Question 1
Real assets such as buildings, machines, land and knowledge are:
⚡ The means of production of goods and services of an economy. Real assets are those that produce goods and services in the economy.
☐ The means by which individuals in an economy can hold the income generated by the real assets in the process of production of good and services.
☐ None of the above.
Question 2
Financial assets are securities in which individuals can invest their wealth with the expectation to obtain a return in the future.
☐ FALSE.
⚡ TRUE Financial assets are claims to future cash flows. Examples are bonds, stocks, derivatives, etc.
Question 1
You expect the Federal Reserve will begin to loosen credit and force yields down by 50 basis points across all maturities in the very near future. (A basis point is equal to 1/100th of 1 percent so 50 basis points are equal to ½ of 1%.) How do you expect the Fed’s policy effect will show up in the bond market?
☐ Bond prices will decrease. No! Think about how a decrease in yields affects the present value of the bond’s promised cash flows.
⚡ Bond prices will increase. There is an inverse relationship between bond prices and yields.
☐ Bond prices will remain the same.
☐ Not enough information. No! What are the two things that you need to calculate the value of a bond? Is the yield on the bond one of those things? Does a decrease in the yield make the bond more or less valuable?
Question 2
The price of a US government issued five year zero coupon bond, with a face value of $1000, is $744.09. What is the yield to maturity of the bond if the interest is compounded yearly? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (i.e. x.xx)
Review the lecture notes on zero-coupon bond valuation and the definition of yield to maturity. Recall that the yield to maturity is the discount rate that makes the present value of a bond’s promised cash flows equal to its current price. The price of a zero-coupon bond is given by
\(B_0 = \text{Face Value}/(1+r)^T\)
where T is the years to maturity and r is the annual interest rate.
Recall that the yield to maturity is the discount rate that makes the present value of a bond’s promised cash flows equal to its current price. The zero-coupon bond has only face value. Therefore, we can solve for r:
\(B_0 = 744.09 = 1000/(1+r)^5\)
\(r = 6.09%\)
Question 3
What is the market value of a 20-year bond with face value of $1000, which makes quarterly coupon payments at a coupon rate of 10%, if the required rate of return is 8% per year, compounded quarterly? Round off your final answer to three digits after the decimal point. State your answer as ‘x.xxx’
The value of the bond is equal to the present value of the promised cash flows on the bond. This bond has quarterly coupon payments of $25 and the face value of $1000 at maturity.
\(B_0 = PV(\text{coupon payments}) + PV(\text{face value})\)
The coupon payments can be valued as an annuity:
\(PV(\text{coupon payments}) = 25 \times ADF(r = 8\%/4, n= 4\times20) = 25\times[(1 – 1/(1.02)^{80})/0.02]\)
\(PV(\text{face value}) = 1000/(1.02)^{80}\)
\(B_0 =1198.722568 = 1198.723\)
Question 4
Consider a bond, which pays $80 in annual coupon, and has a face value of $1,000. What is its yield to maturity if the bond has 20 years remaining until maturity and currently selling for $1,200?
☐ 8.32%
☐ 9.67%
⚡ 6.22%
☐ 8.77%
Note that it is not possible to solve for the yield to maturity algebraically. You can get an approximate answer by trial and error, or you can use Excel’s RATE function, or a financial calculator. Since the bond is selling at a premium, that is at a price greater than its par value, its yield to maturity should be less than the coupon rate 8%.
Question 5
You have just purchased a newly issued $1,000 five-year Vanguard Company bond at par. This five-year bond pays $60 in semi-annual coupon payments ($60 every six months). You are also considering the purchase of another Vanguard Company bond that pays $30 in semi-annual coupons and has six years remaining before maturity. This bond also has a face value of $1000. Both bonds make coupon payments semiannually.
What is the yield-to-maturity on the five-year bond? State your answer as a percentage rate.
Each coupon is $60. So the annual coupon payments is 120 or the discount rate is 12%.
The yield to maturity is the discount rate that makes the present value of the bond’s promised cash flows equal to its current price. When the bond is selling at par, the yield to maturity is equal to its coupon rate.
12## [1] 12Question 6
Refer to back to Question 5. What is the effective annual yield on the five-year bond? Round off your final answer to two digits after the decimal point. State your answer as a percentage rate (i.e ‘x.xx’)
The yield to maturity is expressed as an annual percentage rate. The effective annual yield represents the effective rate when it is compounded semi-annually. It is computed similar to the effective annual rate.
