21. wJ =
.192 - . 54 ×. 19 ×. 50
.542+. 192 - 2 ×.54 ×.19 ×.50
= –.0675; wS = (1 – (–.0675)) = 1.0675
Even though it is possible to mathematically calculate the standard deviation and expected return of
a portfolio with a negative weight, an explicit assumption is that no asset can have a negative weight.
The reason this portfolio has a negative weight in one asset is the relatively high correlation between
> . In this case,
22. Look at
, which is precisely the expression for the
variance on a two–asset portfolio when the correlation is +1.
23. Look at
2+ 2 × x A× xB×σA×σB×(-1)
, which is precisely the expression for
24. From the previous question, with a correlation of –1:
Set this to equal zero and solve for x to get:
This is the weight on the first asset.
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