Question

The price of a stock is $55 at the beginning of the year and $50 at the end of the year. If the stock paid a $3 dividend and inflation was 3%, what is the real holding-period return for the year?

Answer 1

price of a stock at the beginning of the year =  $55

price of a stock at the end of the year = $50

dividend paid = $3 inflation rate = 3%

We know that:

Holding period return = (dividend income + (price at the year-end - price at beginning of the year)) / price at beginning of the year

Holding period return = ( $3 + ( $50 - $55)) / $55 = ( $3 -$5) / $55 = -$2 / $55 = -0.03636 = -3.6363%

This holding period return is the nominal return we need to adjsut for inflation to get the real rate of return.

According to the The Fisher equation:

1+Nominal rate = (1 + real rate ) * (1 + Inflation rate)

1 + -0.03636 = (1 + real rate ) * ( 1 + 0.03)

0.9636 = (1 + real rate ) * 1.03

1 + real rate = 0.9636 / 1.03 = 0.9355

real rate = 0.9355 - 1 = -0.06446 = -6.446% = -6.45%

The real holding-period return for the year = -6.45%