Compute a 75% Chebychev interval about the mean for x and also for y values. Use the interval to compare two funds. Compute the coefficient of variation for each funds. If standard deviation represents the risk and the mean represents the expected return, then the standard deviation divided by the mean can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.
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!
- Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing the annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index
(60% stock and 40% bond). For the past several years, we have the following data (Reference: Morningstar Research Group, Chicago).
|
x : |
11 |
0 |
36 |
21 |
31 |
23 |
24 |
-11 |
-11 |
-21 |
|
y : |
10 |
-2 |
29 |
14 |
22 |
18 |
14 |
-2 |
-3 |
-10 |
- Compute for the mean and standard deviation for x and y
The mean of x is 10.3 and the SD is 18.831091311977.
The mean of y is 9 and the SD is 12.033287165193.
- Compute a 75% Chebychev interval about the mean for x and also for y values. Use the interval to compare two funds.
Compute the coefficient of variation for each funds. If standard deviation represents the risk and the mean represents the expected return, then the standard deviation divided by the mean can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.
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