still yield the $350,000 necessary for the down payment (sell stock for $320,000 and add the $30,000 in premiums received). b. Buying a protective put at $35 would cost $30,000 in premiums. There is no limit to the gain if the stock price went up. If the stock price dropped below $35, there wouldn't be enough money to make the down payment (the stock could be sold for $350,000, but deducting the premiums would yield a net position of $320,000). If the price dropped below $38, there would not be enough for the down payment. c. The net premium for the collar would be $0. If the price drops below $35, the stock could be sold for $350,000, which is enough for the down payment. If the stock price goes above $45, it must be sold for $450,000, which allows a cash reserve. (c) is the best option. . 17. See question 27. . 22. Call premium (1 contract or 100 options) = $893 Put premium (1 contract or 100 options) = $1,085 Total premium received = $1,978 a.
. b. IBM @ 167 => put payoff = 0, call payoff = 0, premium received = 1978 => profit = $1,978 IBM @ 175 => put payoff = 0, call payoff = -500, premium received = 1978 => profit = $1,478 c. Options expire if the stock price is between 165 and 170. Breakeven points = 165.00 - 19.78 = $145.22 on the downside and 170 + 19.78 = $189.78 on the upside d. The investor is betting the price of IBM will be relatively stable, fluctuating only between $145.22 and $189.78. . 27. The price of a call decreases when the exercise price increases. Therefore, the price of the 50 call is $9 and the price of the 60 call is $3. Writing the 50 call and buying the 60 call results in a net premium of +$6 per option. a.
b.
c. The breakeven point is $56 per share. Writing the 50 call means $1 is lost for every dollar above $50. The net premium of $6 received would cover a stock price increase to $56. The investor is bearish on the stock, i.e., thinks it will sell for less than $56 per share. . Chapter 16 5. a. Because B is more volatile, its price should be higher. But its price is the same as A. That means that A's price is higher for some reason. With puts, a lower stock price means the option price is higher. Therefore, A is written on the stock with the lower stock price. b. B is written on the stock with the lower stock price because the price is higher. c. B must have the lower time to expiration because its price is lower. d. B is written on the stock with the higher volatility because its price is higher. e. A is written on the stock with the higher volatility because its price is higher. . 16. D1 = [ln (50 / 50) + (0.03 + 0.52 / 2) * 0.5] / (0.5 * 0.50.5) = 0.22 D2 = .22 - (0.5 * 0.50.5) = -0.13 N(0.22) = 0.5871 N(-0.13) = 0.4483 C = 50 * 0.5871 - 50 * e-0.03*0.5 * 0.4483 = $7.27 . 17.
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