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Suppose two assets A & B are uncorrelated, with standard deviation of returns equal to σ each.
a) What is the standard deviation of an equally-weighted portfolio invested in A and B?
b) If we keep adding more uncorrelated assets, then what value will the portfolio standard deviation converge to? Motivate your answer.
Now suppose A and B are both exposed to factor X but otherwise uncorrelated. Factor X has a standard deviation equal to σX = 0.3; the loading of A on X is βA = 1.5; the loading of B on X is βB = 0.8. The standard deviation of A and B equals σ = 0.6.
c) What is the standard deviation of an equal-weighted portfolio invested in A and B?
d) If we keep adding assets to our portfolio that are also exposed to X but otherwise uncorrelated and with an average loading to X equal to 1, then what value will the portfolio standard deviation converge to? Motivate your answer.
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