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The following data represent the probability distribution of the holding period returns for an investment in...

The following data represent the probability distribution of the holding period returns for an investment in Lazy Rapids Kayaks (LARK) stock.

State of the Economy Scenario #(s) Probability, p(s) HPR
Boom 1 0.328 30.00%
Normal growth 2 0.402 9.40%
Recession 3 0.27 -18.30%

a. What is the expected return on LARK? (Round your answer to 2 decimal places.)

Expected return               %

b. What is the standard deviation of the returns on LARK? (Round your answer to 2 decimal places.)

Standard deviation              %

Solutions

Expert Solution

A) Expected return = probability × return

= 0.328 × 30% + 0.402 × 9.40% + 0.27 × (-18.30%)

= 9.84% + 3.78% - 4.94%

= 8.68%

B) Standard deviation= √ probability (return - expected return)^2

= √ 0.328 × (0.30 - 0.0868)^2 + 0.402 (0.0940 - 0.0868)^2 + 0.27 (-0.1830 - 0.0868)^2

= √ 0.328 (0.2132)^2 + 0.402 (0.0072)^2 + 0.27 (-0.2698)^2

= √ 0.328 (0.04545) + 0.402 ( 0.00005184) + 0.27 (0.07279)

= √ 0.01491 + 0.00002084 + 0.01965

= √ 0.034581

= 0.1860 or 18.60%

jeff jeffy answered 2 years ago
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