CH 11

Question 1

How do you calculate the ‘weight’ associated with the ‘cash flow’ for Macaulay’s duration?

Answer 1

w = (CF / (1+y)^t) / Bond Price
t

Where:

CF = cash flow (principal/coupon payment)
y = the bonds yield to maturity 
t = time t
w    = Weight of the cash flow
    t

Question 2

Define “Macaulay’s duration”?

Answer 2

A measure of the effective maturity of a bond, defined as the weighted average of the times until each payment, with the weights proportional to the present value of the payment.

Question 3

How do you calculate the present value of a cash flow occurring at time t?

Answer 3

PV = CF / (1+y)^t

Question 4

What is the formula for ‘Macaulay’s duration’?

Answer 4

D = sum [ t x w ]
t

Where:
D = Macaulay’s Duration
t = time t where cash flow occurs

w = Weight of cash flow at time t
t

Question 5

Define ‘modified duration’.

Answer 5

Macaulay’s duration divided by (1+YTM). Measures interest rate sensitivity of bond.

Question 6

Provide the formula for ‘modified duration’.

Answer 6

D* = D / (1+y)

Question 7

What does the ‘duration’ of a zero coupon bond equal?

Answer 7

The ‘duration’ of a zero coupon bond equals its time to maturity.

Question 8

What is the equation for the ‘duration of a perpetuity’?

Answer 8

Duration of perpetuity = ( 1+y ) /y

Question 9

Define ‘immunization’.

Answer 9

A strategy to shield net worth from interest rate movements.

Question 10

Define ‘rebalancing’.

Answer 10

Realigning the proportions of assets in a portfolio as needed.

Managers must adjust the portfolio as interest rates change to realign its duration with the duration of the obligation.

Therefore immunization is a passive strategy in the sense that it does not involve active attempts to identify undervalued securities, however the positions must still be proactively updated and monitored.

Question 11

What is 1 basis point as a percentage?

Answer 11

0.01%

100 basis points = 1%

Question 12

Define ‘cash flow matching’.

Answer 12

Matching cash flows from a fixed-income portfolio with those of an obligation.

Question 13

Define ‘dedication strategy’.

Answer 13

Multiperiod cash flow matching.

Question 14

Define ‘convexity’.

Answer 14

The curvature of the price-yield relationship of a bond.

Question 15

Provide the formula for ‘convexity’.

Answer 15

chg.P/P = -D*chg.y + 1/2 x Convexity x (chg.y)^2

Question 16

When is the convexity rule more important for improving the calculation for the duration approximation?

Answer 16

Under small interest rate changes, the convexity term will be very small, therefore it will add very little to the duration approximation.

However under potentially large interest rate changes, the convexity term is much larger and would help calculate a much more precise duration approximation.

Question 17

Why is convexity desirable?

Answer 17

Bonds with greater curvature gain more in price when yields fall than they lose when yields rise.

Question 18

Define a ‘substitution swap’.

Answer 18

Exchange of one bond for a bond with similar attributes but more attractively priced.

Two bonds can be exactly the same in terms of maturity, risk and so on, however for the same price you believe that bond B is more mis-priced than bond A.

This technique relies on inside information.

Question 19

Define ‘inter-market spread swap’.

Answer 19

Switching from one segment of the bond market to another.

An example of this is if the yield spread between 10-year treasury bonds and 10-year Baa rated corporate bonds is 3%, and historically have been 2%, if the yields narrow in the future then the returns on the Baa bonds were successful.

NOTE: this is only if the yield spreads were to narrow, if they don’t they can be a larger indicator to a potential increased perceived credit risk due to an incoming recession for example.

Question 20

Define ‘rate anticipation swap’.

Answer 20

A switch made in response to forecasts of interest rate changes.

Example: if an investor believes that interest rates will decrease, they will swap out their 5 year bonds for example for 25 year maturity bonds, they would just increase duration in this context.

If investors thought interest rates would increase, they would swap long maturity bonds for shorter term bonds.

Question 21

Define ‘pure yield pickup swap’.

Answer 21

Moving to higher yield bonds, usually with longer maturities.

This swap is pursued not in response to perceived mis-pricing but as a means of increasing return by holding higher-yielding bonds.

Question 22

Define a ‘tax swap’.

Answer 22

Swapping two similar bonds; motivated by a reduction in total tax obligations.

For example: an investor may swap from one bond that has decreased in price to another similar bond if realization of capital losses is advantageous for tax purposes.

Question 23

Define the ‘horizon analysis’.

Answer 23

Forecast of bond returns based on a prediction of the yield curve at the end of the investment horizon as well as the interest rate on reinvested coupon income.