An asset has had an arithmetic return of 11.30 percent and a geometric return of

Question

An asset has had an arithmetic return of 11.30 percent and a geometric return of 9.30 percent over the last 74 years. What return would you estimate for this asset over the next 12 years? 17 years? 33 years?

An asset has had an arithmetic return of 11.30 percent and a geometric return of 9.30 percent over the last 74 years. What return would you estimate for this asset over the next 12 years? 17 years? 33 years? (Round your answers to 2 decimal places. (e.g., 32.16)) Future annual returns 12 years 17 years 33 years

Explanation / Answer

To solve this question, we have to apply Blume's formula which is as follows:

R(T) = (T-1/N-1 x G.M) + (N-T/N-1 x A.M); where T = Forecast horizon; N= No.of years of historical data we are working with i.e in the given problem 74 years. Substituting this formula, we can get answers

a. Return for next 12 years = R(12) = (12-1/74-1 x 9.30) + (74 - 12/74 -1 x 11.3)

                                                        = (0.15 x 9.30) + (0.85 x 11.3)

                                                        = 1.40 + 9.61 = 11.01%

b. Return for next 17 years = R(17) = (17-1/74-1 x 9.30) + (74-17/74-1 x 11.3)

                                                        = (0.22 x 9.30) + (0.78 x 11.3)

                                                        = 2.04 + 8.81 = 10.85%

c. Return for next 33 years = R(33) = (33 -1/74 - 1 x 9.3) + (74 - 33/74-1 x 11.3)

                                                        = (0.44 x 9.3) + (0.56 x 11.3)

                                                         = 4.09 + 6.33 = 10.42%

Note: T must be less then N

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