Question

What would be the effect on the price of bonds if (1) an unexpected rise in interest rates,
and (2) an unexpected fall in interest rates? Would these interest rate changes have a similar
effect on the price of shares? Explain in details and give examples

Answer 1

If interest rates rise unexpectedly, then the required return on bond (YTM) also rises. YTM and price of the bond has inverse relation, so if YTM rises price of the bond will fall.

If interest rates fall unexpectedly, then the required return on bond (YTM) also falls. As said like earlier, YTM and price of the bond has inverse relation, so if YTM falls price of the bond will rise.

Interest rate fall or rise affects the market risk premium also. While determining required return on equity by using capital asset pricing model (CAPM), market risk premium affects it. While determining price of the share by using required return on equity, it will affect price inversely. So change in interest rate also have similar effect on the price of shares.

For example:

At present, risk free rate = 4%, Market return=14%, beta of share=0.5, last dividend paid =$1.5 constant growth rate=5%

Return of equity = risk free rate+[Beta*(Market return-risk free rate) = 4%+[0.5(14%-4%)] = 4%+[0.5*10%] = 4%+5% = 9%

Price of the share = Last dividend*(1+constant growth rate)/(Return of equity-constant growth rate) = 1.5*(1+0.05)/(9%-5%) = (1.5*1.05)/4% = $39.375

If interest rate rises by 2%, then market return rises by 2%: market return=16%

Return of equity = risk free rate+[Beta*(Market return-risk free rate) = 4%+[0.5(16%-4%)] = 4%+[0.5*12%] = 4%+6% = 10%

Price of the share = Last dividend*(1+constant growth rate)/(Return of equity-constant growth rate) = 1.5*(1+0.05)/(10%-5%) = (1.5*1.05)/5% = $31.5