Recall \(EAR = (1 + APR/m)^m − 1\)
where APR is the annual percentage rate and m is the number of compounding periods.
\(\text{effective annual yield} = EAR = (1 + 12\%/2)^2 − 1 = 12.36\%\)
Question 7
Refer back to Question 5. Assume that the five-year bond and the six-year bond have the same yield. What should you be willing to pay for the six-year bond? Round off your final answer to three digits after the decimal point. State your answer as ‘x.xxx’
The value of the bond is equal to the present value of its coupon payments plus the present value of the face value.
The six-year bond makes $30 coupon payments every six months and has twelve coupon payments remaining in addition to the face value. The yield is 12 percent per year.
\(B_0 = PV(\text{coupon payments}) + PV(\text{face value})\)
The coupon payments can be valued as an annuity:
\(PV(\text{coupon payments}) = 30 \times ADF(r = 12\%/2, n=2\times6) = 30\times[(1 – 1/(1.06)^{12})/0.06\)
\(PV(\text{face value}) = 1000/(1 + 0.12 / 2)^{2\times6}\)
\(PV(\text{coupon payments}) + PV(\text{face value}) = 748.4846 = 748.485\)
Question 8
Suppose that you purchased a 15-year bond that pays semi-annual coupon of $20 and is currently selling at par. What would your realized annual return be if you sold the bond five years later when the yield is 5.5%? State your answer as a percentage rate rounded to three digits after the decimal point, i.e. ‘x.xxx’
The bond is currently selling at par. That means its price is equal to its face value $1000. It also means that the currently its yield to maturity is equal to its coupon rate of 4%. In order to compute your realized return you first need to find the price at the end of five years, when the bond yield goes up to 5.5%.
\(B_5=20\times[(1-1/(1.0275)^{20} )/0.0275]+1000/(1.0275)^{20} =885.796\)
You then need to find the internal rate of return on your investment: We are now looking for the internal rate of return on our investment. Recall that in this case the internal rate of return is the discount rate that makes the present value of the bond’s cash flows equal to the value of the bond when purchased.
\(1000=20\times[(1-1/(1+r)^{10} )/r]+885.80/(1+r)^{10}\)
Solving for r gives the six-month rate so do not forget to multiply by two.
The six-month rate is 0.90363%. The annual yield is 1.807%
Question 1
The financial press conventionally reports Treasury bill prices as:
⚡ Discounts from $100 face value for 360-day
☐ Discounts from $100 face value for 365-day
☐ None of the above
Question 2
What would be the price of a U.S Treasury bill with a face value of $ 100,000 that has 180 days left to maturity and has a discount quote of 0.358%?
⚡ 99,821.00
☐ 98,851.36
☐ 99,713.66
☐ 94,456.36
Recall that the Treasury bill prices can be computed as
\(B_0 = \text{face value} × (1 – d \times D/360)\)
where d = discount, D = days to maturity
\(B_0 = 100,000 * (1 - 0.358\% * 180 / 360) = 99,821.00\)
Question 3
A $100,000 face value Treasury bill with 54 days to maturity is selling for $98,999. What is the yield to maturity on this security? Round off to two-digits after the decimal point. State your answer as a percentage rate (if your answer is one point two three percent, input 1.23) Please consider the year as 360 days when calculating the yield
Recall that yield to maturity is expressed as an annual percentage rate. You need to first find the 54-day rate of return and then annualize it to express it as a yield to maturity.
[((Face value - purchase price)/Purchase price) - 1] x (360 / D)
The 54-day rate of return is (100,000 - $98,999)/$98,999 = 1.011%
We annualize this rate of return to express it as a yield to maturity:
1.01 % x (360/54) = 6.7408%
Question 4
Refer back to question 3. What is the effective annual yield? Round off to two digits after the decimal point. State your answer as a percentage rate (if your answer is one point two three percent, input 1.23)
Remember that \(EAR = (1 + APR / m) ^ m − 1\)
Similarly, the effective annual yield will be the compounded rate of return over the year. Think about how many times this investment will compound.
Recall that the 54-day return is 011%. To find the effective annual yield, we need to compound it:
\(EAR = (1 + 1.011\%) ^ {360 / 54} − 1 = 6.937\%\)
Question 8
Which of the following corporate bonds would you expect to have a higher yield?
