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The concepts of holding period return and yield to maturity in bond investment. It provides formulas, examples, and illustrations to help investors understand how to calculate these rates of return. The document also discusses the differences between current yield and yield to maturity, and the importance of assumptions in yield to maturity calculations.
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Lecture 3 Bond return
Holding period return- An investor buys a bond and sells it after holding for a period. The rate of return in that holding period is:
Holding period return =
Price gain or loss during the holding period + Coupon interest rate, if any Price at the beginning of the holding period
The holding period rate of return is also called the one period rate of return. This holding period return can be calculated daily or monthly or annually. If the fall in the bond price is greater than the coupon payment the holding period return will turn to be negative.
Illustration 7. (a) An investor ‘A’ purchased a bond at a price of Rs. 900 with Rs. 100 as coupon payment and sold it at Rs. 1000. What is his holding period return?
(a) If the bond is sold for Rs. 750 after receiving Rs. 100 as coupon payment, then what is the holding period return?
Solution.
(a) Holding period return =
Price gain + Coupon payment Purchase price 100 + 100 = 900 =
Holding period return = 22.22% Gain or loss + Coupon payment (b) Holding period return = (^) Purchase price
= – 150 + 100 900 = –^50 900 = 0.
Holding period return = 5.5%
The current yield- The current yield is the coupon payment as a percentage of current market prices Annual coupon payment Current yield = (^) Current market price
With this measure the investors can find out the rate of cash flow from their investments every year. The current yield differs from the coupon rate, since the market price differs from the face value of the
return.
In the above example, if coupon receipts are re-invested at say, 10 per cent for the rest of the period then the realised rate of return will be less than the YTM. Conversely, if the coupon receipts are reinvested at 14 per cent, the realised rate of return will be higher than the YTM.
Any difference in the re-investment rate will cause a difference between the actual return and the YTM. In this sense, the YTM is only a measure of yield. It cannot be regarded as a measure of return from a coupon-paying bond.
The YTM concept has a slightly different meaning for Zero Coupon Bonds (ZCB), popularly known as Deep Discount Bonds (DDB). ZCBs do not carry any coupon but are issued at a price discounted to the face value. On maturity, these bonds are redeemed at face value. Since thee bonds do not have any coupon payments during the life of the bond, the question of re-investment of coupon payments does nto arise at all. There is no re-investment risk for ZCBs.
To find out the yield to maturity the present value technique is adopted. The formula is,
Present value =
Coupon 1 (1 + y)^1 +^
Coupon 2 (1 + y)^2 + …^ +
(Couponn + face value) (1 + y)n
Y = The yield to maturity.
Illustration 8. A four-year bond with the 7% coupon rate and maturity value of Rs. 1000 is currently selling at Rs. 905. What is its yield to maturity?
Solution. Since all the three values are known out of the four values, it can be found out by using trial and error procedure. Let us try ten per cent.
Cash flow PV for 10% PV of CF 70 0.9091 63. 70 0.8264 57. 70 0.7513 52. 1070 0.6830 730. Rs. 904.
The yield to maturity is 10 per cent
The approximate yield to maturity can be found out by using the following formula too. C + (P or D/years to maturity) (PO + F) / 2
Y = Yield to maturity
C = Coupon interest
P or D = Premium or discount
PO = Present value
F = Face value
In the case of previous sum
