The following is a sample of a newsletter under Knowledge Series from The middle Road.
In my previous email, we discussed bonds and understood in simplistic terms coupons and yield of a bond. Recently there was a lot of noise globally when Germany issued a 30-year zero-coupon bond at 0% interest.
So, what is a Zero-Coupon Bond
A zero-coupon bond, as the name implies, does not include a coupon or interest rate. Investors are compensated for the difference between the issue and maturity price for holding the zero-coupon bond. Bonds are issued at par value. Example a bond of face value $1000 issued at a purchase price less than $1000. The difference between the purchase price and maturity price is the interest rate compensation given to the investor. The present price of a bond is the present value of all the future cash flows, i.e., the sum of coupons and the maturity value of the bond.
P= ∑ C/(1+r) t + M/(1+r) n
For a zero-coupon bond, C=0.
P= M/(1+r) n
Here, M= $1000
Let’s take a zero-coupon bond of 20 years with a yield of 4%. To derive the present value of the bond, we divide the yield by two to make it half-yearly, and the time duration is multiplied by 2. This is a simple rule of compounding. I am substituting the values to calculate the present value of the bond.
Here the investor buys the bond @ $452.98, and after 20 years, the payment of $1000 delivered to the investor on redeeming the bond. The compensation takes place through appreciation of the bond price. The investor gets the following return for holding the bond until maturity = 1000-452.89 = $547.1096
Zero-coupon bonds are generally issued for the long term and helps in locking reinvestment risk. If the interest rate is expected to go down due to an incoming recession, it makes sense to buy a zero-coupon bond at present, locking in a higher return.
For a bond, the price change is always in the opposite direction to change in the yield. As stated, before the price of the bond is the present value of the cash flows.
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