Chapter 6
第六章
Bonds, Bond Prices, and the Determination of Interest Rates
債券、債券價格及利率決定
Conceptual and Analytical Problems
概念與分析問題
Consider a U.S. Treasury Bill with 270 days to maturity. If the annual yield is 3.8 percent, what is the price? (LO1)
考慮一張 270 天到期的美國國庫券。如果年收益率為 3.8%，其價格是多少？（LO1）
Answer:
回答：
*You are an officer of a commercial bank and wish to sell one of the bank’s assets—a car loan—to another bank. Using equation A5 in the appendix to Chapter 4, compute the price you expect to receive for the loan if the annual interest rate is 6 percent, the car payment is $430 per month, and the loan term is five years. (LO1)
您是商業銀行的員工，希望將銀行的一項資產——汽車貸款——賣給另一家銀行。使用第四章附錄中的方程式 A5 計算，若年利率為 6%，汽車付款金額為每月 430 美元，貸款期限為五年，預期收到的貸款價格為多少。（LO1）
Answer: The present value of the payments can be found by using equation A5 in the appendix to Chapter 4:
答案：透過參考第四章附錄中的公式 A5，可以計算付款的現值：
PV =
The monthly payment, C, is given as $430 per month and there are 60 months in the five year horizon. The annual interest rate is 6 percent, so the monthly rate in decimal form is
每月付款金額，C，為每月 430 美元，並在五年期限內共有 60 個月。年利率為 6%，因此每月利率的十進制形式為
im = (1.06)1/12 – 1 = .00487
Thus, the value of the car loan is
因此，汽車貸款的價值是
PV =
= $22,326*Your financial adviser recommends buying a 10-year bond with a face value of $1,000 and an annual coupon of $80. The current interest rate is 7 percent. What might you expect to pay for the bond (aside from brokerage fees)? (LO1)
您的財務顧問建議購買面值為 1,000 美元、年利率為 80 美元的 10 年期債券。當前利率為 7％。您可能預期為這張債券支付多少（除了經紀費以外）？（LO1）
Answer: The value of the bond has two components: the present value of the coupon payments and the present value of the return of principal at maturity. This is:
答：債券價值的兩個組成部分：債券支付的現值和到期時本金回歸的現值。這是：
P =
+In this expression, C is the coupon payment, i is the interest rate, n is the number of periods the coupon payments are made, and F is the face value. Using the information in the question, we have
在此表達式中，C 是券息支付，i 是利率，n 是券息支付的期數，F 是面值。使用問題中的資訊，我們有
P =
+ = 561.89 + 508.35 = 1,070.24*Consider a coupon bond with a $1,000 face value and a coupon payment equal to 5 percent of the face value per year. (LO2)
考慮一張面值為 1,000 美元的債券，其年利息支付等於面值的 5%（LO2）
If there is one year to maturity, find the yield to maturity if the price of the bond is $990.
若到期日為一年，則當債券價格為 990 美元時，計算到期收益率。
Explain why finding the yield to maturity is difficult if there are two years to maturity and you do not have a financial calculator.
解釋為何在還有兩年期滿的情況下，沒有金融計算器時計算到期收益率會困難。
Answer:
回答：
a. The yield to maturity can be found by equating the current price of the bond to the present value of the coupon payment plus the present value of the face value when both payments are due in one year. Specifically,
a. 到期收益可通過將债券的當前價格等於一年內到期的票面價值和利息支付的現值來計算。具體而言，
990 =
Then
然後
(1 + i) =
= 1.061 so that i = .061 or 6.1 percent.
所以 i = .061 或 6.1 百分比。
b. If there are two years to maturity, then we would need to solve
b. 若到期日為兩年，則我們需要解決
990 =
The presence of the quadratic term makes this equation much more time- consuming to solve without a financial calculator.
