Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the second having μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated, with ρ = −0.8. Denote the expected return and its standard deviation as functions of π by μ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as π varies from 0 to 1. Plot this curve in R.
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!
Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the second
having μ2 = 0.8 and σ2 = 0.12. Suppose that they are
with ρ = −0.8.
Denote the expected return and its standard deviation as
μ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as π
varies from 0 to 1. Plot this curve in R.
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