Relationships between the price of a bond and the prevailing interest rate?
- The relationships between the price of a bond and the prevailing interest rate is inverted.
- Higher prevailing interest rates result in lower prices for existing bonds, and lower interest rates result in higher bond prices.
- In addition, with a change in interest rate, the price changes in proportion to the term to maturity on a bond. - Investors perceive long-term bonds to be riskier than short term bonds. This is partly due to the fact that problems associated with the repayment of debt increases as the term to maturity increases. It is also due to the fact that the present value of a bond also varies more dramatically in response to changes in interest rates as the term to maturity increases.
According to the liquidity preference theory, investors need to be compensated for holding bonds with longer terms to maturity because they are exposed to greater amount of interest rate risk. As a result, the normal-shaped yield curve shows that the longer term bonds can be expected to yield higher return than shorter term bonds of the same class.
What is a Trust indenture of a bond?
Is a formal agreement between an issuer of bonds and the bondholders specifying such details as the type of bond, the amount of issue, security for the issue, protective covenants, any working capital requirements of the issuer, any redemption rights of the bondholders and any call privileges of the issuer.
What is default risk?
- A default risk is a risk that arises from the possibility that the issuer of a fixed income investment willnot be able to make timely payments of interest and principal. A higher credit rating on a bond indicates that the bond issuer is less likely to lack the funds to make interest payments. Because making interest payments is an essential part of the trust indenture of a bond, a high credit rating means that the bond is less susceptible to default risk.
The coupon payment of a semi-annual bond
- Most corporate bonds pay interest semi-annually, but the returns is expressed as an annual rate, paid semi-annually.
- The coupon payment of a semi-monthly bond is calculated as:
(face value x (interest / 2 )) - Bonds that are bought or sold at their face value are said to trade at par value or simply at par.
- Bond usually trade In units of par value, which is arbitrarily set at 100.
- Any difference between the market price and the face amount is then made relative to 100.
- For example, a bond that is priced at 95 can be purchased for 95/100ths of its face value.
What happens when Bonds are bought or sold for less than face value?
- Bonds that are bought or sold for less than face value are said to trade at discount, while those that are bought and sold for more than face value are said to trade at premium
- The purchase price of a bond that is trading at a premium or a discount to face value is calculated as:•
((unit price / 100) x face value)
Where are bonds readily available?
- Bonds are readily available in the secondary market, and they rarely trade at par after they are issued.
- Changes in interest rates affect the fair market value of a bond. If an investor purchased a bond at its par value when first issued, a subsequent decline in interest rates will raise the value of the bond above par.
- Conversely, a rise in interest rates will cause the value of the bond to drop below par. If an investor sells a bond before maturity at a price other than par, it will give rise to a capital gain or a capital loss.
How is the value of a bond calculated?
Value of a bond is calculated by: P/Y = payments per year N = (Number of years x payments in a year) I/YR = nominal interest rate PMT = (face amount x (coupon rate/payment per year) FV = Future value of the bond Timing of payment = END Solving for PV
What is the Yield to maturity?
The yield to maturity is the bond-equivalent yield that an investor would receive if she holds the bond to maturity.
The YTM is an accurate measure of a bond’s true return /yield because it accounts for both the current yield and capital gain or loss from any premium or discount realized at maturity.
f a bond is trading at a premium, its YTM will be less than the coupon rate. This is because the YTM calculation considers that the higher price being paid for the bond will ultimately result in a capital loss when she redeems the bond.
A bond’s value varies as prevailing interest rates change, such that the bond usually sold at either a discount or a premium in the secondary market. When the bond matures, the investor will realize a capital loss if she purchased the bond at a premium, and she will realize a capital gain if she bought the bond at a discount. While she holds the bond, she will continue to receive the full coupon rate of the bond.
What is Yield to call?
The yield to call is the bond equivalent yield that the investor would receive if the bond is held until an anticipated call date. If the bond is called, the investor would receive the original face amount of the bond plus any call penalty.
What is the current yield?
The current yield measures the annual return as a percentage of the current value of the bond.
The current yield is calculated as:•
(annual interest payments / current price of the bond)
•The current yield does not consider the effect that a premium or discount would have on the return.
The current yield will only equal the nominal annual interest rate if the bond is trading at par.
What is the Effective Yield to maturity?
The effective yield to maturity is the effective annual return on a bond that is held to maturity, taking into to account the effect of multiple compounding periods, and the gain or loss that an investor will realize if the purchase price differs from the par or face value.
If a bond is priced at a discount, the effective yield to maturity will be greater than the coupon rate.
Conversely, if a bond is priced at a premium, the effective yield to maturity will be less than the coupon rate.
The effective yield to maturity is calculated by:
P/Y = payments per year
N = (Number of years x payments in a year)
PV = Present Value((Price /100) x face value))
PMT = ((face value x coupon) / 2)
FV = Future Value
Solving for I/YR And solving for EFF% = effective annual rate
Bond equivalent yield to maturity and effective yield to maturity…
The bond equivalent yield or bond yield is the nominal annual interest rate compounded semi-annually.
The bond equivalent yield to maturity can be calculated by solving for NOM% or I/YR.
The effective yield to maturity can be calculated by solving for EFF%.
What is a callable bond?
A callable bond is a bond that the issuer has the right to redeem the bond prior to maturity after a period of time as specified in the trust indenture.
The issuer is free to call the bond at any time after this date. By including the call feature, the issuer is protecting himself from a drop in interest rates.
However, the investor does not know when the bond might be called.To compensate for this uncertainty, the bond issuer offers a call penalty, which must be paid if the bond is called prior to maturity.
