Reading 46 - Term Structure and Volatility of Interest Rates

Question 1

Explain parallel and nonparallel shifts in the yield curve.

Answer 1

In a parallel shift, the yields on all maturities change in the same direction by the same amount.

In a nonparallel shift, not all maturities change by the same amounts.

Question 2

What are Yield Curve butterfly shifts?

Answer 2

Changing in the degrees of curvature of the yield curve.

Question 3

What are the 3 factors that drive U.S. Treasury securities?

Answer 3

1. Changes in the level of interest rates (parallel shifts in the yield curve.
2. Changes in the slope of the yield curve (twists in the yield curve)
3. Changes in the curvature of the yield curve (butterfly shifts)

Question 4

Of the three factors that drive Treasury returns, rank them from most important to least important and put the contribution (%) to each.

Answer 4

Changes in the level of interest rates (explains 90% of returns)

Slope Changes (explains 8.5% of returns)

Curvature changes (explains 1.5% of returns)

Question 5

What is bootstrapping?

Answer 5

The process of sequentially calculating spot rates from securities with different maturities, using the yields on Treasury bonds from the yield curve.

Question 6

What are the advantages and disadvantages of using All On-the-run Treasury securities to construct the theoretical spot rate curve?

Answer 6

Adv:

Uses only the most accurately priced issues

Dis:

Large maturity gaps after the 5-year note

Question 7

What are the advantages and disadvantages of using All On-the-run and Some Off-the-run Treasury securities to construct the theoretical spot rate curve?

Answer 7

Adv:

Reduces maturity gaps

Dis:

• Still doesn’t use all the rate information contained in Treasury issues
• rates may be distorted by the repo market

Question 8

What are the advantages and disadvantages of using All Treasury coupon securities and Bills to construct the theoretical spot rate curve?

Answer 8

Adv:

Does not ignore information from issues excluded by other approaches.

Dis:

1. Some maturities have more than one yield
2. Current prices may not reflect accurate interest rates for all maturities

Question 9

What are the advantages and disadvantages of using Treasury Strips to construct the theoretical spot rate curve?

Answer 9

Adv:

1. Provides yields at most maturities and reduces maturity gaps
2. intuitive approach that does not require bootstrapping to derive spot prices

Dis:

1. liquidity premium embedded in the strip rates
2. tax treatment affects observed rates

Question 10

What is the swap rate curve (aka LIBOR curve)?

Answer 10

a series of swap rates quoted by swap dealers over maturities extending from 2 - 30 years

Question 11

What are the 4 reasons market participants prefer using the swap rate curve rather than a government bond yield curve?

Answer 11

1. Swap market is not regulated by any government, which makes swap rates in different countries more comparable.
2. The supply of swap and the equilibrium pricing that results from the interaction of supply and demand depends only on the number of participants willing to enter a swap
3. Swap curves across countries are more comparable because they reflect similiar levels of credit risk.
4. More yield quotes, Swap curve has 11 maturies between 2 - 30 years, goverment has just 4 (2,5,10,30)

Question 12

Explain the pure (unbiased) expectations theory…

Answer 12

That forward rates are solely a function of expected future spot rates. ie. long term interest rates equal the mean of future expected short term rates

Example:

An investor could earn the same return investing in a 5 yr bond or by investing in a 3 yr bond and then a 2 yr bond after the 3 yr bond expires

Question 13

Explain the implications for the shape of the yield curve under pure expectations theory for each of these scenarios…

1. If the yield curve is upward sloping
2. If the yield curve is downward-sloping
3. If the yield curve is flat

Answer 13

1. If upward slopping, short term rates are expected to rise
2. If downward-sloping, short term rates are expected to fall
3. If flat, the market expects short term rates to remain constant.

Question 14

What is an implied forward rate?

Answer 14

Using an example:

If the 1 yr spot rate is 5% and the 2 yr spot rate is 7%, the implied forward 1 yr rate, one year from now is 9%.

***You will get a total of 14% over two years. If you only get 5% the first year, subtract 5 from 14 to get 9 for the implied rate in one year.

Question 15

What are 3 interpretations of an implied forward rate?

Answer 15

1. Breakeven rate refers to the forward rate that leaves investors indifferent between investing for two years, or investing for 1 yr and then reinvesting at the breakeven rate for the second yr.
2. Forward rates can be interpreted as the locked-in rate for some future period.
3. How does the forward rate relate to expected future spot rates? Pure Expectations theory predicts that the expected spot in 1 yr is equal to the implied 1yr forward rate… ie expectations are unbiased.

Question 16

The pure expectations theory has a significant shortcoming b/c it fails to consider the riskiness of bond investing.

What are the 2 things the theory fails to recognize?

