Home Forums CFA CFA Level 1 Need help! Quantitative Analysis on standard deviation computation

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  • #2134

    Hi,

    I don’t understand the explanation given in the CFA Institute book. I wonder if someone can help solving this problem please?

    An exchange rate has a given expected future value and standard deviation.

    A. Assuming that the exchange rate is normally distributed, what are the probabilities that the exchange rate will be at least 2 or 3 standard deviations away from its mean?

    B. Assume that you do not know the distribution of exchange rates. Use Chebyshev’s inequality (that at least 1 – (1/k)^2 proportion of the observations will be within k standard deviations of the mean for any positive integer k greater than 1) to calculate the maximum probabilities that the exchange rate will be at least 2 or 3 standard deviations away from its mean.

    • This topic was modified 1 year, 6 months ago by  admin.
    • This topic was modified 1 year, 6 months ago by  admin.
    #2143

    admin
    Keymaster

    Since this question comes from quantitative methods section of the curriculum, it is best to answer it from the quantitative methods point of view.

    A. The question has stated that assume that the exchange rate follows a normal distribution. Recall that one of the properties of the normal distribution mentioned in the curriculum is 2 and 3 standard deviations from the mean cover 95% and 99.7% of the area under the curve respectively. Therefore, only with 5% and 0.3% probabilities that the exchange rate is not within 2 and 3 standard deviations away from the mean.

    B. The 95% and 99.7% mentioned above holds true when the distribution is assumed to be normal. In general case, where we do not know the exact distribution, we should use Chebyshev’s inequality. Since the question has provided the Chebyshev’s inequality and the explanation on it, it is just simply putting values into the formula.

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