Question

How are bond prices determined in the market? What is the relationship between interest rates and bond prices? Have you ever purchased a bond? If so, what was your experience with the purchase price and the value of the bond over time? Explain the different type of risk that a bond investor and issuer face. How does a bond's term and collateral changed to affect its interest rate?

Answer 1

A Bond is a security that is issued in connection with a borrowing arrangement. The borrower issues a bond to the lender for some amount of cash; the bond is the IOU of the borrower.

Pricing of the Bond:

I am simplifying the assumptions by taking only one interest rate which can be relaxed for further.A bond is issued at Par with or without coupon rate. An investor who is purchasing the bond pays a price and receive the coupon payments periodically and the par value at the maturity. But at what price should the issuer sell the bond. we can understand it through following way:

To value a security, we discount its expected cash flows by the appropriate discount rate. The cash flows from a bond consist of coupon payment until the maturity date plus the final payment of par value.

Bond Value/price= Present value of coupons that will be received in future + Present value of Par value of the bond

if we call the maturity date T and call the interest rate r, the bond value can be written as

Bond Value = where T is the Maturity Date and t is the no. of periods till maturity date.

we can also see this valuation as follows

Bond Price = Coupon * Present value Annuity factor (r,T) + Par value * PVF(r,T)

Example:

Let there is 10% coupon, 30 year maturity bond with par value of $1,000 paying 60 semiannual coupon payments of $40 each. Suppose that the interest rate is 8% annually, or r=5% per 6 month period. Then the value of the bond can be written as

Price of the Bond = $40 X Annuity factor (5%,60) + $1000 X PVF(5%,60) = $757.17 + $53.54 = $810.71

Relationship Between the Bond price and the Interest Rate:

There is negative relationship between the Bond price and the Interest rate of the Bond.

It is because Interest rate here works as a discount rate. So if it is higher then your future cash flows in the form of coupon payments and par value will be less as you can see in the formula the denominator will go up making your price down.

we can understand this logic practically also. For example you have issued $1000 bond in the market at the interest rate of 5%. After some time the interest rate goes up to 8%. so as an issuer you have to compensate your investor by keeping your bond price down because now they have better choice of getting 8% in future instead of 5%. so to compensate this difference you have to sold your bond at low price or vice versa. its like supply and demand function.

you can take the above example, lets say in the above example the interest rate goes down to 4% semi annually then

Bond price = $40 X PVAF(4%,60) + $1000 X PVF($4,60) = $904.94

so as you can see that price of bond went up from $810.71 to $904.94.

Risks in issuing Bonds:

Interest rate risk:The main risk in the bond market is the interest rate risk. If the interest rate rise the price of bond will fall hurting the issuer or vice versa it will hurt the investor. Now interest rate also get affected by inflation rate, the stage of business cycle, global events. government policies like fiscal or monetary policies.

Reinvestment Risk: One risk is that the proceeds from a bond will be reinvested at a lower rate than the bond originally provided. For example, imagine that an investor bought a $1000 bond that had an annual coupon of 12%. Each year the investor receives $120 (12% X $1000), which can be reinvested back into another bond. But imagine that over time the market rate falls to 1%. Suddenly, that % 120 received from the bond can only be reinvested at 1%, instead of the 12% rate of the original bond.

Call Risk: Another risk is that a bond will be called by its issuer. Callable bonds have call provisions which allow the bond issuer to purchase the bond back from the bondholder and retire the issue. This is usually done when interest rates have fallen substantially since the issue date.

Default Risk for Bond Investors this risk mainly have trust issue. In other words may be the issuer of the bond go bankrupt and your all investments go down.

Inflation Risk : The risk refers to an event wherein the rate of price increases in the economy deteriorates the returns , associated with the bond. This has the greatest effect on Fixed Bonds. Which have a set interest rates.

I haven't purchased any bond. But yes i can say that Bond market is highly volatile and an investor must be very cautious before investing in it.