The call penalty schedule is specified in the trust indenture, and is usually expressed as a percentage of the face amount or par value. The call penalty decreases as the time remaining to maturity decreases.
The yield to call is the bond equivalent yield from the purchase date to the anticipated call date.
What is a strip bond?
A strip bond or a zero coupon bond is a bond that is purchased at a discount and mature at face value. They do not make interest payments.
When a strip bond is first issued, it is priced at the Present Value of the face amount, based on the interest rates that prevailed at the time the strip was issued. If the investor holds the strip to maturity, the rate of return is guaranteed, and consists solely of interest income. Although the investor does not receive the face value until maturity, he must accrue the interest income annually for tax purposes.
However, if an investor holds a strip to maturity, the difference between the purchase price and the cost + commission is interest income.
On the other hand, if an investor sells a strip prior to maturity, she would receive an amount equal to the PV of the face amount, based on the prevailing interest rates at the time that she sells the bond. This could result in a capital loss, depending on interest rate movements.
The capital loss would be calculated as:•(proceeds of sale – (purchase price + interest earned and reported as taxable income))As the income interest is reported, it increases the ACB of the investment. The ACB of a strip bond at anytime is the original purchase price, plus any commissions paid at the time of purchase, plus the accrued interest that has been reported for tax purposes.
he ACB of a strip bond at any time is:
•(Original cost + commissions + accrued interest)Value of bond after 1 year•(purchase price x (1 + nominal annual yield)
What is a Normal Yield Curve?
The r’ship between the terms to maturity of bonds within the same risk class is called the term structure of interest rates. This r’ship is depicted graphically by a yield curve.
Normal Yield Curve is a graph of interest rates verses term that slopes upward to the right (i.e. has a positive slop), such that the yield to maturity on the bonds increases as the term to maturity increases.
What is an Inverted Yield curve?
An inverted yield curve is a graph of interest rates versus term that slopes downward to the right ( i.e. has a negative slope), such that the yield to maturity on the bonds decreases as the term to maturity increases.
An inverted yield curve can occur in times of economic and political crisis.
Unbiased expectation theory..
Is a theory that a positively sloped yield curve is the result of investor expectations that interest rates will rise in the future.
Liquidity Preference theory…
Is a theory that investors require that a long-term bond must have a higher return than a short-term bond because investors perceive a long-term bond to be riskier to hold than a short-term bond.
Bcoz investors prefer liquidity to being locked-in over the long term, investors must be adequately compensated for the added risk of long-term bonds.
What happens once a bond is called and is there any advantage to an investor holding the callable bond?
A high coupon is expensive for the issuing company to maintain.
If interest rates fall, the issuer may decided that it would be more economical to pay the higher coupon rate.
Once a callable bond is called, it does not pay any additional interest after the call date.
There is no advantage to holding a bond past the call date, and the investor should redeem it promptly.
What is a Sinking Fund?
Sinking Fund is a fund that is set aside by the company to ensure that the full debt can be retired by maturity.
For the investor, this lowers the element of default risk because the issuer has a systematic plan of repaying the debt at maturity.
However, the investor then faces uncertainty of when her bond will be called, and this can make investment planning more difficult.
Bcoz sinking fund bonds are often called before they mature, the yield to call is the yield that the investor would realize if the bond is held to the expected call date.
Where do Bondholders rank in terms of their claims against the assets of a corporation?
- All investments in a corporation are subject to financial risk, but some investments are more secure than others.
- A bond is secured by specific assets of issuing the corporation, while a debenture is secured only by the general credit worthiness of the company.
- Bondholders rank senior to shareholders in terms of their claims against the assets of the corporation, so in the event of bankruptcy, shareholders will not receive anything unless the company has money left over after redeeming all outstanding bonds.
- Usually, this does not happen, and even secured bond-holders only receive a fraction of their investment.
What should an investor consider when choosing to invest in a new issue of corporate bonds in a company in a bio tech industry with an unproven track record?
- Bondholders face the risk that the issuer of the bond will default on either the face of the maturity or the coupon payments.
- The higher the credit rating on the bond, the lower the risk of default, lower yield to maturity.
- A bond downgraded to a lower credit rating will have to provide a higher yield to maturity to attract investors.
- Because the coupon on a bond is fixed, the only way to obtain a higher yield to maturity is to decrease the price of the bond in the open market.
- In this way the investor is more likely to realize a capital gain upon maturity, and this will increase the overall yield to maturity on the bond.
What is an immunization strategy?
- An immunization strategy is a passive investment strategy to reduce the gains and losses resulting from interest rate changes.
- It involves matching a bond’s duration to the bondholder’s holding period, instead of matching it with a term to maturity.
- According to this strategy, regardless of the changes in interest rates, the cash or wealth received by the bondholder at the end of the duration period will remain constant.
- To successfully implement and immunization strategy, an investor must hold the bond for it’s duration and reinvent the coupon payments. The duration of the bond with coupons is less than the term of the bond and the investor would have to sell the bond with coupons before the term of the bond.
- Coupon payments are reinvested at different rates over the duration of the bond and the bond’s value also varies as interest rates change.
- A bond immunization strategy is designed to minimize interest rate risk and reinvestment rate risk.
What is interest rate risk?
An interest rate risk is a risk that arises from an increase in interest rates. When interest rates rise, bond prices fall. Fixed-rate investments, such as term deposits, lock-in a set interest rate and the investor is protected from an interest rate risk.
- Long-term marketable bonds carry a high level of interest rate risk.
- If a strip bond is held to maturity, the return will not vary regardless of changes in interest rate and there is no interest rate risk.
