Csc3 Inv Products Ch 7

CSI Global Education Inc.

Investment Products

CHAPTER 7: Fixed-Income Securities: Pricing and Trading

2CSI Global Education Inc.

Chapter Highlights

• Most bonds and fixed-income securities trade in the market on the basis of their yield or yield to maturity

• Changes in interest rates play an important role in the pricing of bonds and fixed-income securities

• The fair price to pay for a bond or fixed-income security is a function of current interest rates, the term to maturity, the coupon or income component on the security, and the required rate of return for that investment


Present Value

• Used to determine the value of a bond.

• How much should be invested today to receive the face value of the security in the future.

• Sum of the present value of the bond’s cash flows determines what you should be willing to pay for the bond today.


Present Value

The present value is calculated using the following formula:

Where:

PV = present value

FV = future value (the cash flows received)

r = the market discount rate

n = number of compounding period

n

FVPV =

(1 + r)


Present Value

a) What is the present value of $1,040 to be received in 1 year’s time, discounted at 4%?

b) What is the present value of a 1-year bond with a $1,000par value, a 4% coupon paid annually, discounted at 6%?

c) What is the present value of a 1-year bond with a $1,000 par value, a 4% coupon paid annually, discounted at 2%?


Present Valuea) What is the present value of $1,040 to be received in 1

year’s time, discounted at 4%?

Solution:

This is a thinly disguised bond question. The investor receives $1,000 par and $40 in interest.

Since the discount rate equals the coupon rate the bondtrades at par.

1

$1,040PV =

(1 + .04)

PV $1,000


Present Value

b) What is the present value of a 1-year bond with a $1,000par value, a 4% coupon paid annually, discounted at 6%?

In the last year the bond repays par plus $40 (4% x 1000) in interest.

Solution:

Since the discount rate is greater than the coupon rate the bond trades at a discount.

1

$1,040PV =

(1 + .06)

PV $981.13


Present Value

c) What is the present value of a 1-year bond with a $1,000 par value, a 4% coupon paid annually, discounted at 2%?

Solution:

Since the discount rate is less than the coupon rate, the bond must trade at a premium.

1

$1,040PV =

(1 + .02)

PV $1,019.61


Present Value

What is the present value of an 8% 6 year semi-annual bond with a $10,000 par value and a 6% discount rate?

The cash flows are as follows (using a time line):

+ +

PV $400 $400$10,000


Present Value

This problem may be solved treating each value separately, or combining the last interest payment with the principal.

Solution:

Where:

FV1 = $400

FV2 = $10,400

r = 6% ÷ 2 = 3%

PV = $400/1.03 + $10,400/1.0609 = $388 + $9,803= $10,191

1 2

1 2

FV FVPV = +

(1 + r) (1 + r)


T-Bill Yields

How to remember the formula:

Yield = (positive number) × (number = or > 1)

100 – Price 365ield Price Term

Y


T-Bill Yields

a) What is the yield on a 181 day T-bill purchased for $98,000?

b) What is the yield on a 90 day T-bill purchased for 99?


Y


T-Bill Yields

a) What is the yield on a 181 day T-bill purchased for $98,000?

= (100,000 – 98,000) / 98,000 × 365/181 = 2,000 / 98,000 × 365/181 = 4.12%

b) What is the yield on a 90 day T-bill purchased for 99?

= 100 – 99 / 99 × 365/90

= 1/99 × 365/90 = 4.10%


Y


Current Yield

Current Yield is a short-term measure of return.

It allows investors to compare investments in bonds with other short-term investment opportunities (GICs, savings accounts, T-Bills etc.)

It is the actual interest income rate of return, compared with the coupon rate earned on the bond, based on the prevailing bond price and market interest rate.

Annual Dollar Amount of Interest

Current Market PriceCurrent Yield =


Current Yield

NFR issued a bond with a 10% coupon, a $1,000 par value and 10 years to maturity.

a) If an investor purchases the bond for $1,000, what is its current yield?

b) If an investor purchase the bond for 90 ($900), what is the investor’scurrent yield?

c) If an investor purchased the bond for 110, what is the investor’scurrent yield?


Current Yield

a) If an investor purchases the bond for $1,000, what is itscurrent yield?

$100/$1000 = .10 or 10%

Notice that since the bond sells at par, the coupon and thecurrent yield are the same.


Current Yield

b) If an investor purchases the bond for 90 what is the bond’s current yield?

$100/$900 = 11.11%

The price of 90 is simply 90% of par. Since par is $1,000, the price of the bond is: 0.90 × $1,000 = $900.

Why is the current yield higher than the coupon in this case?


Current Yield

c) If an investor purchases the bond for 110, what is thebond’s current yield?

$100/$1,100 = 9.09%

Same rule applies here, the purchase price is 110% of par.

Why is the current yield less than the coupon in this case?


Approximate Yield to Maturity (AYTM)

Where:

Annual Cash flow is the annual dollar amount of interest received on a bond.

Annual Capital gain (or loss) is the ending value (always par or $1,000) less the beginning value divided by the number of years from the calculation date to maturity.

Average Cost is amount at maturity plus present price divided by 2.

