The Knowles/Armitage (KA) group at Merrill Lynch advises clients on how to create a diversified investment portfolio. One of the investment alternatives they make available to clients is the All World Fund composed of global stocks with good dividend yields. One of their clients is interested in a portfolio consisting of investment in the All World Fund and a treasury bond fund. The expected percent return of an investment in the All World Fund is 6.30% with a standard deviation of 17.40% . The expected percent return of an investment in a treasury bond fund is 6.00% and the standard deviation is 4.50%. The covariance of an investment in the All World Fund with an investment in a treasury bond fund is -11.2. a. Which of the funds would be considered the more risky? Why? b. If KA recommends that the client invest 75% in the All World Fund and 25% in the treasury bond fund, what is the expected percent return (to 3 decimals) and standard deviation (to 3 decimals) for such a portfolio? What would be the expected return and standard deviation, in dollars, for a client investing $10,000 in such a portfolio? (both to the nearest cent) c. If KA recommends that the client invest 25% in the All World Fund and 75% in the treasury bond fund, what is the expected return and standard deviation for such a portfolio? (both to 3 decimals)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The Knowles/Armitage (KA) group at Merrill Lynch advises clients on how to create a diversified investment portfolio. One of the investment alternatives they make available to clients is the All World Fund composed of global stocks with good dividend yields. One of their clients is interested in a portfolio consisting of investment in the All World Fund and a treasury bond fund. The expected percent return of an investment in the All World Fund is 6.30% with a standard deviation of 17.40% . The expected percent return of an investment in a treasury bond fund is 6.00% and the standard deviation is 4.50%. The
a. Which of the funds would be considered the more risky?
Why?
b. If KA recommends that the client invest 75% in the All World Fund and 25% in the treasury bond fund, what is the expected percent return (to 3 decimals) and standard deviation (to 3 decimals) for such a portfolio?
What would be the expected return and standard deviation, in dollars, for a client investing $10,000 in such a portfolio? (both to the nearest cent)
c. If KA recommends that the client invest 25% in the All World Fund and 75% in the treasury bond fund, what is the expected return and standard deviation for such a portfolio? (both to 3 decimals)
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