# General Expressions of Bond Returns

**General Expressions of Bond Returns. ****Bond Yields and Prices: **Bond returns can be calculated in many ways though they are prefixed. The followings are **general expressions of bond returns** which are usually found in the securities markets.

*Coupon Rate*

It is the fixed annual interest rate affixed on the face of the bond and is calculated on the face value. It is the fixed rate of return at which income is payable to the bondholder.

Example – Suppose a bond of face value of Tk. 500 with 15 per cent coupon rate will generate Tk. 75 to bondholder annually till maturity.

*Current Yield*

Since a bond can be sold before maturity, it might be performed in the prevailing market price. The current market price of a bond in the secondary market may differ from its face value. Current yield is the ratio of annual interest receivable on a bond and its current market price which can be shown mathematically as:

Current yield = I_{n}/P_{0}

where,

I_{n} = amount of annual interest

P_{0} = current market price of the bond

Current yield can be expressed in percentage term by multiplying the ratio by 100 as:

Current yield (per cent) = [I_{n}/P_{0}] ×100

In the earlier example, if the current market price of the bond is Tk. 490, the current yield would become:

Current yield = [I_{n}/P_{0}] ×100

= [75/490] ×100 = 15.31 per cent

The properties of current yield are: the lower the selling price of the bond the higher the current yield and higher the market price the lower the current yield. It implies that there is an adverse relationship between current market price of a bond and its current yield. On the other hand, if the current yield of the bond is lower than the coupon rate, the bond is selling at a premium and vise versa. The current yield measures the annual return to a bondholder who purchases the bond from the secondary market and sells before maturity at the same price at which it was bought. It does not measure the entire returns from a bond held till maturity.

*Spot Interest Rate*

A zero coupon bond is a bond which is sold with no coupons, no interest to be paid during the life of the bond and is redeemed for face value at maturity. It is a special type of bond paying no annual interest. Therefore, the return on this bond represents a discount on issue of the bond. As for example a two-year bond with a face value of Tk. 1000 may be issued for Tk. 800 at discount. The investor purchasing the bond at Tk. 800 will receive Tk. 1000 after two years from now. This type of bond is called pure discount bond. The return received from a zero coupon bond expressed on an annualized basis is called spot interest rate. Hence, spot interest rate represents the annual rate of return on a bond having only one cash inflow. It can be expressed as the discount rate that equates the redemption value to the discounted value at which the investor purchased it. Thus, the spot interest rate of a two-year bond of face value Tk. 1000 issued at a discount for Tk. 800 can be estimated as:

800 = 1000/(1 + k)^{2}

(1 + k)^{2} = 1000/800

(1 + k)^{2} = 1.25

(1 + k) = √1.25 = 1.1180

Therefore, k = 1.1180 -1 = .1180 = 11.80 per cent

A zero coupon bond with a face value of Tk. 1000 with a maturity period of three years is issued at discount for Tk. 700. The spot interest rate can be shown as below:

700 = 1000/(1 + k)^{3}

(1 + k)^{3} = 1000/700

(1 + k)^{3} = 1.4286

(1 + k) = ^{3}√1.4286 = 1.1263

Therefore, k = 1.1263 -1 = .1263 = 12.63 per cent

The spot interest rate depends on the life of the bond and the difference between the face value and discounted value of the bond.

*Yield to Maturity (YTM)*

Yield to maturity (YTM) is most widely used measure of return on bond. It is the compounded rate of return an investor expects to receive from a bond purchased at current market price which he holds till maturity.

*Yield to Call (YTC)*

At the option of the issuer or of the investor, some bonds may be redeemable before their maturity period. If such option is executed, the subject bond would be called for redemption at the specific call price on the specified call date.