☐ Secured bonds No. Investors would be willing to accept a lower yield on secured bonds because the payments on the bonds are secured by a collateral.
⚡ Callable bonds Yes. Because the issuer can call back the bonds at a time that is favorable to the issuer, the investors will typically be compensated by a higher yield than one on a similar non-callable bond.
☐ Convertible bonds No. Convertible bonds give the investors an opportunity to convert their bonds into equity shares when it is attractive. Therefore investors will be willing to accept lower yields on convertible bonds.
Question 9
Which of the following correctly describes a repurchase agreement?
⚡ The sale of a security with a commitment to repurchase the same security at a specified future date and a designated price.
☐ The purchase of a security with a commitment to purchase more of the same security at a specified future date. No. A repurchase agreement is not a commitment to purchase more.
☐ The sale of a security with a commitment to repurchase the same security at a future specified date at a future negotiated price. No. A repurchase agreement is not a commitment to repurchase the same security at a future specified date at a future negotiated price.
Question 10
What would you expect to happen to the spread between yields on commercial paper and Treasury bills if the economy were to enter a steep recession?
⚡ The spread is likely to increase. Yes, it may be more difficult to borrow.
☐ The spread is likely to decrease. No. Think about how the recession is likely to affect the issuers.
☐ It would not change. No. Think about how the recession is likely to affect the issuers.
Question 11
Which of the following statements is correct? (There may be multiple answers)
⚡ The interest rate on Treasury Inflation Protected Securities (TIPS) is a risk-free real rate. That is correct. The yield on TIPS bonds should be interpreted as the real rate. Since TIPS are issued by the U.S. Treasury, they can be viewed as the risk-free real rate.
⚡ The par value on TIPS is tied to the Consumer Price Index. That is correct. The par value is adjusted in proportion to increases in the Consumer Price Index for inflation.
☐ The coupon payments made on a TIPS remain constant in nominal terms through its maturity. No, that is not correct. The coupon payments increase proportionally since the par value is adjusted with the general price level. They remain constant in real terms.
⚡ The par value on TIPS remains constant in real terms. That is correct. The par value increases with the price level nominally, but it remains constant in real terms.
annuity_compound_factor <- function(r, n) ((1 + r) ** n - 1) / r
annuity_discount_factor <- function(r, n) (1 - (1 + r) ** -n) / rQuestion 1
Which of the following is correct about money market instruments?
☐ They are very short-term debt instruments that meet the needs of investors who want to invest in liquid assets. Yes. Money market instruments are short-term debt instruments. Refer to the lecture slides to review money market instruments.
☐ An important channel for the U.S. Federal Reserve to conduct its monetary policy Yes. The U.S. Federal Reserve conducts its monetary policy by influencing the availability and the cost of liquidity through the Federal Funds market. Refer to the lecture slides to review money market instruments.
☐ They include long-term corporate debt issues. No. Long-term corporate debt is not part of the money market. Money market instruments are short term debt instruments. Refer to the lecture slides to review money market instruments.
⚡ A and B. Yes, both A and B are correct.
Question 2
What is the value of a 5-year 10% coupon bond with face value of $1000 if the yield is 4% per year? Assume that coupon payments are semi-annual. Round off to two digits after the decimal point. (i.e. “x.xx”)
round(50 * annuity_discount_factor(0.02, 10) + 1000 / (1 + 0.02) ** 10, digits = 2)## [1] 1269.48Question 3
One of the most common money market instruments are U.S. Treasury bills. Find the price of a $10,000 face value Treasury bill with 81 days to maturity if it is quoted at a discount of 2.54 percent. Round off to two digits after the decimal point. (i.e. “x.xx”)
P <- 10000 * (1 - 0.0254 * 81 / 360)
round(P, digits = 2)## [1] 9942.85Question 4
Refer to Question 3. What would be your yield to maturity if you bought this Treasury at this price and kept it until maturity? Round off to two digits after the decimal. (i.e. “x.xx”) Ex 0.112 or 11.2% should be entered as 11.2
The yield to maturity is the discount rate that makes the present value of the bond’s cash flows equal to its price. Remember that the yield to maturity is expressed as an annual percentage rate. Refer to the lecture handouts to review the definition of yield to maturity.
The yield to maturity is the discount rate that makes the present value of the bond’s cash flows equal to its price.
9942.85 = 10000 / (1 + r)
Solving for r = 0.5748%
Note however this is the rate of return for the 81-day period.