Annual Cash Flows + Annual Capital Gain (or Loss)AYTM = Average Cost


Approximate Yield to Maturity

DKE Inc. issues a bond with an 10% coupon, a $1,000 par value and 10 years to maturity.

a) What is the bond’s AYTM?

b) If an investor purchase the bond for 90, what is the bond’s AYTM?

c) If an investor purchased the bond for 110, what is the bond’s AYTM?



a) What is the bond’s AYTM?

Interest + [($1,000 – Purchase Price)/Years] ($1,000 + $900)/2

$100 + [($1,000 – $1,000)/10] $1,000

AYTM = 10%



b) AYTM when the bond is purchased for 90

Interest + [($1,000 – Purchase Price)/Years]

($1,000 + $900)/2

$100 + [($1,000 – $900)/10] $950

AYTM = 11.57%



c) AYTM when the bond is purchased for 110

Interest + [($1,000 – Purchase Price)/Years] ($1,000 + $1,100)/2

$100 + [($1,000 – $1,100)/10] $1,050

AYTM = 8.57%


Rules for AYTM, CY and Coupon Rates

Using what you have learned from the calculations above, lets establish some rules:

a) If the bond sells at par…

Coupon Rate = AYTM = Current Yield

b) If the bonds sell at a discount…

AYTM and the Current Yield must be greater than the couponrate.

c) If the bond trades at a premium…

AYTM and the Current Yield must be less than the coupon rate.


Bond Pricing Properties

• Bond prices move inversely to bond yields.

• The longer to maturity the greater the price fluctuation.

• Bonds with higher coupons move less (%) than bonds withlower coupons.

• Special features lead to different pricing (e.g. convertible bonds).

• Bond prices are more volatile when interest rates are low.

• Bonds are subject to reinvestment risk.


Implications: Bond Pricing Properties

Also:

Holding maturities constant, you make more money with a 1% price decline (capital gain), than you lose with the same percentage increase

Bonds with Higher Coupons Move Less (%) than Bondswith Lower Coupons

Example: Two 15-year bonds

Bond C (10% coupon) – 17.3% increase

Bond D (15% coupon) – 16% increase


Implications: Bond Pricing Properties

Bond Prices Move Inversely to Bond Yields

Trading opportunities – “if” you can predict interest rate changes

The Longer to Maturity the Greater the Price Fluctuation

Example: Two bonds with 10% coupon and rates fall to 8%

Bond A (15 years) – $1,172.90 – 17.29% increase

Bond B (25 years) – $1,214.80 – 21.48% increase


Reinvestment Risk

• Since interest rates fluctuate, the interest rate prevailing at the time of purchase is unlikely to be the same as the interest rate prevailing at the time the investor reinvests cash flows from each coupon payment.

• The longer the term to maturity, the less likely it is that interest rates will remain constant over the term. The risk that the coupons cannot be reinvested at the same interest rate that prevailed at the time the bond was purchased is called reinvestment risk.


Duration

• A measure of the sensitivity of a bond’s price to changes in interest rates.

• It is the approximate percentage change in the price or value of a bond for a 1% point change in interest rates.

• The higher the duration of a bond, the more it will react to a change in interest rates.

– i.e. the higher the duration the riskier the bond


Duration

• Duration is used to determine the volatility or riskiness of a bond or a bond fund.

• If the duration of a bond is 10, then its price will change by approximately 10% if interest rates change by 1%.

• Assume you hold a bond with a 5% coupon that is currently priced at 104.

• If interest rates rise by 1% then the price of the bond will fall by approximately 10% to 93.60.


Bond Investment Strategies

What would you look for in a bond if your primary concern was “receiving a fixed amount”?

If your goal was improving your portfolio?

If you were a speculator?



What would you look for in a bond if your primary concern was “receiving a fixed amount”?

• High coupon rate or nominal yield

• Look for high current yields

DANGER?

No hedge against inflation.



If your goal was improving your portfolio?

Bond Switches:

a) Net Yield Improvement:

– Match bond choices with tax bracket.

b) Term Extension or Reduction:

– Switch one comparable bond for another with a longer orshorter term.



Bond Switches (continued):

c) Improvement in Credit:

– Switch bonds in anticipation of a better credit rating.

d) Portfolio Diversification:

– Rebalance bonds to decrease risk.

e) Cash Take-Outs:

– Sell high-price bonds and replace with lower priced bonds and pocket the extra.



If you were a speculator?

Depends on your prediction as to the change in interest rates.



If rates are expected to decline?

• Buy long-term low coupon bonds

If interest rates are expected to increase?

• Buy short-term high coupon bonds

OR: Hold cash, short bonds


Settlement Exercise

T-Bills _________________

Govt. of Canada’s(less than 3 years) _________________

Govt. of Canada Guaranteed bonds(less than 3 years) _________________

All bonds with maturities of over 5 years _________________

Confirmation notices _________________

A trade on a mortgage-backed security _________________


Settlement Exercise

T-Bills Same day

Govt. of Canada’s(less than 3 years) T + 2

Govt. of Canada Guaranteed bonds(less than 3 years) T + 2

All bonds with maturities of over 5 years T + 3

Confirmation notices Same or next working day

A trade on a mortgage-backed security 1st clearing day on or afterthe 15th

Csc3 Inv Products Ch 7

Economy & Finance