二次項的存在使得這個方程在沒有金融計算器的情況下解起來更加耗時。
Which of these $100 face value one-year bonds will have the highest yield to maturity and why? (LO2)
這些$100 面值的 1 年期債券中，哪一種的到期收益率最高？為何？（LO2）
A 6 percent coupon bond selling for $85
A 6% 優惠債券，售價為 85 美元.
A 7 percent coupon bond selling for $100
A 7% 優惠債券，售價為 100 美元.
An 8 percent coupon bond selling for $115
$115 售出的 8%優惠券債券.
Answer:
回答：
a.
b.
c.
Option (a) has the highest yield to maturity. The yield to maturity depends both on the coupon payment and any capital gain or loss arising from the difference between the selling price and the face value of the bond. While (a) has the lowest coupon rate, it is selling below face value, and so there is a capital gain. Option (b) is selling at face value, so there is no capital gain and option (c) is selling above face value and so there is a capital loss. As the calculations above show, the combination of the coupon payment and the capital gain on option (a) produces the highest yield to maturity.
選項(a)的到期收益率最高。到期收益率既取決於息票支付，也取決於由於賣價與債券面值的差異而產生的任何資本損益。雖然(a)的息票率最低，但它以面值以下的价格出售，因此有資本獲利。選項(b)以面值出售，因此沒有資本獲利，而選項(c)以面值以上出售，因此有資本損失。正如上述計算所顯示，選項(a)的息票支付和資本獲利的組合產生了最高的到期收益率。
You are considering purchasing a consol that promises annual payments of $4. (LO2)
您正在考虑購買一個承諾每年支付 4 美元的債券。（LO2）
If the current interest rate is 5 percent, what is the price of the consol?
如果當前利率為 5%，無息債券的價格是多少？
You are concerned that the interest rate may rise to 6 percent. Compute the percentage change in the price of the consol and the percentage change in the interest rate. Compare them.
您擔心利率可能上升至 6%。計算債券價格的百分比變化和利率的百分比變化。進行比較。
Your investment horizon is one year. You purchase the consol when the interest rate is 5 percent and sell it a year later, following a rise in the interest rate to 6 percent. What is your holding period return?
您的投資期限為一年。當利率為 5%時購買永續債，一年後在利率上升至 6%時賣出。您的持有期回報是多少？
Answer:
回答：
a.
Price falls by 16.7%; and interest rises by 20%
價格下跌 16.7%；利率上升 20%.
c.
*Suppose you purchase a three-year, 5-percent coupon bond at par and hold it for two years. During that time, the interest rate falls to 4 percent. Calculate your annual holding period return. (LO2)
假設您以面值購買一張三年期、5%票面利率的債券，並持有兩年。在此期間，利率下降至 4%。計算您的年度持有期回報。（LO2）
Answer: The total holding period return over the two years consists of two coupon payments of $5 each plus the capital gain from the rise in the price of the bond due to the interest rate fall.
答：兩年總持有期回報包括兩次每張 5 美元的息票支付以及由於利率下降導致債券價格上升的資本利得。
The price at which you sell the bond after two years will be (5/1.04) + (100/1.04) = $100.96.
兩年後你賣出債券的價格將是 (5/1.04) + (100/1.04) = $100.96。
Holding period return over two years = (10/100) + [(100.96 –100)/100] = 0.1096 or 10.96%
持有期收益率超过两年 = (10/100) + [(100.96 –100)/100] = 0.1096 或 10.96%.
The total payoff on the bond for which you paid $100 is $110.96
$100 買的債券總回報為$110.96.
To calculate the annual rate of return, we refer to the footnote on p. 140. It is assumed, for simplicity, that the first-year coupon is not reinvested for the second year. The annual rate of return is [(110.96/100)1/2 – 1] = .0534 or 5.34 percent. Because the interest rate fell during the holding period and you made a capital gain, the annual holding period return is higher than the coupon rate.
