Bond Valuation

I have heard a lot of finance parlance on CNBC, Bloomberg and other business news networks but much of it did not make any sense until I did read about this topic. Now I am able to value a bond given a set of parameters. Of most importance was the relationship of Yield, Bond Price, Default Risk  and Interest rates Risk. And oh yes… I bought a Financial Calculator after doing this topic. You will understand why when I talk about Yield To Maturity (YTM) or jut ‘yield’.

I will discuss the following on this topic:

• Bond Prices and Yield
• Default Risk
• Interest rate Risk

A bond is a financial security that obligates the issuer to make specific payments to the bond holder.

The bond price is in essence the Present Value (PV) of all streams of cash flows (face value and coupon (ordinary payments)). If you want buy a  3 year 6% Treasury Bond at 5.6% total return, how much will you be willing to pay for this stream of cash.

PV = PV (coupons) + PV (face value).

Looking at this formula, notice the at the PV(coupons) is an annuity i.e. the coupons will be paid in regular installments and a regular interval for a specified amount of time; the PV(face value) is the discounted face value of the bond. Therefore:

PV = (coupon * annuity factor) + (face value * discount factor)

Bonds and Interest Rates

When interest rates rises above the coupon rate, it becomes lucrative for investors to invest in other securities that offers higher returns (it could be bonds as well) and hence demand a discount on a bond (lower price than face value) that has less return than the market interest rate. Another way of arguing this effect is the fact that the a low paying  (relative to the market interest rates)bond demand decreases hence the price decreases (fundamentals of supply and demand) as well.  The Yield To Maturity (YTM) increases since the bond price is guaranteed to increase to face value when it maturity. The opposite effect occurs if interest rates dip below the coupon rate. If the coupon rate is paying more than the current market interest rate, the bond price is higher than its face value. The demand for these bonds increases and hence their price. A higher price on a bond however means lower YTM since the bond price is guaranteed to decrease to face value when it matures.

Bond Prices and Yield

I got confused by the rate of return on a bond especially because the ‘rate of return’ could be loosely used to mean different things. There are three important rates of returns and should not be confused with each other:

1. The Yield To Maturity (YTM) or just ‘Yield’:  Is the total interest rate return on a bond i.e. total return on a bond if  held until maturity.
2. Current yield: Is the annual coupon payments divided by the bond price. It ignores the fact that bond prices must increase or decrease to to equal to the face value on maturity. With that, the current yield will overstates the return of a premium bond (bought at more than the face value) and understates the return on a discount bond (bought at less than the face value).
3. Rate of Return : Total Income per period per dollar invested. The total income in this instance includes the annual coupon rate plus capital gains/losses. The capital gains or losses are realized when the price of the bond changes.

Now that I have that out of the way, the Yield puts into account the PV of all future cash flows. In essence, the Yield is the discount rate that all future cash flows must be discounted with to equal to the price of the bond. With the coupon rate and time to maturity being constant, the higher the bond price the lower the yield and vice versa. The bond price is inversely proportional to its yield.

Note: When interest rates do not change, the bond prices decrease over time so that the total return on a bond equals the YTM. If the YTM increases the Rate of Return for that year would be less than the yield. This is because to calculate the Rate of Return you add the capital gains (price change) to the coupon payment. If the Yield increases, the prices decreases and hence the price change is negative. The opposite case is also true for decreased YTM.

Interest Rate Risk: This is the risk in bond prices due to fluctuations in interest rates. The longer the maturity date the more the sensitivity to interest rates fluctuations. It is because the gain or loss will be felt longer for bonds with a long maturity date.

Yield Curve: The graph showing the relationship between the time to maturity and the YTM. The YTM of long term bonds is usually higher than that of the short-term bonds. However, investors might shy away from long-term debts them for two reasons:

• Price fluctuations are more in long term debt. I mentioned earlier that this type of debt is more sensitive to interest rates than short term debt
• Should interest rates rise, short term debt holders could benefit since their bond matures faster and they could reinvest back their money at a higher interest rate.

Nominal and Real Interest rates: Most quoted interest rates are that are quoted are nominal meaning that they are not adjusted to inflation. You can buy Indexed Bonds (Inflation-Indexed) to offset the inflation effect. In this case, the real cash flows are fixed but the nominal cash flows are increased as the CPI increases.

Default Risk: The risk that the bond issuer may default on its bonds. To compensate for higher default risk, investors demand higher rate of interest for corporate bonds. Governments bonds are considered default free since the government could just print money to pay off its debt. The difference between the Treasury bonds rates and the corporate bond rates is called the default premium –  the additional yield on a bond investors require for bearing credit risk. Corporate rates are rated; Investment grade are bonds rated Baa and above by S&P and Junk bonds are bonds rated below Baa. Junk bonds are also called high yield or speculative bonds.

Promised YTM differs considerable from the expected YTM if a company goes bankrupt. The Promised YTM is the originally agreed rate while the Expected YTM is the yield realized after a bankruptcy litigation etc.