Bonds

A bond is a debt security used by governments and companies to raise capital. In exchange for lending funds, the holder of the bond is entitled to receive coupons paid periodically as well as the return of the initial investment at the maturity date of the bond. Usually, the coupon rate is constant throughout the life of the bond. The coupons can also be linked to an index; we then talk about floating rate notes. Bonds can have a range of maturities classified as: short (less than 1 year), medium (1 to 10 years) and long term (greater than 10 years). 

 

The market price of a bond is then equal to the sum of the present values of the expected cashflows.  

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The market price of a bond may include the interest that has accrued since the last coupon date. The price, including accrued interest, is known as the dirty price and corresponds to the fair value of a bond. It is important to note that the dirty price is the price effectively paid for the bond. However, many bond markets add accrued interest on explicitly after trading. Quoted bonds, such as those whose prices appear in the Financial Times are the clean prices of these bonds. 

 

Bonds are generally considered to be a safer investment than stocks due to many reasons, one being that bonds are senior to stocks in the capital structure of corporations, and in the event of default bondholders receive money first. Also, bonds generally suffer from less liquidity issues than stocks. In times of high volatility in the stock market, the bond can serve as a diversification instrument to lower volatility. 

 

Nonetheless, bonds are not free of risk, because bond prices are a direct function of interest rates. In fact, fixed rate bonds are attractive as long as the coupons paid are high compared to the market rates, which vary during the life of the product. Consequently, bonds are subject to interest rate risk, since a rise in the market’s interest rates decreases the value of bonds and vice versa. We can also understand this effect by looking at the bond price formula: if the interest rate used to discount the coupons goes up, their present value goes down and the price of the bond decreases. Alternatively, if interest rates go down, bond prices increase. 

 

Moreover, bond prices depend on the credit rating of the issuer. If credit rating agencies decide to downgrade the credit rating of an issuer, this causes the relevant bonds to be considered a riskier investment, therefore a bondholder would require a higher interest for bearing greater credit risk. Since the coupons are constant, the price of the bond decreases. 

 

2.1.4. Zero Coupon Bonds

ZC bonds are debt instruments where the lender receives back a principal amount plus interest, only at maturity. No coupons are paid during the life of the product. In fact the interest is deducted up front and is reflected in the price of the ZC bond since it is sold at a discount, which means that its price is lower than 100% of the notional.

 

The price of a ZC is equal to the present value of the par value, which is the only cashflow of this instrument and paid at maturity T. ZC bonds are tradeable securities that can be exchanged in the secondary market.

 

Using continuous compounding to discount CFs,           B(t,T) = er(t,T)×(Tt)

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