8.2) Forward rates, Spot rates and short rates

Question 1

What is a forward rate?

Answer 1

Interest rate/yield that the market expects to prevail during a future period

Question 2

What does notation 1f2 mean?

Answer 2

Question 3

How is the notation ofthe forward rate writen? (2)

Answer 3

First = Length of the forward rate
Second = Period where it is located

Question 4

How would:
- 1-year forward rate in period 3
- 2-year forward rate starting in period 3
be written?

Answer 4

1f3
2f3

Question 5

True or false, the fn is not viewed as the market consensus?

Answer 5

False, Under certain conditions the fn can be viewed as a market’s consensus of future interest rates.

Question 6

Why is it important to udnerstand forward rates? (3)

Answer 6

1. To implement bond strategies
2. Time your trade
3. Infer future interest rates & inflation

Question 7

How does an investor implement bond strategies? (2)

Answer 7

• Alternative 1: Buy a 2-year bond (Buy & Hold strategy)
• Alternative 2: Buy a 1-yr bond & when it matures after 1 yr, buy another 1-yr bond ( Rollover Strategy)

Question 8

How does an investor time their trade? (2)

Answer 8

• Now vs later
• If interest rates will drop in a few months, then wait to sell

Question 9

How does an investor infer interest rates and inflation? (2)

Answer 9

1) Interest rates going to drop → buy a long-term bond (based on forward rates)
▪ Exposes you to capital gains → bond prices increase (will increase by a greater
margin if long term) and you lock in a higher coupon.
2) Interest rates going to increase → buy a short-term bond (based on forward rates)
▪ Will minimise capital losses → bond prices will drop (drop by a greater margin if long-term)

Question 10

What is a spot rate? (3)

Answer 10

• It is the YTM of a zero-coupon bond
• It’s a rate that exist today and prevails for a time period corresponding to the maturity of the ZCB or the instrument
• The current interest rate appropriate for discounting a cash flow of some given maturity.

Question 11

What is the short term interest rate?

Answer 11

The interest rate for a given time interval (one period interest rate). - One period interest rate, can be current or future

Question 12

What is the forward interest rate?

Answer 12

Is an interest rate for a future period, it’s uncertain that this rate will prevail in future

Question 13

What are the assumptions for forward interest rates?

Answer 13

An environment of certainty, with no risk (Liquidity risk)

Question 14

What is the basic principles of forward interest rates?

Answer 14

Bonds of different maturities are perfect substitutes.

Question 15

Define:
- Liquidity risk
- Interest rate risk

Answer 15

• Liquidity risk: The ease at which you can buy and sell an instrument or trade an instrument
  without affecting its fair value.
• Interest rate risk: Impact on the price of a change in interest risk

Question 16

Different bond investment strategies with _________ terminal dates must provide _________ rates of returns

Answer 16

common
equal

Question 17

Give two examples of different strategies that must provide equal rates of returns? (2)

Answer 17

Roll Over Strategy and Buy & Hold Strategy.

Question 18

Different bond strategies with the same time to maturity will produce the same what?

Answer 18

Two different bond strategies with the same time to maturity will produce the same return

Question 19

In summary how is a forward rate calcualted?

Answer 19

Calculated as the “break-even” interest rate that equates the return on an n-period ZCB to that of an (n-1)-period ZCB rolled over into a 1-year bond in year n

Question 20

Calculate:
- a 1 year froward rate after 1 years
- 1 year forward rate after 2 years
- 1 year forward rate, after 3 years

Answer 20

Question 21

How is a forward rate determined?

Answer 21

Derrived from the geometric average formula used to calcualte the spot rate

Question 22

What are the differences and similarities between a spot rate and a short rate? (2x1)

Answer 22

Differences:
▪ A short rate is just for one period while the spot rate can be for longer periods
▪ The short rate can be for a future period, but the spot rate exists today, and it can never exist in future.

Similarity:
▪ The spot rate for the first period is equivalent to the current short rate

Question 23

What are the differences and simialrities betweeen a spot rate and a forward rate? (2x1)

Answer 23

Difference:
▪ The forward rate exists in the future period whereas the spot rates exist today.
▪ The two will never overlap if you are standing at one point

Similarities:
▪ There is no similarity, but of course the spot rates give birth to the forward rates

Question 24

What are the differences between the short rate and the forward rate?

Answer 24

Differences:
▪ The forward rate can be for more than one period, it can be a 2-year or 3- year while the short rate is for one period.
▪ The short rate be a current rate, meaning it can exist today, while the forward rate is always a future period if you are standing at period zero.

Question 25

What is the relationship between spot rates and forward rates? (2)

Answer 25

• Forward rates are derived from spot rates, they are implicit rates that link any two spot rates.
• Forward rates represent a break-even rate or a rate of indifference that links two spot rates.

Question 26

What is the spot rate equal to?

Answer 26

The spot rate is a geometric average of the current short rate (n-1) (current spot rate) and forward rates (fn) that lie along its path.

E.g., Y3 will be the geometric average of Y2 spot rate and forward rate for year 3

Question 27

What if:
-Next years froward rate (f2) > this years spot rate (y1)
Next year’s forward rate (f2) < this year’s spot rate (y1)

Answer 27

-yield curve slopes up
-yield curve slopes down

Question 28

What do yield curves represent?

Answer 28

in an environment of certainty → yield curve reflects the market’s assessment of future interest rates.