Managing Bond Portfolio

Presented By:

Group 2

Abhisek Pokhrel, 13124

Srijana Shrestha, 13130

Annapurna Sthapit, 13134

11/26/2014

1

What is bond?

• A long- term debt instrument under which the issuer owes the holders a debt and depending on the terms of the bond, is obliged to pay them interest and/or to repay the principal at a later date, termed the maturity date

• Bond are sometimes called fixed income securities

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Features of bonds

• Par value – face amount of the bond, which is paid at maturity (normally $1,000)

• Coupon interest rate – stated interest rate (generally fixed) paid by the issuer

• Maturity date – years until the bond must be repaid

• Issue date – when the bond was issued

• Yield to maturity - rate of return earned on a bond held until maturity (also called the “promised yield”)

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Yield to maturity

• The rate of return that an investor would earn if

he bought the bond at its current market price

and held it until maturity

• Alternatively, it represents the discount rate

which equates the discounted value of a bond's

future cash flows to its current market price

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Yield to call

• The rate of return that an investor would earn if

he bought a callable bond at its current market

price and held it until the call date given that the

bond was called on the call date

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Types of bonds

Treasury bonds and notes

• A marketable government security with a

fixed interest rate. Treasury notes

maturities range up to 10 years, while

treasury bonds maturities range from 10 to

30 years.

Corporate bonds

• Like the government corporations borrow

money by issuing bonds.11/26/2014

6

Contd……

Call Provisions on corporate bonds

• Call provisions allows the issuer to repurchase the bond at a specified call price before the maturity date

• For example: a company issues a bond with a high coupon rate when market interest are high , and when interest rate fall, the firm might like to retire the high coupon debt and issue new bonds at a lower coupon rate to reduce interest payments. This is called refunding.

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Contd……

• Callable bonds typically come with a period of call protection. Such bonds are referred to as deferred callable bonds.

Convertible bonds

• Gives bondholders an option to exchange each bond for a specified number of shares of common stock of the firm

Puttable bonds

• Gives option to the bondholders to extend or retire the bond.

• If the bonds coupon rate exceeds current market yields the bondholder will choose to extend

• If the bonds coupon rate is too low it not extend instead reclaim principals and invest in current yields

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Contd……

Floating rate bonds

• Floating rate bonds make interest

payments that are tiied to some measures

of current market rates

• For example the rate might be adjusted to

the current T- bills rate plus 2%

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Bond Pricing

Bond value= Present value of coupons+ Present value of par value

Bond value=

P= C x PIVFA(r , n) + M x PVIF (r , n)

Where,

P= value of bond

n = number of years to maturity

C = annual coupon payment

r = periodic required return (yield return)

M= maturity value

t = time period when the payment is received

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Contd……

Alternative formula,

Bond value=

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Relationship Between Bond

Prices and Yields

Relationship Between Bond Prices and

Yields

• Bond prices are inversely related to interest rates(or yields)

• A bond sells at par only if its coupon rate equals

the required yield

• A bond sells at a premium if its coupon rate is

above the required yield

• A bond sells at a discount if its coupon rate is

below the required yield

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Determinants of Bond safety

• Coverage ratio

Ratios of company earning to fixed costs, Example: times interest earned ratio

Low or failing coverage ratio signals possible cash flow difficulties

• Leverage ratio

Example: Debt-to equity ratio

Too high leverage ratio indicates excessive indebtedness, signals possible cash flow difficulties

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Contd…..

• Liquidity ratio

Current ratio, quick ratio

Indicates firms ability to pay bills coming due with most liquid assets

• Profitability ratio

Indicators of a firm’s financial health

Examples: return on assets, return of equity

• Cash flow to debt ratio

Ratio of total cash flow to outstanding debt

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Bond portfolio risk

• Major risk: interest rate risk

• Reinvestment Risk

• Default Risk

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Interest rate risk

• a risk that arises for the bond owner from the fluctuation of interest rate

• The sensitivity of risk depends on:The time to maturity

Coupon rate

• Others things remaining same, the longer the maturity of a bond, the higher will be its sensitivity to the interest rate changes

• Similarly, the price of a bond with low coupon rate will be more sensitive to the interest rate changes

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Bond price at given market interest rate

Time to maturity 4% 6% 8% 10% 12%

1 year 1,038.83 1,029.13 1,000.00 981.41 963.33

10 years 1,327.03 1,148.77 1,000.00 875.35 770.60

20 years 1,547.11 1,231.15 1,000.00 828.41 699.07

30 years 1,695.22 1,276.76 1,000.00 810.71 676.77

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Bond prices at different interest rates (8% coupon bond, coupons paid

semiannually)