為計算年化回報率，我們參考第 140 頁的註釋。為了簡化，假設第一年的息票在第二年並未再投資。年化回報率為[(110.96/100) 1/2 – 1] = .0534 或 5.34 百分比。因為在持有期間利率下降且您獲得了資本利得，所以年持有期回報率高於息票率。
In a recent issue of the Wall Street Journal (or on www.wsj.com or an equivalent financial website), locate the prices and yields on U.S. Treasury issues. For one bond selling above par and one selling below par (assuming they both exist), compute the current yield and compare it to the coupon rate and the ask yield listed. (LO2)
在最近一期的《華爾街日報》（或 www.wsj.com 或相當於的金融網站），尋找美國國庫券的價格和收益率。對於一張售價高於面值的債券和一張售價低於面值的債券（假設這兩者都存在），計算當前的收益率並將其與列出的票面利率和要價收益率進行比較。（LO2）
Answer:
回答：
a. For the Treasury bond due February 15, 2029 with a coupon of 5.25%, on April 23, 2019, the bond price was 122.9531 and the asked yield 2.587%. That means the current yield was (5.25/122.9531) × 100 = 4.35%, so the coupon rate > current yield > asked yield, in line with Table 6.1 when the bond price is above the face value of 100.
a. 2029 年 2 月 15 日到期的國庫券，票面利率為 5.25%，2019 年 4 月 23 日的券面價格為 122.9531，要求收益率為 2.587%。這意味著當前收益率为(5.25/122.9531) × 100 = 4.35%，因此票面利率 > 當前收益率 > 要求收益率，與表 6.1 中券面價格超過 100 元面值的情況相符。
b. For the Treasury bond due November 15, 2027 with a coupon of 2.25%, on April 23, 2019, the bond price was 97.7031 and the asked yield 2.55%. That means the current yield was 2.25/97.7031 × 100 = 2.30%, so the coupon rate < current yield < asked yield, in line with Table 6.1 when the bond price is below the face value of 100.
b. 2027 年 11 月 15 日到期的國庫券，票面利率為 2.25%，2019 年 4 月 23 日的價格為 97.7031，要求收益率為 2.55%。這意味著當前收益率为 2.25/97.7031 × 100 = 2.30%，因此優先利率 < 當前收益率 < 要求收益率，與表 6.1 中當券價低於 100 元面值時的情況相符。
In a recent issue of the Wall Street Journal (or on www.wsj.com), locate the yields on government bonds for various countries. Find a country whose 10-year government bond yield was above that on the U.S. 10-year Treasury bond and one whose 10-year yield was below the Treasury yield. What might account for these differences in yields? (LO4)
在最近一期的《華爾街日報》（或 www.wsj.com），尋找各國政府債券的收益率。找到一個其 10 年期政府債券收益率高於美國 10 年期國庫券的國家，以及一個其 10 年期收益率低於國庫券收益率的國家。這些收益率差異可能是由什麼原因造成的？（LO4）
Answer: As of Tuesday, April 23, 2019, the 10-year U.S. Treasury yield was 2.571%, while the 10-year government bond yields in Australia and Italy were 1.906% and 2.677%, respectively. As the bonds all have the same maturity, yield differentials reflect differences in default risk and inflation risk. In the case of Australia, they most likely reflect differences in long-run inflation expectations, with inflation in Australia expected to be lower than in the United States. In the case of Italy, where inflation should remain similar to other members of the euro area (perhaps slightly lower than in the United States), the yield differential may reflect higher default risk.
答案：截至 2019 年 4 月 23 日星期二，10 年期美國國庫券收益率為 2.571%，而澳洲和義大利的 10 年期政府債券收益率分別為 1.906%和 2.677%。由於這些債券的到期日相同，收益率差異反映了違約風險和通脹風險的差異。在澳洲的情況下，這可能反映了長期通脹預期上的差異，預期澳洲的通脹將低於美國。在義大利的情況下，通脹應該與歐元區其他成員國相似（可能略低於美國），收益率差異可能反映了更高的違約風險。
A 10-year zero-coupon bond has a yield of 6 percent. Through a series of unfortunate circumstances, expected inflation rises from 2 percent to 3 percent. The face value of the bond is $100. (LO2, LO4)
十年零息债券的收益率为 6%。由于一系列不幸的情况，预期通货膨胀率从 2%上升到 3%。债券的面值为 100 美元。（LO2，LO4）
Assuming the nominal yield rises in an amount equal to the rise in expected inflation, compute the change in the price of the bond.
