Topic 4 - Interest Rate Risk

Question 1

A number of theories have been advanced to explain the term structure of interest rates and the yield curve

The four most popular theories are:

Answer 1

1. The expectations hypothesis
2. The liquidity premium hypothesis
3. The inflation premium hypothesis
4. The market segmentation hypothesis

Question 2

1.The expectations hypothesis

Answer 2

The expectations hypothesis contends that the term structure of interest rates is determined by investor expectations regarding future interest rates

It is based on the assumption that capital markets are perfect and that investors are indifferent between investments with differing maturities –they will always choose the investment providing the highest return

If those two assumptions hold, current longterm rates will be the geometric average of expected future short-term rates

If this were not the case, arbitrage opportunities would exist –arbitrageurs could borrow at the point on the yield curve where rates are lowest and invest where they are highest, and the resulting market forces would restore an equilibrium in which the above prediction holds

Question 3

2.The liquidity premium hypothesis

Answer 3

The liquidity premium hypothesisis based on pure expectations theory, but with a modification to the underlying assumptions
This hypothesis assumes that, all else being equal, investors seek the highest possible return, but they prefer short-term securities to long-term securities because they enjoy the liquidity associated with short-term securities
This will result in a lack of demand for long-term securities Issuers of long-term securities (i.e. borrowers) will be need to offer slightly higher interest rates in order to attract investors, resulting in an “upward bias” to the yield curve, compared to the pure expectations yield curve
The additional yield is called a liquidity premium

Question 4

The inflation premium hypothesis

Answer 4

The inflation premium hypothesisis similar to the liquidity premium hypothesis, and has similar implications for the yield curve
It predicts that uncertainty regarding future levels of inflation results in a preference for short-term securities
Hence, issuers of securities will have to offer an inflation premiumto attract long-term investors

Question 5

The market segmentation hypothesis

Answer 5

The market segmentation hypothesisis very different from the other three
It predicts that borrowers and lenders have specific preferences for securities with different maturities, and won’t swap from one to another
As a result, the yield for each maturity will be determined by demand and supply for securities of that maturity

Question 6

DEFINITION OF INTEREST RATE RISK

Answer 6

If interest rates go up, interest rate sensitive assets earngmore revenue, and interest rate sensitive liabilities incur more expenses
The net effect on income will depend on whether there are more interest rate sensitive assets or more interest rate sensitive liabilities
This was the premise underlying the interest rate risk ratio in Topic 3, but we will adopt a more sophisticated approach in this topic to estimate interest rate risk, known as gap management

Question 7

GAP MANAGEMENT

Answer 7

The “gap” in this case refers to the difference between the value of assets and the value of liabilities that will repricewithin a given time period
If an asset (or liability) matures within a given period, and it is “rolled over” into a similar asset or liability, it is said to “reprice”, because it will be subject to the prevailing interest rate at the time
If interest rates have changed before or during that period, revenue or expenses will be affected

Question 8

The process of gap management is carried out with the aid of gap reports:

Answer 8

Gap reports show the value of assets and liabilities maturing within each time period 

The difference between assets and liabilities maturing in each period creates a “gap” 

The effect of interest rate sensitive off-balance-sheet activities adds to or subtracts from the gap 

The direction of the gap –positive or negative – indicates how income will be affected by a change in interest rates before or during that period

Question 9

Positive gap

Answer 9

IR-sensitive assets > IR-sensitive liabilities

Revenue is more sensitive to interest rate changes than expenses

Interest rates up - Revenue up by more than expenses -Income increases

Interest rates down - Revenue down by more than expenses - Income decreases

Question 10

Negative gap

Answer 10

IR-sensitive liabilities > IR-sensitive assets

Expenses are more sensitive to interest rate changes than revenue

Interest rates up - Expenses up by more than revenue - Income decreases

Interest rates down -Expenses down by more than revenue - Income increases

Question 11

If management expects interest rates to go up with a given period of time:

Answer 11

They will strive for a positive gap

Question 12

If they expect interest rates to go down:

Answer 12

They will strive for a negative gap

Question 13

DURATION

Answer 13

We need a way to measure the sensitivityof a security’s value to interest rate changes, and hence the effect of interest rate changes on wealth (value of assets minus liabilities)
Duration attempts to measure that sensitivity

Question 14

There are 7 steps required to calculate duration:

Answer 14

1. Determine the cash flows for each time period 2.Calculate the discount factor for each period 3.Calculate the present value of each cash flow
2. Sum the present values
3. Calculate the weighted cash flows
4. Sum the weighted cash flows
5. Divide this by the total present value

Question 15

duration gap

Answer 15

D = DA - kDL

k=L /A

Question 16

the effect on wealth (i.e. net equity) as a result of a change in the interest rate using the following equation:

Answer 16

Change in E = -Dgap x (change in r/ 1+r) A

∆E= the change in net equity 
∆r= the change in the interest rate 
r= the initial interest rate 
A= the value of assets

Question 17

Positive duration gap

Answer 17

Duration of assets > duration of liabilities

Asset value is more sensitive to interest rate changes than the value of liabilities

Interest rates up - Assets down by more than liabilities - Wealth decreases

Interest rates down - Assets up by more than liabilitie -Wealth increases

Question 18

Negative duration gap

Answer 18

Duration of assets < duration of liabilities

The value of liabilities is more sensitive to interest rate changes than asset value

Interest rates up - Liabilities down by more than assets - Wealth increases

Interest rates down - Liabilities up by more than assets -Wealth decreases

Question 19

If management expects interest rates to go up:

Answer 19

They will strive for a negative gap

Question 20

If they expect interest rates to go down:

Answer 20

They will strive for a positive gap