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# Maths probability question/ Standard deviation HELP! Watch

1. Ms Jones is considering an investment in three different portfolios. The performance of the portfolios depends on market conditions, as is detailed in the following table:

Market Conditions Expected Annual Returns
Portfolio J Portfolio K Portfolio L
Recession 10% 18% 13%
Stable 11% 17% 17%
Boom 18% 15% 18%

It has been estimated that the probability of any year being classified as “recession” is 15%, “stable” is 60%, and “boom” is 25%.

11. What would be the expected annual return if Ms Jones invested one-third of her money in Portfolio J and two-thirds in Portfolio K.

A. 12.6%
B. 14.0%
C. 15.3%
D. 16.7%
E. 18.0%

12. What is the risk of investing in Portfolio L, as measured by standard deviation?

A. 0.46
B. 1.59
C. 2.00
D. 2.53
E. 4.00

2. (Original post by Tony_Soprano1)
Ms Jones is considering an investment in three different portfolios. The performance of the portfolios depends on market conditions, as is detailed in the following table:

Market Conditions Expected Annual Returns
Portfolio J Portfolio K Portfolio L
Recession 10% 18% 13%
Stable 11% 17% 17%
Boom 18% 15% 18%

It has been estimated that the probability of any year being classified as “recession” is 15%, “stable” is 60%, and “boom” is 25%.

11. What would be the expected annual return if Ms Jones invested one-third of her money in Portfolio J and two-thirds in Portfolio K.

A. 12.6%
B. 14.0%
C. 15.3%
D. 16.7%
E. 18.0%
Calculate the average performance of J an K weighting by 1 and 2
for every portfolio, and calculate the average of these values
weighted by the given probabilities.

12. What is the risk of investing in Portfolio L, as measured by standard deviation?

A. 0.46
B. 1.59
C. 2.00
D. 2.53
E. 4.00

First calculate the mean of performance of L. This will be the
average of performance of L in the portfolios weighting
by the given probabilities (for recession, stable etc.)
THe risk will be the square root of the sum of the square of
differences between the performance and the mean value
weighting by the given probabilities (that is the standard deviation)
3. (Original post by ztibor)
Calculate the average performance of J an K weighting by 1 and 2
for every portfolio, and calculate the average of these values
weighted by the given probabilities.

First calculate the mean of performance of L. This will be the
average of performance of L in the portfolios weighting
by the given probabilities (for recession, stable etc.)
THe risk will be the square root of the sum of the square of
differences between the performance and the mean value
weighting by the given probabilities (that is the standard deviation)
thanks for your reply could you possibly run through it as im still quite confused many thanks.
4. (Original post by ztibor)
Calculate the average performance of J an K weighting by 1 and 2
for every portfolio, and calculate the average of these values
weighted by the given probabilities.

First calculate the mean of performance of L. This will be the
average of performance of L in the portfolios weighting
by the given probabilities (for recession, stable etc.)
THe risk will be the square root of the sum of the square of
differences between the performance and the mean value
weighting by the given probabilities (that is the standard deviation)
hello mate could you message me and help on some other questions too many thanks?

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Updated: December 29, 2010
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