Reinvestment risk

• Risk that is concern that if r (interest rate)

will fall, and future cash flows will have to

be reinvested at lower rates, hence

reducing income

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Default risk

• The possibility that a bond issuer will be

unable to make interest or principal

payments when they are due

• If these payments are not made according

to the agreements in the bond

documentation, the issuer can default

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Interest Rate Risk

• As interest rates rise and fall, bondholders

experience capital losses and gains which

makes the fixed investment risky

• Interest rate risk arises, as bond prices

respond to interest rate fluctuations

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Bond Pricing Relationships

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1. Bond prices and yields are inversely

related

2. An increase in a bond’s yield to maturity

results in a smaller price change than a

decrease of equal magnitude

3. Long-term bonds tend to be more price

sensitive than short-term bonds

Bond Pricing Relationships

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4. As maturity increases, price sensitivity increases

at a decreasing rate

5. Interest rate risk is inversely related to the bond’s

coupon rate

6. Price sensitivity is inversely related to the yield to

maturity

Bond Pricing Relationships

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Prices of 8% Coupon Bond

(Coupons Paid Semiannually)

Yield To

Maturity

T=1 years T= 10 years T=20 years

8% 1000 1000 1000

9% 990.64 934.96 907.99

Fall in price

(%)

0.94% 6.50% 9.20%

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Prices of Zero-Coupon Bond

(Semiannual Compounding)

Yield To

Maturity

T=1 years T= 10 years T=20 years

8% 924.56 456.39 208.29

9% 915.73 414.64 171.93

Fall in price

(%)

0.96% 9.15% 17.46%

Need for a summary measure

Bond Maturity Coupon Rate

A 30 14%

B 20 7%

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Which bond is more risky?

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• It is the weighted average of time in which cash flow is expected to be received

• Important measure for investors : as bonds with higher durations are more risky and have higher price volatility than bonds with lower durations

• For all bonds, duration is shorter than maturity except zero coupon bonds, whose duration is equal to maturity

Duration

Duration – Coupon rate and Yield

Coupon Rate

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High Duration

Low Duration

Yield

Low Low

High High

1,1

twwhereT

t

Price)1( yCFwt

t t

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Duration: Calculation

CFt=cash flow at time t

twD t

T

t

1

Calculation of duration of 8%

Coupon bond with YTM 10%

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Calculation of duration of zero

coupon bond with YTM 10%

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Modified duration

• It is the measure of bond’s exposure to

changes in interest rates

• To calculate the percentage change in

price

• % change in price= Modified Duration * %

change in YTM

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Formula

• Modified duration (Md) =

Duration/ (1+r)

• % change in price =

ΔP/P= -Md* Δr

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Modified Duration (calculation)

• Previous example of 8% coupon bond with

YTM=10%

• Duration= 1.8852 years

• Duration of bonds is 1.8852 x 2 = 3.7704

semiannual periods

• Modified D = 3.7704/1+0.05 = 3.591 periods

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Example 16.1 Duration

• Suppose the semiannual interest rate

increases by 1%. Bond prices fall by:

=-3.591 x 0.01% = -0.03591%

rMP

P d

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Rules for Duration

Rule 1 The duration of a zero-coupon bond equals its time to maturity

Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower

Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity

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Rules for Duration

Rule 4 Holding other factors constant, the duration of a bond is higher when the bond’s yield to maturity is lower

Rules 5 The duration of a level perpetuity is equal to: (1+y) / y

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Table 16.3 Bond Durations (Yield to

Maturity = 8% YTM; Semiannual Coupons)

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Figure 16.2 Bond Duration versus

Bond Maturity

Implications of duration

• It allows bonds of different maturities and

coupon rates to be directly compared

• Construction of bond portfolio based on

weighted average duration

• Reduce interest rate risk by changing the

overall value of duration i.e. by adding

shorter maturities or higher coupon bonds

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Limitation of duration

• Duration assumes that relationship

between change in interest rate and price

is linear

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Convexity

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Price

Yield

In reality, the relationship between the changes in price and yield

is convex

As indicated, the larger the change in interest rates, the larger the error in estimating the

price change of the bond.

Convexity contd..

• Convexity is degree to which the duration

changes when the yield to maturity changes

• Higher the coupon, the lower the convexity

• Bond A and Bond B:

– Assume Same Duration and yield

– greater convexity bond less affected by interest

rate change.

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2)(

2

1yConvexityrM

P

Pd

Convexity: Graphical Illustration

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Conclusion

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• Duration and convexity allow investors to

quantify the uncertainty of change in

interest rate and are useful tools in the

management of fixed-income portfolios

Bonds in Nepalese Context

• Nepse has not seen transaction of any single bond unit since it

began listing bonds

• From fiscal year 2008-09 till 2011-12, NRB has issued Citizens

Saving Bonds and Foreign Employment Bonds worth Rs 19.6

billion -only Rs 2.75 million were subscribed (Source: Nepalsharemarket.com)

• Mostly issued at par irrespective of the difference between

market interest rate and bond coupon

• Coupon rate fixed as per the trend or whatever institutions like

• Corporates and the government bonds primarily absorbed by

banks and financial institutions to maintain their Statutory

Liquidity Ratio

• Vast unawareness in the market

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Examples:

• Siddhartha Bank Limited Debenture– Coupon 8.5% issued in 2067

– 7 years maturity

• Nepal SBI Bank Ltd. Debenture– Coupon 7.9% issued in 2070

– 10 years of maturity

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