Financial Risk Manager Part 1

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Explanation:

Since the returns of the two funds are independent and normally distributed, the combined (merged) portfolio has:

The portfolio weights are:

\mu = 0.20 \times 3\% + 0.80 \times 7\% = 0.6\% + 5.6\% = 6.2\%

Because the returns are independent, the portfolio variance is the weighted sum of the individual variances (no covariance term):

\sigma = \sqrt{(0.20)^2 (0.07)^2 + (0.80)^2 (0.15)^2}

= \sqrt{0.04 \times 0.0049 + 0.64 \times 0.0225}

= \sqrt{0.000196 + 0.0144} = \sqrt{0.014596} \approx 0.1208 \approx 12.1\%

We want $P(R > 26\%)$ :

Z = \frac{26\% - 6.2\%}{12.1\%} = \frac{19.8\%}{12.1\%} \approx 1.64

From standard normal tables (or calculator):

P(Z > 1.64) = 1 - P(Z \leq 1.64) \approx 1 - 0.9495 = 0.0505 \approx 5.0\%

Final estimate: ≈ 5.0%

Explanation:

Since the returns of the two funds are independent and normally distributed, the combined (merged) portfolio has:

The portfolio weights are:

\mu = 0.20 \times 3\% + 0.80 \times 7\% = 0.6\% + 5.6\% = 6.2\%

Because the returns are independent, the portfolio variance is the weighted sum of the individual variances (no covariance term):

\sigma = \sqrt{(0.20)^2 (0.07)^2 + (0.80)^2 (0.15)^2}

= \sqrt{0.04 \times 0.0049 + 0.64 \times 0.0225}

= \sqrt{0.000196 + 0.0144} = \sqrt{0.014596} \approx 0.1208 \approx 12.1\%

We want $P(R > 26\%)$ :

Z = \frac{26\% - 6.2\%}{12.1\%} = \frac{19.8\%}{12.1\%} \approx 1.64

From standard normal tables (or calculator):

P(Z > 1.64) = 1 - P(Z \leq 1.64) \approx 1 - 0.9495 = 0.0505 \approx 5.0\%

Final estimate: ≈ 5.0%

Comments (1)

Yash ParwaniMar 3, 2026 4:03 AM

No details on the fund has been provided

LeetQuiz .Mar 3, 2026 4:03 PM

Hi Yash, Sorry for inconvenience. We've retrieved the original question and updated it accordingly. Now the fund information has been provided.

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Last updated: March 3, 2026 at 16:04

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