An asset has had an arithmetic return of 11.80 percent and a geometric return of

Question

An asset has had an arithmetic return of 11.80 percent and a geometric return of 9.80 percent over the last 84 years. What return would you estimate for this asset over the next 7 years? 22 years? 38 years? (Round your answers to 2 decimal places. (e.g., 32.16))

An asset has had an arithmetic return of 11.80 percent and a geometric return of 9.80 percent over the last 84 years. What return would you estimate for this asset over the next 7 years? 22 years? 38 years? (Round your answers to 2 decimal places. (e.g., 32.16))

Explanation / Answer

As per Blume's formula, if we have N years of data and we wish to forecast over T years,

R(T) = geometric mean * (T-1)/(N-1) + arithmetic mean * (N-T)/(N - 1)

a. N = 84 years

R(7) = 9.8 * 6/83 + 11.80 * (84-7)/83 = 0.708 + 10.947 = 11.65 %

R(22) = 9.8 * 21/83 + 11.80 * (84-22)/83 = 2.4795 + 8.8145= 11.29%

R(38) = 9.8 * 37/83 + 11.80*(84 - 38)/83 = 4.3687 + 6.5397 = 10.91%

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