The yield to maturity is expressed as an annual percentage rate.
YTM = 0.5748 x (360 / 81) = 2.55%
Question 5
Which of these securities is considered risk free?
☐ Apple stock No. Stock is an example of equity instrument.
☐ Emerging market debt No. Emerging market debt is not considered risk-free.
⚡ U.S. Treasury bills Yes. U.S. Treasury bills are backed by the U.S. government and are as close as what we think of risk-free.
☐ Commercial paper No. Commercial paper is not considered risk-free.
Question 6
Which of the following is not a distinguishing feature of municipal bonds?
☐ Municipal bonds are issued by state and local governments. Yes. Municipal bonds are issued by state and local governments typically issued to finance particular projects.
☐ Municipal bonds have tax-exempt status. Yes. Interest income on munis is exempt from federal income taxation. The interest is also exempt from state and local taxes in the issuing state.
⚡ Munis are an example of money market instruments. No, this is not correct. Municipal bonds are not a type of money market instruments. Money market securities are very short term debt obligations.
☐ Investors typically accept a lower yield on these securities. Yes. Because they pay neither federal nor state taxes on the interest income, investors accept a lower yield on municipal bonds.
Question 7
Assume you have a 1-year investment horizon and trying to choose among three bonds. All have the same degree of default risk and mature in 10 years. Which of the following bonds would you choose if you expect the yields to go down to 7 percent one year from now after the coupon payment and want to maximize your 1-year return?
☐ A 9% annual coupon bond currently priced to yield 8%
No, this is not the highest return. Your one-year return will be determined by the new bond price one year later plus the coupon (if any) and what you pay for they bond today. Find current bond price, the new bond price one year later. Your oneyear return is equal to: r = ((new bond price + coupon if any) / bond price today) – 1
⚡ A zero-coupon bond currently priced to yield 8%
Yes. Your one-year return will be determined by the new bond price one year later plus the coupon (if any) and what you pay for they bond today.
Find current bond price, the new bond price one year later. Your one-year return is equal to: r = ((new bond price + coupon if any) / bond price today) - 1
The current price of this bond is $463.193. When the yield goes down to 7%, the bond price will be $543.93. So you can solve for your one-year return as 493.193 = 543.93 / (1 + r) or r = 17.431%
☐ A 6% coupon bond currently priced to yield 8%
No. Your one-year return will be determined by the new bond price one year later plus the coupon (if any) and what you pay for they bond today.Find current bond price, the new bond price one year later. Your one-year return is equal to:
r = ((new bond price + coupon if any)/bond price today) - 1
Question 8
Which of the following is correct?
☐ When bonds are subject to potential default, the stated yield to maturity is the minimum possible yield that can be realized by the bondholder. No. When bonds are subject to potential default, the stated yield to maturity is the maximum possible yield that can be realized by the bondholder.
☐ In the event of default, bondholders always get their promised payments. No. In the event of default, bondholders may not get their promised payments.
⚡ To compensate bond investors for default risk, bonds must offer default premiums, that is, a yield higher than those offered by default-free government securities. Yes, A higher yield than the risk-free rate compensates investors for default risk.
☐ Junk bonds or high-yield bonds have on average lower default risk than investment grade bonds. No. Junk bonds have higher default risk and that is why they typically have higher yields.
Question 9
A bond with a call feature
☐ Is attractive because there is less default risk. No. The call feature does not affect the default risk of the bond.
☐ Is more likely to be called when interest rates are high because the interest savings will be greater. No. A callable bond is more likely to be called when interest rates are lower because the interest savings will be grater.
⚡ Will usually have a higher yield to maturity than a similar noncallable bond. Yes. The option to call the bond is valuable to the firm. To compensate investors, callable bonds are issued with higher coupons and primed yields to maturity than noncallable bonds.
☐ None of the above.
Question 10
Which security has a higher effective annual rate?
☐ A Treasury bill with 89 days left to maturity selling at $97,660 with par value $100,000
No. This is the not the highest. First, find the 89-day return and then find the effective annualized rate assuming that it compounds every 89 days in the year.
⚡ A coupon bond selling at par and paying 10% coupon quarterly.
Yes. Since the bond is selling at par, the yield to maturity is equal to the annual coupon rate. That is, the YTM = 10%.
Therefore, the effective annual rate \(= (1 + 10\% / 4) ^ 4 − 1 = 10.38\%\)