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ACCA PM风险：Expected values and dispersion

文章来源：ACCA全球官网

发布时间：2021-09-03 17:24

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Expected values and dispersion

Using the information regarding the potential outcomes and their associated probabilities,the expected value of the outcome can be calculated simply by multiplying the value associated with each potential outcome by its probability.Referring back to Table 1,regarding the sales forecast,then the expected value of the sales for year one is given by:

Expected value

=($500,000 x 0.1)+($700,000 x 0.2)+($1,000,000 x 0.4)+($1,250,000 x 0.2)+($1,500,000)(0.1)

=$50,000+$140,000+$400,000+$250,000+$150,000

=$990,000【点击免费下载>>>更多ACCA学习相关资料】

In this example,the expected value is very close to the most likely outcome,but this is not necessarily always the case.Moreover,it is likely that the expected value does not correspond to any of the individual potential outcomes.For example,the average score from throwing a dice is(1+2+3+4+5+6)/6 or 3.5,and the average family(in the UK)supposedly has 2.4 children.A further point regarding the use of expected values is that the probabilities are based upon the event occurring repeatedly,whereas,in reality,most events only occur once.

In addition to the expected value,it is also informative to have an idea of the risk or dispersion of the potential actual outcomes around the expected value.The most common measure of dispersion is standard deviation(the square root of the variance),which can be illustrated by the example given in Table 2,concerning the potential returns from two investments.

original (19).gif

To estimate the standard deviation,we must first calculate the expected values of each investment:

Investment A

Expected value=(8%x 0.25)+(10%x 0.5)+(12%x 0.25)=10%

Investment B

Expected value=(5%x 0.25)+(10%x 0.5)+(15%x 0.25)=10%

The calculation of standard deviation proceeds by subtracting the expected value from each of the potential outcomes,then squaring the result and multiplying by the probability.The results are then totalled to yield the variance and,finally,the square root is taken to give the standard deviation,as shown in Table 3.

original (20).gif

original (21).gif

In Table 3,although investments A and B have the same expected return,investment B is shown to be more risky by exhibiting a higher standard deviation.More commonly,the expected returns and standard deviations from investments and projects are both different,but they can still be compared by using the coefficient of variation,which combines the expected return and standard deviation into a single figure.

【ACCA PM知识点：The risks of uncertainty】

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