假設名義收穫率與預期通脹上升的幅度相等，計算債券價格的變化。
Suppose that expected inflation is still 2 percent, but the probability that it will move to 3 percent has risen. Describe the consequences for the price of the bond.
假設預期通脹仍為 2%，但通脹上升至 3%的機率已增加。描述對債券價格的影響。
Answer:
回答：
Price (with 2% expected inflation) = 100/(1.06)10 = $55.84
價格（預期 2%的通脹）= 100/(1.06) 10 = $55.84
Price (with 3% expected inflation) = 100/(1.07)10 = $50.83
價格（預期 3%通脹）= 100/(1.07) 10 = $50.83
The price has fallen by $5.01
價格下跌了 5.01 美元
There is increased inflation risk. Investors will require compensation for taking on additional risk, so the price will fall and the yield will rise.
通脹風險增加。投資者將要求補償以承擔額外風險，因此價格將下跌，收益將上升。
You are sitting at the dinner table and your father is extolling the benefits of investing in bonds. He insists that as a conservative investor he will only make investments that are safe, and what could be safer than a bond, especially a U.S. Treasury bond? What accounts for his view of bonds? Explain why you think it is right or wrong. (LO4)
你正坐在餐桌前，你的父亲在赞扬投资债券的好处。他坚持认为作为一个保守的投资者，他只会进行安全的投资，还有什么比债券更安全呢，尤其是美国国债？是什么构成了他对债券的看法？解释你认为这是正确还是错误（LO4）
Answer: Like most people, your father believes that the government guarantee means that he will get his investment back. He’s right that the U.S. Treasury is extremely unlikely to default. But he’s wrong about interest-rate and inflation risk. The value of the bond will fluctuate when the interest rate changes (moving inversely) and the purchasing power of the coupon and principal repayment will fluctuate with inflation. So, the bond is not risk free.
答案：像大多数人一样，你父親認為政府保證意味著他將收回投資。他確實認為美國國庫極不可能違約。但他在利率和通脹風險方面是錯的。當利率變化時（呈反比），債券的價值將會波動，而息票和本金還款的購買力將隨著通脹波動。因此，債券並非沒有風險。
*Consider a one-year, 10-percent coupon bond with a face value of $1,000 issued by a private corporation. The one-year risk-free rate is 10 percent. The corporation has hit on hard times, and the consensus is that there is a 20 percent probability that it will default on its bonds. If an investor were willing to pay at most $775 for the bond, is that investor risk-neutral or risk averse? (LO4)
考慮一張面值為 1000 美元、年利率為 10%的私人公司發行的 1 年期債券。1 年期無風險利率為 10%。該公司遭遇困難時期，公認的風險是該公司有 20%的機率會違約。如果投資者願意以最多 775 美元購買這張債券，該投資者是風險中性的還是風險规避的？（LO4）
Answer: If the bond were risk free, it would pay off $1,100 in one year’s time - $100 coupon payment and $1,000 face value of the bond.
答：如果這個債券沒有風險，它將在一年後支付 $1100 - $100 的債券息金和 $1000 的債券面值。
If there is a 20% risk of default, then the expected value of these payment flows associated with the bond are ($1,100 × 0.8) + ($0 × 0.2) = $880
如果預計有 20%的違約風險，則與該債券相關的付款流量的預期值為（$1,100 × 0.8）+（$0 × 0.2）= $880
The present value of $880 in one year’s time is $880/1.1 = $800. This would be the price a risk-neutral investor would be willing to pay.
