A stock had returns of 21.70% (1 year ago), 2.40% (2 years ago), X (3 years ago), and ‑14.60% (4 years ago) in each of the past 4 years. Over the past 4 years, the geometric average annual return for the stock was 2.85%. Three years ago, inflation was 3.62% and the risk-free rate was 4.47%. What was the real return for the stock 3 years ago?

The real return for the stock 3 years ago is 1.47

Explanation:

In order to calculate to calculate the real return for the stock 3 years ago we would have to make first the following calculation Using geometric return:

(1+0.0285) = ((1+0.217) * (1+0.024) * (1+X) * (1-0.146)) ^ (1/4)

X = 5.14%

Therefore, to calculate the real return we have to use the following formula:

Real return = ((1+nominal return) / (1+inflation rate) - 1) * 100

Real return = ((1+0.0514) / (1+0.0362) - 1) * 100

Real return = 1.47

The real return for the stock 3 years ago is 1.47