Interest Rate Changes Affect the Price of Bonds

Question

Answer:

1. Price of a bond = c *F* 1- (1+r)^-t + F/(1+r)^t

                                               R

Where c = coupon rate, F = par value, r = yield to maturity, t = time period

C = 6% (semi annually, F = $1000, r = 7% (taken semi-annually), t = 20

Therefore price of Triangle bonds = 6% *1000*(1-(1+0.07)^-20)/0.07 +1000/ (1+0.07) ^20

                                                             = $894.06

P.S = The interest rate and yield to maturity have been taken semi annually since the coupon is paid semi annually.

b) Required rate of return on a bond is the interest rate that is expected by the investor from a bond in order to purchase the bond. This rate is influenced by the market forces and is determine d by the price at which both investor and the issuer of bonds agree. (Ingram, 2009)

If the interest rate decreases, the price of the bond will increase. The price of the bond is determined by discounting the future cash flows of the interest payments and bond price to be made till the maturity of the bond. The value of a dollar today is definitely more than the dollar value in the future. If the interest rate decreases due to inflation, Federal Reserve actions or economic conditions, the future cash flows will be discounted at a lower rate and this will increase the price of the bond. The discount rate is the market rate for instruments which have similar risk and maturity. Therefore when there is a change in the interest rate, it affects the price of all bonds in the market but to varying degree. A bond having longer maturity has greater price volatility.

The price of a bond with lower coupon rate will increase more than the bond with a higher coupon rate as the required rate of return falls. This is because for a low coupon rate, most of the future cash flow is in the form of face value as there is less coupon payment. Hence with a lower discount rate, the future value of cash flows will increase and thereby the price of the bond will increase.

(AAII, 2008)

2. Yield curve is a graphical representation of the yields of a bond with different maturities. Usually treasury bonds are used to create the yield curve as they are the best benchmark for bonds having similar maturity. The shape of the yield curve denotes the future economic activity and the interest rate changes expectations which will have an impact on the return of bond investments. There are generally three types of yield curves i.e. normal yield curve, flat yield curve and inverted yield curve.

The following data has been provided in the question regarding the yield curve:

The yield curve for the above data is given below:

From the above graph, we see that the yield curve is inverted and is downward sloping. This means that for bonds with short term maturities, the yield is higher and for long term bonds, it is lower. This shows that the market expects the interest rates to fall in the future; however, this is a rare situation because normally the yield is higher for a long term maturity bond and vice versa. (PICTET, NA)

This situation normally arises when the economy is on the verge of entering into a recession. The investors prefer to invest their money in risk free instruments for long term even though the return is low as they expect the economy to deteriorate. The investors become risk averse and instead of investing in a new venture or in riskier assets, the investors prefer to invest on risk free bonds and therefore settle for lower yields as they expect the interest rates to further go down in the future. However, this scenario is not long lasting as the outlook of the economy improves with time with the help of government policies and investors again have normal expectations about the interest rates and risk, thus the yields on long term bonds increase and is more than the yield on short term bonds. (Guidotti, NA)

Reference

AAII, (2008), How Interest Rate Changes Affect the Price of Bonds, accessed online on 28^th July, 2016, available at https://www.aaii.com/journal/article/how-interest-rate-changes-affect-the-price-of-bonds.mobile

Ingram, D, (2009), What is the Difference Between Yield to Maturity and Required Rate of Return        on a Bond, accessed online on 28^th July, 2016, available at, http://budgeting.thenest.com/difference-between-yield-maturity-required-return-bond-3679.html

Guidotti, D., (NA), Calculating and Understanding Yield Curve, accessed online on 28^th July, 2016, available at http://www.pfhub.com/calculating-yield-and-understanding-yield-curve/

PICTET, (NA), Yield Curve, accessed online on 28^th July, 2016, available at, http://perspectives.pictet.com/glossary/yield-curve/