現值為一年後的 880 美元是 880/1.1 = 800 美元。這將是風險中立的投資者願意支付的價格。
If the investor is willing to pay at most $775 for the bond, he or she requires compensation for bearing the risk associated with the bond and so is risk averse.
如果投資者願意為債券支付最多 775 美元，他或她需要為承擔與債券相關的風險獲得補償，因此是風險规避的。
If, after one year, the yield to maturity on a multi-year coupon bond that was issued at par is higher than the coupon rate, what happened to the price of the bond during that first year? (LO2)
若在滿一年的時候，一張以面值發行的多年期附息債券的到期收益率高於票面利率，那麼在那第一年裡債券的價格發生了什麼變化？（LO2）
Answer: The price of the bond fell below par. When a bond is at par, the yield to maturity equals the coupon rate. If the yield to maturity rises, the price of the bond falls. If you buy the bond below par, the capital gain you receive by holding it to maturity is included along with the coupon payments, so the yield to maturity is higher than the coupon rate alone.
答：債券價格下跌至面值以下。當債券為面值時，到期收益率等於票面利率。如果到期收益率上升，債券價格下跌。如果您以面值以下價格購買債券，持有至到期時所獲得的資本利得將與票面付款一併計入，因此到期收益率將高於單獨的票面利率。
Use your knowledge of bond pricing to explain under what circumstances you would be willing to pay the same price for a consol that pays $5 a year forever and a 5-percent, 10-year coupon bond with a face value of $100 that only makes annual coupon payments for 10 years, at which point principal is returned. (LO1, LO2)
使用您對債券價格的知識，解釋在何種情況下您願意為每年支付 5 美元永遠的無期債和一張面值為 100 美元、僅支付 10 年每年利息的 5%十年期債券支付相同的價格，在這 10 年期滿後，本金將被歸還。（LO1，LO2）
Answer: The price you are willing to pay for a bond reflects the present value of the payment flows from the bond. In this case, if i = 5%, the present value of the payment flows for both these bonds would be $100. Intuitively, while the consol makes coupon payments forever, the 10-year coupon bond pays back the principal at maturity, which then can be reinvested. Assuming you have no reason to believe that rates will rise or fall over the 10-year period, you would be indifferent between these bonds. If you are certain that rates will be higher in ten years, you would prefer the 10-year coupon bond, whose proceeds can then be reinvested at the higher rate while the value of the consol would have fallen. Similarly, if you are certain that rates will be lower in ten years, you would prefer the consol.
:::傳統中文翻譯：
答：您願意為一張債券支付的價格反映了該債券付款流的現值。在這種情況下，如果 i = 5%，這兩張債券的付款流現值都將是 100 美元。直觀來說，雖然永續債永遠支付利息，但 10 年期債券在到期時將還本，這後續可以再投資。假設您沒有理由相信利率在 10 年內會上升或下降，您會對這些債券無所謂。如果您確定 10 年後利率會更高，您會傾向於選擇 10 年期債券，其收益可以以更高的利率再投資，而永續債的價值則會下降。同樣，如果您確定 10 年後利率會更低，您會傾向於選擇永續債。
*You are about to purchase your first home and receive an advertisement regarding adjustable-rate mortgages (ARMs). The interest rate on the ARM is lower than that on a fixed rate mortgage. The advertisement mentions that there would be a payment cap on your monthly payments and you would have the option to convert to a fixed-rate mortgage. You are tempted. Interest rates are currently low by historical standards and you are eager to buy a house and stay in it for the long term. Why might an ARM not be the right mortgage for you? (LO4)
您即將購買您的第一個家園，並收到一則關於可調整利率貸款（ARM）的廣告。ARM 的利率低於固定利率貸款的利率。廣告中提到，您的每月付款將設有付款上限，並且您有選擇轉為固定利率貸款的選項。您感到誘惑。根據歷史標準，當前的利率相對低，您急於購買房屋並長期居住。為什麼 ARM 可能不是適合您的貸款呢？（LO4）
Answer: There are several factors to consider. First, with a fixed rate mortgage, your payments are fixed over the life of the loan. The interest rate on this mortgage is higher because the lender is assuming the interest rate risk. The ARM has a lower interest rate in part because you will assume risk associated with interest rate movements over the life of the loan (your payments will rise if rates rise). Given that interest rates are currently relatively low, it is more likely that they will rise, pushing up your payments. This problem is more likely to be an issue the longer you plan to stay in the house. Second, converting later to a fixed-rate mortgage from an adjustable rate loan often involves restrictions and fees. Third, payment caps may limit how much your monthly payments can rise, but may be associated with negative amortization if your payments don’t cover the interest costs of your loan. Shortages are added to the principal of your loan, pushing up your costs.
