Bond price
Bond is a financial instrument, which calls for a stated amount of money to be paid to the investor:
* Either at a single future date (maturity)
* Or at a series of future dates including final maturity.
The first type of bond price is a pure discount bond, also termed as Zero coupon bond in financial parlance.
The second type of bond price is known as a coupon bond, which pays interest (usually semi-annually) along with a final payment on maturity.
Bond analysis is based on the premise that public information can be utilized to identify instruments that are not fairly priced. However, an analytical procedure is required to achieve this goal.
Financial analysts use the Capitalization of Income method of Valuation to determine whether a bond is undervalued or overvalued. Two of the most commonly used tools under this method of valuation are:
1. YIELD TO MATURITY (YTM): This analysis involves the Internal Rate of Return (IRR) method.
The actual YTM of the bond price is compared to an expected yield (EY) calculated by the investor. The EY is calculated after factoring the characteristic of the bond and taking into account the current market conditions.
If YTM > EY then the bond is under-priced and a buy signal is generated.
Calculation of YTM
The zero coupon bond is where the issuer promises to make a single payment (which is the face value of the instrument) on maturity.
YTM is the IRR, which equates the cash inflows, in this case the Future Value FV (also the face value) to the cash outflows in this case the current market price (CMP).
Coupon Bonds are more prevalent in the financial instruments market. Generally, these bonds pay a semi-annual interest and a final principal payment (face value) at maturity.
YTM is the IRR, which equates the cash outflow (CMP) to the aggregate of cash inflows (all interest payments received added to the principal payment received).
2. INTRINSIC VALUE
Firstly, the Value (PV) of the bond price is calculated (by discounting the cash flow over the life of bond to its present value). The Net Present Value (NPV) is then ascertained as follows:
NPV = PV CMP
If the NPV is positive (NPV>0) then the bond is under priced and a buy signal is generated. This theory will always hold good when the bonds YTM > EY.
Conversely, if the NPV is negative, then the bond is overpriced and a sell signal is generated. This will always be the case when the bonds YTM
Using the Capitalization of Income method of Valuation requires three key inputs to be determined. The interest payment and the CMP are easily identifiable as they are the bonds promised cash flows and market price respectively. However, the value of the expected yield (EY) is a complex calculation as this involves the investors subjective evaluation of the characteristic of the bond and the current market conditions.
Let us examine the attributes of a bond price that require minute consideration to evaluate the EY.
FACTORS INFLUENCING BOND VALUATION
The following attributes of a bond assume significant importance during valuation.
1) Interest rate or coupon rate and the length of time to maturity require in-depth consideration. They determine the quantum and the timing of the cash inflows. They are used to arrive at the bonds YTM that the investor will eventually compare with the EY.
2) Call options on a bond enable the issuer to redeem the bonds prior to maturity. The issuer incorporates such an option in a bond as a cover when the yields are bound southward. It is financially advantageous for an issuer to exercise the call option and retire existing costlier debt and replace them with lower cost debt when interest rates are falling.
3) Taxation norms also affect the pricing of bonds.
4) Marketability or liquidity of the bond is an important factor. This highlights how quickly the instrument can be converted into cash and at what discount.
5) Bonds are rated on the basis of likelihood of default, which also influence the valuation.
BOND PRICING THEOREMS
* The price of a bond and its yield are inversely proportional. When the price of a bond rises then its yield must decrease and vice-versa.
* If a bonds yield remains constant over its duration, then the size of discount or premium will decrease as its life gets shorter
* If a bonds yield remains constant over its duration, then the size of discount or premium will decrease at an increasing rate, as its life gets shorter.
* A decrease in bonds yield will increase its price by an amount that is greater in size than the corresponding fall in bonds price that would occur if there were an equal sized increase in the bonds yield.
* Higher the coupon rate, smaller will be the percentage change in bonds price owing to change in yield (not applicable to bonds with maturity of one year or perpetual bonds).
DURATION
Duration is used to measure the Average Maturity of the cash flow stream associated with a bond. To be more precise, it is a weighted average of the lengths of time until the remaining payments are made.
Let us understand the concept of calculation of Duration with the help of a hypothetical illustration.
Consider a bond with annual coupon payments of Rs 80, a remaining life of three years (maturity), and a par value (face value) of Rs 1000. Also, let us assume that the bond is trading at Rs 950.25 (Current Market Price). Based on these assumptions and as per calculation explained above the bond will have an YTM of 10%. For ease of exposition, a bond with annual coupon (annual compounding) is considered. Based on this data let us now calculate the Duration of the bond.
Time cash flow PV PV of Weighted
Factor Cash Flow amount
A B C D E
(B*C) (A*D)
1 Rs 80 0.9091 Rs 72.73 Rs 72.73
2 Rs 80 0.8264 Rs 66.12 Rs 132.24
3 Rs 1080 0.7513 Rs 811.40 Rs 2434.20
Summation Rs 950.25 Rs 2639.17
Duration (D) = E/D that is Rs 2639.17/Rs 950.25 = 2.77734 Years.
Alternatively, the duration may also be calculated as under:
Time PV CMP Weight Duration
A B C D E
(B/C) (A*D)
1 Rs 72.73 Rs 950.25 0.07653 0.07653
2 Rs 66.12 Rs 950.25 0.06958 0.13916
3 Rs 811.40 Rs 950.25 0.85388 2.56164
Summation (Duration) 2.77733
The above calculations do not apply to a zero coupon bonds. As such a bond has only one cash flow associated to it, duration is equal to the time remaining to maturity.
The relationship between a bonds price and its durations is established as below:
% Change in price of bond approximately equal the product of (-ve) Duration and (1+%change in the bonds yield).
BONDS VERSUS STOCKS
Bonds and stocks are different kinds of securities, with different characteristics. Therefore, investment decisions should not be based on a simple one-dimensional comparison. In practice this decision, also termed as Asset Allocation, will involve investing in both stocks and bonds.
Historically, based on average returns, bond price appear to have a substantial advantage for the investors with a reasonably long horizon. For an investor concerned with month-to-month variation (need for liquidity or with a known short horizon), bonds look relatively more attractive than stocks.
0ther articles