Answer 16

1. Price risk - the uncertainty associated with the future price of a bond that may be sold prior to its maturity.
2. Reinvestment risk - the uncertainty associated with the rate at which bond cash flows can be reinvested over an investment horizon.

Question 17

What is the Liquidity Preference Theory?

Answer 17

Addresses the shortcomings of the Pure Expectations theory by proposing that forward rates reflect investors’ expectations of future spot rates plus a liquidity premium to compensate them for exposure to interest rate risk.

Liquidity premium is positively related to maturity: a 25 yr bond has a larger liquidity premium than a 5yr bond

Question 18

What is the Preferred Habitat Theory?

Answer 18

Proposes that forward rates represent expected future spot rates plus a premium, but it does not support the view that this premium is directly related to maturity.

It suggests that the existence of an imbalace between the supply and demand for funds in a given maturity range will induce lenders and borrowwers from their preferred habitats.

Question 19

What are two differences between the Preferred Habitat Theory and the Liquidity Preference Theory?

Answer 19

1. The premium is a positive or negative risk premium related to supply and demand for funds at various maturities, not necessarily a liquidity premium
2. This risk premium is not necessarily related to maturity.

Question 20

Define key rate duration….

Answer 20

The sensitivity of the value of a security or portfolio to changes in a single spot rate, holding all other spot rates constant.

Question 21

When is key rate duration particularily useful regarding the yield curve on a bond portfolio???

Answer 21

For nonparallel shifts in the yield curve.

Question 22

What are 3 common bond portfolio structures?

Answer 22

1. Barbell portfolios
2. Ladder portfolios
3. Bullet portfolios

Question 23

Describe a Barbell portfolio….

Answer 23

it contains a relatively large % of long and short maturity bonds

Question 24

Describe a Ladder portfolio…..

Answer 24

contains bonds that are evenly distributed throughout the maturity spectrum

Question 25

Describe a Bullet portfolio……

Answer 25

typically have a relatively high concentration of bonds at some intermediate maturity.

Question 26

How is yield volatility calculated??

Answer 26

Using historical data, it is measured by the standard deviation of daily yield changes.

Question 27

Assume that today’s yield is 7.56% and yesterday’s yield was 7.5%. Compute the percentage yield change from yesterday to today, assuming continuous compounding…

Answer 27

Question 28

What is implied volatility and how is it calculated?

Answer 28

It is when yield volatility is derived from option prices.

Is calculated by plugging in the observed price of an option in the option pricing model, along with the model’s other observable variables, then solve the model for the unknown volatility.

Question 29

What are the 2 reasons why implied volatility is often criticized?

Answer 29

1. It is based on the assumption that the option pricing model is correct.
2. Models make the simplifying assumption that volatility is a constant.

Question 30

Describe what yield curve twists look like and what they imply for the spread between short and long term rates when they change?

Answer 30

• When the yield curve twists flatter, this means the spread between short and long term rates is less
• When the yield curve twists steeper, this means the spread between short and long term rates increases

Question 31

Describe what yield curve butterfly shifts look like and what they imply for the spread between short and long term rates when they change?

Answer 31

• A positive butterfly means that the yield becomes less curved.
• A negative butterfly means that the yield becomes more curved.

Question 32

Give the below information for an equally wieghted U.S. Treasury portfolio what is the effective duration for the portfolio?

Answer 32

If given key rate duration, you just add them up.

= 0.73+0.34+3.09+063+1.22

Question 33

Using the data from our previous example. What is the impact on the portfolio of a 25 bp increase in the 5yr rate and a 50 bp increase in the 20yr rate, holding all other rates equal?

Answer 33

Question 34

If there are 250 trading days in a year and the daily historical yield volatility is 0.34%, the annual standard deviation of the yied is equal to?

Answer 34

Question 35

Based on the the below, using the bootstrapping method what is the 2 year spot rate?

• A 1 Yr (zero cpn) Treasury is trading at a YTM of 5%.
• A 2 Yr note with a 6% coupon is trading at a YTM of 5.5%.

Answer 35

1. Calculate the current price of each bond.
   
   • N=1,I=5,PMT=0,FV=100, PV=? ….. PV = 95.2381
   • Repeat for second bond
2. Create a timeline of cash flows.
3. Solve the equation

Question 36

Based on the the below, using the bootstrapping method what is the 3 year spot rate?

• A 1 Yr (zero cpn) Treasury is trading at a YTM of 5%.
• A 2 Yr note with a 6% coupon is trading at a YTM of 5.5%.
• A 3 Yr T-note with a 7% coupon trading at a YTM of 6%

Answer 36

• Calculate the current price of each bond.

N=1,I=5,PMT=0,FV=100, PV=? ….. PV = 95.2381

• Repeat for second bond
• Create a timeline of cash flows.
• Solve the equation