a)
Expected Return of Portfolio = Weight of Index Fund * Expected
Return of Index Fund + Weight of Risk-Free Asset * Risk-Free
Rate
X= weight of the index fund, then the weight of the risk-free
asset will be (1-x).
Substituting the given values in the formula:
10% = x *15% + (1-x) * 2.5%
x = 0.6
Therefore, the investor should invest 60% of his funds in the
TSX index fund and the remaining 40% in the risk-free asset.
b)
To calculate the standard deviation of the portfolio from (a), we
can use the following formula:
Standard Deviation of Portfolio = Weight of Index Fund *
Standard Deviation of Index Fund
Substituting the given values in the formula:
Standard Deviation of Portfolio = 0.6 * 20% = 12%
Therefore, the standard deviation of the portfolio is 12%.
c) To find the highest expected return the investor can achieve
with a standard deviation of 30%, we can use the formula for
the expected return of the portfolio from part (a), and solve for
x:
Expected Return of Portfolio = x * 15% + (1-x) * 2.5% = 0.1
Simplifying the equation:
x = (0.1 - 2.5%) / (15% - 2.5%) = 0.5714
Therefore, the investor should invest approximately 57.14% of
his funds in the TSX index fund and the remaining 42.86% in
the risk-free asset to achieve an expected return of 10% with a
standard deviation of 30%. The highest expected return he can
achieve with a standard deviation of 30% is:
Expected Return of Portfolio = 0.5714 * 15% + 0.4286 * 2.5%
= 9.29%