Question 1

A Treasury bill is a zero-coupon instrument. Therefore, its annualized yield is equal to the spot rate. Similarly, for the one-year Treasury, its cited yield is the one-year spot rate. Given these two spot rates, we can compute the spot rate for ________.

Accepted Answer

The spot rate for a 1.5-year zero-coupon Treasury can be computed using the given spot rates for the 0.5-year and 1-year Treasuries through interpolation or bootstrapping methods.

Question 2

As quoted on a bond equivalent basis, what is the forward rate (f) for if the six-month spot rate is 3.50% and the one-year spot rate is 6.55%?

Accepted Answer

The forward rate can be calculated using the formula: (1 + one-year spot rate)^1 / (1 + six-month spot rate)^0.5 - 1. Plugging in the given rates, the forward rate is approximately 9.65%.

Question 3

The convention in the marketplace is to refer to a Treasury positively sloped yield curve whose maturity spread (measured by the six month and 30-year yields) as a ________ when the spread is 300 basis points or less.

Accepted Answer

The convention in the marketplace is to call a Treasury positively sloped yield curve with a maturity spread of 300 basis points or less a normal yield curve. This convention is used to distinguish between a normal yield curve and a steep yield curve, where the spread is greater than 300 basis points, or an inverted yield curve, where short-term yields are greater than long-term yields.

Question 4

Market participants have tended to construct yield curves from observations of prices and yields in the Treasury market. Two reasons account for this tendency. Which of the below is ONE of these reasons?

Accepted Answer

The Treasury market is the largest and most active bond market, which minimizes issues related to illiquidity or infrequent trading, making it a preferred source for constructing yield curves.

Question 5

Consider the following two investment alternatives for an investor who has a one-year investment horizon. For Alternative 1, the investor buys a one-year instrument. For alternative 2, the investor buys a six-month instrument and when it matures in six months the investor buys another six-month instrument. Which of the below statements is FALSE?

Accepted Answer

The statement A is false because it implies that there is only one specific future rate for the six-month instrument that would make the investor indifferent between the two alternatives. In reality, there could be a range of future rates that would yield the same return as the one-year instrument, depending on the actual rates realized in both periods.

Question 6

Suppose that the six-month spot rate is 4.00% and one-year spot rate is 8.10%. Additionally, suppose that you can look into a crystal ball and know for sure that six months from now that the six-month rate will be 3.60%. Finally, suppose that there is an investor who expects that six months from now, the six month rate will be 4.10%. That is, the investor expects that the six-month rate will be higher than its current level of 4.00%. How would you advise an investor who wants to buy a six-month instrument and when it matures in six months buy another six-month instrument?

Accepted Answer

If the investor buys a 6-month instrument now, they will earn a 4.00% return at maturity. If they then reinvest their funds in another 6-month instrument in six months, they will receive a rate of 3.60%, resulting in a total return of 3.80% for the entire year. However, if the investor waits and buys a 1-year instrument now at 8.10%, they will receive a higher return of 8.10% for the year. Therefore, it is not advisable to buy at the current rate and reinvest in six months as it would result in a lower return.

Question 7

With an upward-sloping yield curve, the yield rises steadily as the ________.

Accepted Answer

An upward-sloping yield curve indicates that long-term interest rates are higher than short-term interest rates. As a result, the yield (interest rate) rises steadily as the maturity (time until the bond's principal is repaid) increases. This is because lenders require a higher return for lending money for a longer period of time.

Question 8

There have not been many instances in the recent history of the U.S. Treasury market where the yield curve exhibited ________.

Accepted Answer

A downward-sloping yield curve, also known as an inverted yield curve, is rare in the history of the U.S. Treasury market. It occurs when short-term interest rates are higher than long-term interest rates, which is typically seen as a sign of economic recession ahead. In contrast, a normal or upward-sloping yield curve is more common, where long-term interest rates are higher than short-term interest rates. A reverted yield curve is not a recognized term in finance.

Question 9

Which of the below statements is FALSE?

Accepted Answer

The false statement is A because the yield necessary to determine the value of each zero-coupon instrument is not called the forward rate but the spot rate. The forward rate refers to the interest rate agreed today for a loan that will start at a future date, while the spot rate is the current interest rate for immediate settlement and is used to price zero-coupon instruments.

