A stock has had returns of 14 percent, 32 percent, 15 percent, −20 percent, 32 percent, and −7 percent over the last six years. what are the arithmetic and geometric returns for the stock? (do not round intermediate calculations. enter your answers as a percent rounded to 2 decimal places,

e. g., 32.16.)

The correct answer is 11% and 9.24%.

Explanation:

According to the scenario, the computation of the given data are as follows:

Arithmetic return=[ r1 + r2 + r3 + r4 + r5 + r6 ] ÷ 6

By putting the value we get,

= [0.14 + 0.32 + 0.15 - 0.20 + 0.32 - 0.07 ] ÷ 6

 =0.66 ÷ 6

=0.11 or 11%

Geometric Return =  [( 1+r1 ) ( 1+r2 ) ( 1 + r3 ) ( 1 + r4 ) ( 1 + r5 )( 1 + r6]^1÷6 -1

By putting the value, we get                                  

=[(1+0.14) (1+0.32) (1+0.15) (1-0.20) (1+0.32) (1-0.07)]^1÷6 -1

=[1.14 × 1.32 × 1.15 × 0.80 × 1.32 × 0.93]^1÷6 -1

=[16.9950]^1÷6 -1

=0.9241 or 9.24%

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