Risk and Standard Deviation Conceptual Overview: Explore how standard deviation

Question

Risk and Standard Deviation

Conceptual Overview: Explore how standard deviation measures the risk of an investment.

For both U.S. Water (blue curve) and Martin Products (red curve) the expected return is 10%. However, the spread of possible outcomes for U.S. Water is "tighter" (i.e., closer to the expected return of 10%) than the spread for Martin Products. The depicted distributions are both normal distributions, but with different standard deviations. Use the slider at the bottom to change the standard deviation for the distribution of outcomes for Martin Products. Drag the vertical dashed line on the graph to the left or right to observe the probability of exceeding a particular rate of return.

-20-15-10-50510152025303540P(Water > 0.0) = 1.00P(Martin > 0.0) = 0.84

Martin Products Standard Deviation:

246810sd = 10

1. As the standard deviation for Martin Products' distribution increases, the distribution for Martin Products:

becomes steeper and more like the distribution for U.S. Water

does not change

becomes flatter and less like the distribution for U.S. Water

might either become steeper or flatter

-Select-abcdItem 1

2. Use the slider to set the standard deviation for Martin Products to be 6.0. The probability of having a rate of return of at least 5% (move the cursor to 5.0)

is greater for U.S. Water than for Martin Products

is the same for both U.S. Water and the Martin Products distribution

is greater for Martin Products than U.S. Water

cannot be determined

-Select-abcdItem 2

3. Use the slider to set the standard deviation for the Martin Products distribution to 8.0. The probability of having a rate of return of at least 10% (move the vertical line to 10.0)

is greater for U.S. Water than for Martin Products

is the same for both U.S. Water and the Martin Products distribution

is greater for Martin Products than U.S. Water

cannot be determined

-Select-abcdItem 3

4. Suppose the standard deviation for the Martin Products Distribution is 4.0. If an investor is hoping for a return of at least 13%, the chances that investing in Martin Products will return at least 13%

are much less than in investing in U.S. Water

are the same as investing in U.S. Water

are greater than in investing in U.S. Water

cannot be determined

-Select-abcdItem 4

5. As the standard deviation of outcomes for Martin Products increases, investing in Martin Products becomes riskier because

the range of outcomes having some probability becomes wider

an outcome at or near the expected return of 10% becomes less likely

although the chances of some big gains increase, the chances for some big losses also increase.

all of the above reasons

none of the above reasons

-Select-abcdeItem 5

Explanation / Answer

The answers are:

1. (c) Becomes flatter and less like the distribution for U.S Water

to get the logic behind this you can think that as the standard deviation increases the variability in the data values also increases so there will be more number of observation located far from the mean. This reduces the steepness of the curve and it becomes flatter.

2. (a) Is greater for U.S Water than for Martin Products- if standard deviation of U.S Water is less than 6

   (b)Is greater for Martin Products than U.S. Water- if the standardd deviation of U.S Waters is more than 6

I cannot see the graph so depending on the Standard deviation of U.S Water the answer will change.

3.(b)Is the same for both U.S. Water and the Martin Products distribution

This is because the the expected value of both the stocks is 10% so irrespective of the standard deviation of the two stocks the probability of being atleast 10% i.e the probability of the returns being 10% or more is 0.5 for both the stocks. This is a property of normal distribution which says that the probability of the random variable taking a value less than the mean or greater than the mean is equal i.e 0.5.

4.Again here is the same logic as used in two i.e (a) Are much less than investing in U.S Wate- if standard deviation of U.S Water is less than 4

   (c)Are greater than investing in U.S. Water- if the standard deviation of U.S Waters is more than 4

*I cannot see the graph so see and infer accordingly.

5.(d) all of the above reasons i.e a. the range of outcomes having some probability becomes wider. b. Am outcome at or near the expected return of 10% becomes less likely c.Although the chances of some big gains increase, the chances for some big losses also increase. Thus, overall investing in Martin Products becomes riskier. These are the logical consequences as with the increase in standard deviation the variability in the data set i.e the outcomes increases or the returns become more volatile.

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