Question 6: Let R1 and R, be two random variables representing the unit returns of two assets with the same expected value and variance of and o, respectively. Suppose that R1 and R2 are uncorrelated. LetR= w,R +w,R2 be the return of a portfolio of the two assets in which the portfolio weights satisfy wi + w2 = 1, w, 20 and wz 20 %3D (no short selling). Find the weights which minimize the portfolio variance.
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!
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