Question

How would you explain yield to maturity (YTM) and yield to call (YTC) to a friend with no background in finance? What relationship exists between the coupon interest rate and yield to maturity and the par value and market value of a bond? Explain.

Answer 1

Yield to maturity is rate of return for the investors who holds the bond till maturity of the bond.

Yield to call is the maximum rate which bond can earn because of option of call by issuer if there is fall in market rate. Yield to call is forced return on user and issuer doesn’t allow bond holder to hold bonds till maturity because the issue has option to borrow at lower rate.

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Bond price and interest rate relationship:

Bond price and interest rates are inversely related. Interest rates are discounting factors which are used to discount a bond cash flows over the period. The bonds expect inflows in form of coupon during life of the bond and principal payback at maturity. The present values of bond coupon and maturity amount sums up to make the price or present value of the bond. The higher discount rate will reduce the present value of the bond and lower the discount rate will gives us higher present values. Mathematically, the discount rates are places in denominator hence, the higher the weight of denominator lower the present values and lower the weight of denominator higher the present value.

Hence, we see inverse relationship between interest rate and bond price.

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Few more concepts:

The price of discount bonds will increase as bond approaches maturity generating capital gains. We can break down this in numeric understanding. Suppose a discounted bond of par value $ 100 is issued $ 90 which will mature after 2 years. Yield for two years be 5.41% annually. After a year bond will be valued at ~ $ 94.86 (= 90 x (1+5.41%) ) and at the end of the 2^nd year bond will be valued at $ 100 (=$ 94.86 x (1+5.41%)). Hence, we can observe the rise in price of bond for a discounted bond in year 1 from $ 90 to $ 94.86 and in year 2 from $ 94.86 to $ 100. This proves two points that investor see rise in bond price and investor has to register capital gains if his time of entry is before maturity (price increase with increase in time).

The Price of premium bonds will decrease as bond approaches maturity generating capital losses. We can break down this in numeric understanding too. Suppose a bond at par value $ 100 issued at premium $ 109 and matures after two years. The yield be 4.44% for next two years. After a year bond will be become $ 104.44 (=109/1.044) and after end of 2^nd year bond will be at $ 100 (104.44/1.044). We can observe that price of bond is decreasing from year1 to year 2 and proves our point of premium bond decreases as bond approaches maturity. Hence, it will result in capital losses for investors who have entered any time before its maturity date.

All bonds are pulled to the par level at maturity. Whatever be the bond price before maturity the prices will move towards the principal value. Hence, discounted bond move towards par value and premium bond also moves towards par value. So, discounted value appreciates with passage of time and premium value depreciates with passage of time.