TOC
1. Bond Value
1.1 Bond Price
The value of a bond is the aggregated present values of all futures cash flows associated with it. Future cash flows include:
- Coupons C: the regular payments from holding a bond. It is the product of the coupon rate and the face value.
- Face Value M (or principal): is a lump sum payment at maturity.
Bond Price Calculation
When YTM is higher than the coupon rate, a bond sells at a discount (i.e. at a price lower than its face value). Whne YTM is lower than the coupon rate, a bond sells at a premium (i.e. at a price higher than its face value).
The discounted rate is the market interest rate for the financial securities of similar risk.
Clean Price v.s. Dirty Price
Clean price is the quoted price disregards the interest. Accrued interest is coming from the period between last coupon payment date and the purchase/transaction date
Dirty price is the clean price plus accrued interest. When the coupon payment is made, the dirty and clean prices would be the same since there would be no accumulated interest on the bond then. The dirty price is the highest right before the coupon payment is about to be made and is lowest (equal to the clean price) right after the bond has been issued.
1.2 Yield to Maturity
It is the average return to a bond holder from the moment a bond is bought to its maturity. It is the average discount rate for the security’s cash flow. It is the effective interest rate. It equals the contemporaneous market interest rate for those investments with similar risk and it’s also called the yield at redemption.
Current Yield
The current yield is the annual gross (i.e. before tax) cash flow divided by the current market price of the bond expressed as a percentage. It is not the actual annual return on a bond because it does not include the capital gain. For a bond has face value of £100, a coupon rate of 5% payable annually. If the market price is 90, the current yield is 5/90=5.56%.
1.3 Bond Risk
Bond risk is the fluctuation in price. It includes interest rate risk and default risk.
The interest rate risk is linked to the sensitivity of bond price to the change in the prevailing relevant interest rate in the market.
- Firstly, bond price increases (decreases) when the YTM decreases (increases), ceteris paribus.
- Secondly, the higher the sensitivity of a bond’s price to the change in market interest rate, the higher the bond’s interest risk.
Intuitively, if the YTM is the same, the longer the wait of cash flow, the more uncertainty there is.
Macauley Duration
Duration: interest rate sensitivity, elasticity of the bond price (p) with respect to “1 plus yield to maturity”, that is 1% change in discount rate, lead to ?% change in P.
Negative sign implies that when interest rate (discount rate) goes up, price goes down.
The duration is measured as the present-value-weighted average time horizon of all cash flows associated with a bond, where is the present value of the n-th coupon. It’s a weighted value because
Modified Duration
Since , , thus
If interest rate (discount rate) change by 1 percent, and if we know the modified duration, we can calculate the price change.
Duration has double meanings:
- Interest rate risk: sensitivity to interest rate change - how bond price fluctuates when the interest rate changes.
- Weighted average maturity of a bond: average time taken to receive the cash flows. The longer the maturity, the higher the duration. The higher the YTM, the shorter the duration. The higher the coupon rate, the shorter the duration.
A Duration calculation example is shown as below.
1.4 Term Structure
Term structure shows the market interest rate with its corresponding term. For example, the market interest rate to discount cash flow from t1 to t0 is 5%; the market interest rate to discount cash flow from t2 to t0 is 6%; the market interest rate to discount cash flow from t3 to t0 is 8%.
A term structure delineated the relation between the interest rate and the term to maturity. The yield curve is the graphic representation of the term structure.
There are three hypotheses to explain why the yield curve is of a certain shape:
- Expectation hypothesis: Depending on the expected spot interest rate, that is, the rate to discount cash flow from a far-away future date to a near future date.
- The upward or downward shape is related to expectation.
- Liquidity hypothesis: Depending on the demand for liquidity, which explains why the yield curve is generally upward sloping.
- Market-segmentation hypothesis: Depending on the demand and supply on separate markets.
2. Government and Corporate Bond Market
Government Bonds
Governments issue bonds to cover the gaps between government expenditure and tax income. Government bonds are normally very safe financial assets but may also default occasionally.
UK government bond: Gilts (issued by the UK central government): The UK Debt Management Office is responsible for the issuance and management of the Gilts. A Gilt has a face value of 100 pounds carrying coupon which is paid semi annually. Gilt has other names like exchequer, treasure, or funding.
Dated gilts have specific dates fo redemption or a time window for redemption while undated gilts do not have specific dates for redemption.
The market for gilts is a quote-driven market. A market maker on the gilts market is called Gilt-edged Market Maker (GEMMS) which are usually big financial institutions with strong financial fundamentals.
Corporate Bonds
Issued by companies. It is a major source of fund for companies. A corporate bond usually have higher default risk than a government bond. Many corporate bonds are traded on stock exchanges while more are traded on OTC market. Bond holders can also cash out before maturity by selling to other investors.
Debentures
Debentures, also called loan stock, are bonds secured by company assets. It is the safest type of corporate bond. A debenture is often used for more specific purposes than a bond, e.g. a project or an expense plan. Secure means, in the event of default, corporate assets can be sold, and the proceeds can be used to pay back bond holders. A fixed charge debenture is secured by specific company assets like buildings and machinery. A floating charge debenture is secured by a general charge on all company assets (in the event of defaut, a company has the freedom to choose which piece of asset can be sold to pay back debenture holders.) A fixed charge denbenture is ranked above a floating charge debenture in the pay out when default happens.
In UK, Debentures means secured debt while in USA, it means unsecured debt. In Asia, it can be either.
Covenants
Covenants are restrictions put on a borrowing companies aimed at reducing default risk. They make the lending safer and some borrowers voluntarily adopt covenants to reduce the borrowing cost.
Some covenants are affirmative, e.g. the disclosure of financial information and the payment of coupons and principle.
Some covenants are restrictive, e.g.
- the borrowing firm has limits on the amount (the debt ratio cannot exceed a certain level) and type of further borrowing.
- The borrowing firm has restrictions on dividend payment
- bond holders are against the idea of borrowing to pay dividend
- excessive dividend pay out undermines growth and makes debt riskier
- The borrowing firm cannot dispose of assets at will
- The borrowing firm has to meet a certain required financial ratio
3. Credit Rating
It is a score assigned by credit rating agencies as an evaluation of a borrower’s credit worthiness. Credit rating overcomes information asymmetry, encourage bond investment and reduces borrowing costs.
Companies pay the credit rating agencies to obtain a credit rating. Determinants of credit raing includes:
- The quantitative factors inlcude the leverage ratio, cash flows, debt outstanding, etc.
- The qualitative factors include the market share, management quality, sensitivity to economic cycles, etc.
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