Question

Are the following statements true or false? Briefly explain your answers.

a)    If the ROE of a company is higher than its discount rate r, it would be in shareholders’      interest to retain earnings in the company.                                      

        (b)    “Duration is a good measure of interest rate risk if change in yield is small and rates change    in a parallel fashion. Satisfying these two assumptions imply that two portfolios with the        same duration will react in exactly the same way to a given change in yield.” True or false?    Briefly explain your answer.  

Answer 1

Answer to (a):

If the Return on Equity(ROE) is more than the Discount rate (r), which means that the return which the company able to generate is more than required rate of return. If the shareholders get the dividend from the company, shareholders can reinvest the dividend at discount rate (r). But the company is able to reinvest the dividend amount and generate a return which higher than the shareholders can generate. So, for shareholders it is recommended to reinvest the return instead of taking dividend.

Answer to (b):

Duration is a good measure of interest rate risk if change in yield is small and rates change    in a parallel fashion. Satisfying these two assumptions imply that two portfolios with the        same duration will react in exactly the same way to a given change in yield

Any investor will show more liking for present consumption rather than future consumption of return. So, If the there is increase in duration of return there will be automatic increase in the required return on investment.

Hence 2 portfolios of same duration will change exactly the same way to a given change in yield.

So, the given statement is true.