Suppose the rate of return for a particular stock during the past two years was 5 ​% and negative 30 %. Compute the geometric mean rate of return?

geometric return = ⁿ√{(1+r₁) × (1+r₂) × ...} - 1

Where, r = rate of return

n = number of periods

For 1st yr, rate of return = r₁ = 5% = 0.05

For 2nd yr, rate of return = r₂ = -30% = -0.3

Number of years = 2

geometric return = √{(1 + 0.05)(1 - 0.3)}-1= √{(1.05) (0.7)}-1

= -0.143

Geometric return in percent = -14.3%