答：考慮的因數有好幾個。首先，固定利率貸款的付款在貸款期間是固定的。這種貸款的利率較高，因為貸款人承擔了利率風險。可調利率貸款的利率較低，部分原因是你將承擔與利率變動相關的風險（如果利率上升，你的付款將上升）。考慮到當前利率相對較低，它們更有可能上升，推高你的付款。這個問題在你計劃在房子裡住得更久時，更有可能成為問題。其次，將來從可調利率貸款轉為固定利率貸款通常涉及限制和費用。第三，付款上限可能會限制你的月付款上升的幅度，但如果你的付款不夠蓋過貸款的利息成本，則可能會與負面貸款相關。短缺將被加到你的貸款本金上，推高你的成本。
Use the model of supply and demand for bonds to illustrate and explain the impact of each of the following on the equilibrium quantity of bonds outstanding and on equilibrium bond prices and yields: (LO3)
使用债券供需模型来说明和解释以下各项对未偿还债券的均衡数量、均衡债券价格和收益的影响：（LO3）
A new website is launched facilitating the trading of corporate bonds with much more ease than before.
一個新的網站已經上線，使得企業債券的交易比以前更加便利。
Inflationary expectations in the economy fall evoking a much stronger response from issuers of bonds than investors in bonds
經濟通脹預期下降，引發債券發行者比債券投資者更強烈的反應.
The government removes tax incentives for investment and spends additional funds on a new education program. Overall, the changes have no effect on the government’s financing requirements.
政府取消對投資的稅收優惠，並將額外資金用於新的教育計劃。總的來說，這些變化對政府的融資需求沒有影響。
All leading indicators point to stronger economic growth in the near future. The
所有主要指标均指向近期经济更强劲的增长。
response of bond issuers dominates that of bond purchasers.
發行者對債券的回應佔據了債券購買者的回應。
Answer:
回答：
a. The new website would increase the relative liquidity of bonds, shifting the bond demand curve to the right, increasing the equilibrium price of bonds and reducing yields. The equilibrium quantity of bonds outstanding rises.
a. 新網站將增加債券的相對流動性，將債券需求曲線向右移動，提高債券的均衡價格並降低收益率。未償還債券的均衡數量上升。
b. For a given nominal interest rate, a fall in inflationary expectations increases the real interest rate, shifting the bond supply curve to the left and the bond demand curve to the right. If the response of the bond issuers is relatively stronger, the supply curve shift will dominate and the quantity of bonds outstanding will fall. Regardless of the relative size of the shifts, the equilibrium price of bonds will rise and yields will fall.
b. 在給定的名義利率下，通脹預期下降會提高實際利率，將債券供給曲線向左移動，債券需求曲線向右移動。如果債券發行者對應的反應相對較強，供給曲線的移動將佔主導地位，未償還債券的數量將下降。無論移動的相對大小如何，債券的均衡價格將上升，收益率將下降。
c. The removal of tax incentives on investment would make investment more costly, reducing the supply of bonds by corporations, shifting the supply curve to the left. As there is no change in the financing requirements of the government, the supply of government bonds doesn’t change. Equilibrium quantity falls. Equilibrium bond prices rise and yields fall.
