Answer:
amount to be investment in risky portfolio = $405
amount invest in security x = $243
amount invested in security Y = $162
Explanation:
given data
investing = $1,000
Treasury bills = 5%
optimal weights of X = 60 %
optimal weights of Y = 40 %
expected rate of return x = 14%
expected rate of return y = 10%
solution
we know that
weight return return from risky port
X 60 % 14 % 8.4 %
Y 40 % 10 % 4%
total 12.4 %
so here
return from risky portfolio is = 12.4 %
and
return from risk free investment = 5 %
so 'we consider here investment in risky portfolio = x
so investment in risk free = 1 - x
so we can say that
12.4 % × x + 5 % × (1-x) = 8 %
solve we get
x = 0.405
so investment in risky portfolio = 0.405
so investment in risk free =0.595
and
amount to be investment in risky portfolio = $1000 × 0.405
amount to be investment in risky portfolio = $405
and
amount invest in security x = $405 × 60%
amount invest in security x = $243
and
amount invested in security Y = $405 × 60%
amount invested in security Y = $162
