Question

The standard deviation from investing in the asset is: (Round to the nearset hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.))

Answer 1

Here is the complete question.

State of the Economy Probability of Percentage Returns

the States

Economic recession 25% 5%

Moderate economic growth 55% 10%

Strong economic growth 20% 13%

The standard deviation from investing in the asset is: (Round to the nearest hundredth percent. Answer in the percent format. Do not include % sign in your answer (i.e. If your answer is 4.33%, type 4.33 without a % sign at the end.))

Answer:

standard deviation from investing in the asset is: 2.76

Step-by-step explanation:

From the information given above; the main task to do is to calculate for the standard deviation from investing in the asset ,but in order to do that; we must first determine the expected return value and the variance.

The expected return can either be the profit or loss the investor predict to get after investing on an instrument. It can be determined by multiplying the potential outcomes by the chances of them occurring and then totaling these results.

Here;

the potential outcome = Probability of the States

chances of them occurring = Percentage Returns

∴

Expected return = (0.25 × 5%) + (0.55 × 10%) + (0.20 × 13%)

Expected return = (1.25 + 5.5 + 2.6)%

Expected return = 9.35%

Variance = 0.25 × (5% - 9.35%)² + 0.55 × (10% - 9.35%)² + 0.20 × (13% - 9.35%)²

Variance = 0.25 ( -4.35%)² + 0.55 (0.3575%)² + 0.20 (3.65%)²

Variance = 0.0473 + 0.0023 + 0.0266

Variance = 0.0763

Finally; the standard deviation =
`√(variance)`

standard deviation =
`\sqrt {0.0763`

standard deviation = 0.276

To the nearest hundredth percent and by answering in the percent format without including the % sign ; we have

standard deviation = 2.76