c. 投資稅收優惠的取消會使投資成本增加，減少企業債券供應，將供應曲線向左移動。由於政府融資需求無變化，政府債券供應不變。均衡數量下降。均衡債券價格上升，收益率下降。
d. A business cycle upturn increases business investment opportunities, shifting the bond supply curve to the right. Wealth also increases, shifting the bond demand curve to the right. If the supply shift dominates, equilibrium bond prices fall and yields rise. The equilibrium quantity of bonds outstanding increases.
d. 商業循環上升增加商業投資機會，將債券供給曲線向右移動。財富也增加，將債券需求曲線向右移動。如果供給移動佔主導地位，則均衡債券價格下跌，收益率上升。未償債券的均衡數量增加。
Suppose that a sustainable peace is reached around the world, reducing military spending by the U.S. government. How would you expect this development to affect the U.S. bond market? (LO3)
假設全球達成可持續和平，美國政府減少軍事開支。您預期這項發展將如何影響美國債券市場？（LO3）
Answer: As the government’s need to issue bonds to finance military spending is reduced, the supply of government bonds will fall, shifting the supply curve to the left. Bond prices will increase and yields will fall.
答案：隨著政府對發行債券以籌集軍事開支的需求減少，政府債券的供給將下降，使供給曲線向左移動。債券價格將上升，收益率將下降。
Use the model of supply and demand for bonds to determine the impact on bond prices and yields of expectations that the real estate market is going to weaken. (LO3)
使用債券供需模型來確定對債券價格和收益的影響，預期房地產市場將會弱化。（LO3）
Answer: If we think of real estate as an alternative investment to bonds, expected weakness in the real estate market implies an increase in the relative return on bonds. Bond demand shifts to the right, increasing the equilibrium bond prices and lowering yields.
答案：如果我們將房地產視為債券的替代性投資，則房地產市場預期的疲軟意味著債券相對回報率的上升。債券需求向右移動，增加均衡債券價格並降低收益率。
*Suppose there is an increase in investors’ willingness to hold bonds at a given price. Use the model of the demand for and supply of bonds to show that the impact on the equilibrium bond price depends on how sensitive the quantity supplied of bonds is to the bond price. (LO3)
假設投資者願意以特定價格持有債券的意願增加。使用債券需求和供給的模型，來說明對均衡債券價格的影響取決於債券供給量對債券價格的敏感度。（LO3）
Answer: The sensitivity of bond supply to changes in the price of bonds is reflected in the slope of the supply curve. The more sensitive quantity supplied is to a movement in the price, the flatter the supply curve and the smaller the impact on the equilibrium price for any given shift in the demand curve.
回答：債券供應對債券價格變化的敏感度在供應曲線的斜率中體現。供應量對價格變動越敏感，供應曲線就越平緩，對任何給定需求曲線移動的均衡價格影響就越小。
Under what circumstances would purchase of a Treasury Inflation Protected Security (TIPS) from the U.S. government be virtually risk free? (LO4)
在何種情況下，從美國政府購買國庫通膨保護證券（TIPS）將幾乎沒有風險？（LO4）
Answer: Purchasing a Treasury Inflation Protected Security (TIPS) would be virtually risk free if you purchased a bond whose maturity exactly matched your investment horizon. The default risk of holding a U.S. government-issued bond is very low while inflation risk is eliminated by the inflation-indexed nature of the TIPS. If you know your investment horizon with certainty and purchase a bond whose maturity matches that horizon, you eliminate interest rate risk, as you are confident that the bond will be redeemed at par when it matures. Interest rate movements that cause the price of the bond to change before it matures will not affect you.
