Question

Stock A has a beta of 1.5, the risk-free rate is 4% and the return on the market is 9%. If inflation changes by 3%, by how much will the required return on Stock A change?

Answer 1

Required Rate of Return (Ke) = Rf + Beta * (ERM - Rf)

where, Rf = Risk free rate of return

ERM = Expected Return on Market

Ke = 4% + 1.5 * (9% - 4%)

= 11.5%

Real Risk Free Interest Rate is the single period interest rate if no inflation were expected. However if there is inflation then we need to compute Nominal Risk Free Interest Rate, which is computed by formula as follows :-

Nominal Risk Free Rate = (1 + Real Risk Free Rate) * (1 + Rate of inflation) - 1

= (1 + 0.04) * (1 + 0.03) - 1

= (1.04) * (1.03) - 1

= 7.12%

Ke = Rf + Beta * (ERM - Rf)

= 7.12% + 1.5 * (9% - 7.12%)

= 7.12% + 1.5 * 1.88%

= 7.12% + 2.82%

= 9.94%

Change in Required Rate of Return with change in Inflation = 11.5% - 9.94%

= 1.56%

Hence if inflation changes by 3%, Required Rate of Return changes by 1.56%.