Question 10

Because of the different cash flow patterns, it is not appropriate to use ________ to discount all cash flows because each cash flow should be discounted at ________ that is appropriate for the time period in which the cash flow will be received.

Accepted Answer

The answer of Because of the different cash flow patterns,...

Question 11

The market prices its expectations of future interest rates into the rates offered ________.

Accepted Answer

The market prices its expectations of future interest rates into the rates offered on investments with different maturities, reflecting the term structure of interest rates.

Question 12

More recently market participants have come to realize that the traditionally constructed Treasury yield curve is ________ measure of the relation between required yield and maturity with the key reason is that securities with the same maturity may actually provide ________.

Accepted Answer

The question implies that the traditionally constructed Treasury yield curve may not always provide a satisfactory measure of the relation between required yield and maturity. Therefore, choice A is the most logical option as it suggests an "unsatisfactory" measure due to "different yields" among securities with the same maturity.

Question 13

What is the forward rate (f) for if the six-month spot rate is 5% and the one-year spot rate is 9%?

Accepted Answer

The answer of What is the forward rate (f) for...

Question 14

The correct way to think about bonds A and B is not as bonds but as packages of ________.

Accepted Answer

The correct way to think about bonds, especially when considering their pricing or valuation, is as packages of zero-coupon instruments. This approach simplifies the analysis by breaking down a bond into its individual payment components, each of which can be treated as a zero-coupon bond that pays its face value at maturity.

Question 15

Suppose an investor purchases a five-year, zero-coupon Treasury security for $58.48 with a maturity value of $100. The investor could instead buy a six-month Treasury bill and reinvest the proceeds every six months for five years. The number of dollars that will be realized will ________.

Accepted Answer

The amount realized from reinvesting in six-month Treasury bills for five years depends on the six-month forward rates over the investment period. These rates determine the reinvestment returns at each six-month interval.

Question 16

What is the forward rate (f) for a six-month security if z₁ is 2.00% and z₂ is 3.50%?

Accepted Answer

The formula for a six-month forward rate is:
f = [(1 + z₂)^2 / (1 + z₁)] - 1
Using the given values:
f = [(1 + 0.035)^2 / (1 + 0.02)] - 1
f = 0.0502 or 5.02% (rounded to two decimal places)
Therefore, the best choice is B.

Question 17

It is important to remember that the basic principle underlying bootstrapping is that the value of the Treasury coupon security should be equal to the value of the package of ________ that duplicates the ________.

Accepted Answer

Bootstrapping is a technique used to estimate the yield curve for a set of fixed-income securities. In bootstrapping, the current market prices of the bonds are used to derive the implied forward rates for future periods. The basic principle underlying bootstrapping is that the value of the Treasury coupon security should be equal to the value of the package of zero-coupon Treasury securities that duplicates the coupon bond's cash flow. Hence, option B is the best choice as it mentions zero-coupon Treasury securities, which match the concept of bootstrapping.

Question 18

Which of the below equations give the forward rate (f) for a six-month security if z₁ is the six-month spot rate and z₂ is the one-year spot rate?

Accepted Answer

The formula for the forward rate is (1 + z2)^2 / (1 + z1) -1. This is given in option A. Option B has an incorrect formula, as multiplying (1 + z2)^2 and (1 + z1) will not give the correct result. Option C has the numerator and denominator reversed, which would give an incorrect result. Option D has the exponents in the wrong order, which also would not give the correct result.

Question 19

As quoted on a bond equivalent basis, what is the forward rate (f) for a six-month security if z₁ is 2.00% and z₂ is 4.50%?

Accepted Answer

The answer of As quoted on a bond equivalent basis,...

Question 20

The slope of a yield curve is commonly measured in terms of ________, which is the difference between long-term and short-term yields.

Accepted Answer

The slope of the yield curve is commonly measured by the difference between long-term and short-term yields, which is commonly referred to as the maturity spread. Therefore, choice (B) is the best answer. Choice (A) is incorrect as the yield curve spread is not a commonly used term. Choice (C) is incorrect as the default spread is a measure of the difference between the yields on risk-free securities and the yields on securities with some credit risk. Choice (D) is incorrect as the interest rate spread is a broad term that can refer to the difference between any two interest rates, not just short- and long-term yields.

Quiz 11: The Term Structure of Interest Rates