回答：如果您購買一張到期日與您的投資期限完全匹配的國庫通脹保護證券（TIPS），購買國庫通脹保護證券（TIPS）將幾乎沒有風險。持有美國政府發行的債券的信用風險非常低，而通脹風險則由 TIPS 的通脹指數特點消除。如果您確定您的投資期限，並購買一張與該期限相匹配的債券，您就消除了利率風險，因為您有信心該債券到期時將以面值還本。在債券到期前導致債券價格變化的利率變動不會影響您。
In the wake of the financial crisis of 2007-2009, negative connotations often surrounded the term mortgage-backed security. What arguments could you make to convince someone that they may have benefitted from the growth in securitization over the past 50 years? (LO4)
在 2007-2009 年金融危機之後，抵押贷款支持證券這一術語常帶有負面含義。你會提出哪些論點來說服別人，他們可能從過去 50 年證券化增長中獲益？（LO4）
Answer: If the person you are trying to convince is a borrower, they may have received a lower mortgage interest rate due to the increased liquidity provided by securitization. If they are from a small town, they may have found it easier to get a mortgage as securitization broadened the potential sources of funds for their loan. If they are an investor, you might point to the opportunities for diversification provided by securitization.
答：如果您试图说服的人是借款人，他们可能因证券化提供的增加流动性而获得了较低的抵押贷款利率。如果他们是来自小镇的人，他们可能发现更容易获得抵押贷款，因为证券化扩大了他们贷款的资金来源。如果他们是投资者，您可以指出证券化提供的多元化机会。
During the euro-area sovereign debt crisis, the spread between the yields on bonds issued by the governments of geographically peripheral European countries (such as Greece, Ireland, Italy, Portugal, and Spain) and those on bonds issued by Germany widened considerably. Use the model of supply and demand for bonds to illustrate how this could be explained by a change in investors’ perceptions of the relative riskiness of peripheral sovereign versus German bonds. (LO3, LO4).
在歐元區主權債務危機期間，地理邊緣的歐洲國家政府（如希臘、愛爾蘭、義大利、葡萄牙和西班牙）發行的債券與德國發行的債券之間的利差大幅擴大。使用債券供需模型來說明這是如何由投資者對邊緣主權債券與德國債券相對風險性的認知變化來解釋的。（LO3，LO4）。
Answer: Investor worries about the possibility of default on bonds issued by relatively indebted peripheral euro-area governments increased during the crisis. This can be illustrated with a leftward shift of the bond demand curve, lowering the price and raising the yield. For a given German bond yield, this would increase the spread of peripheral government bond yields above those on German bonds, reflecting the need for a larger risk premium to compensate investors.
投資者對於相對負債較重的邊緣歐元區政府發行的債券發生違約的可能性感到擔憂，在危機期間這種擔憂加劇。這可以用債券需求曲線向左移動來說明，降低價格並提高收益率。對於給定的德國債券收益率，這將會增加邊緣政府債券收益率與德國債券收益率之間的利差，反映了為了補償投資者需要更大的風險溢價。
Not long after the United Kingdom’s vote to leave the European Union in 2016, the yields on some British Government bonds (called gilts) turned negative. Assuming that these bonds were issued with a positive coupon rate, would you expect their market prices to be above, below or equal to their face value when the yields were negative? Explain your choice. (LO2)
不久於 2016 年英國舉行脫歐公投後，某些英國政府債券（稱為公債）的收益率變為負值。假設這些債券是以正利的票面利率發行的，當收益率為負值時，您預期其市場價格會高於、低於還是等於其面值？請解釋您的選擇。（LO2）
Answer: If the yield on a bond with a positive coupon rate is negative, the price must be above the face value. Thinking about maturity, if the yield is negative, the investor must suffer a capital loss to offset the positive coupon payments. Therefore, the market price of the bond must be above the face value.
答：如果一張具有正利息率的債券的收益率為負，則其價格必須高於面值。考慮到期日，如果收益率為負，投資者必須承受資本損失以彌補正利息支付。因此，債券的市場價格必須高於面值。