NISM 15 Case Study 1: Rohan & Priya (Portfolio Performance Evaluation)

NISM XV Case Study: Portfolio Performance Evaluation

⚠️ Dhaval's Exam Disclaimer & Tips:

Listen carefully: NISM repeatedly asks this exact question. Usually, the names (Rohan, Priya) and the formulas stay exactly the same. Sometime they change the values, sometimes even the values are not changed!

My Guarantee: Just by-heart these 5 case studies I am posting. If you understand the logic and formulas, you will pass. NISM is asking these only!

Scenario: Rohan allocates Rs. 60 lakhs to a portfolio for investment, giving his fund manager a 4-year period to enhance its value. Two years into this, his friend, Priya, remarks that her investments have been performing better than his. Rohan reviews the statistics:

Entity	Annual Return	Std. Deviation	Beta (β)
Rohan's Portfolio	21%	12%	1.1
Priya's Portfolio	24%	16%	1.4
Market Benchmark	16%	11%	1.0

Risk-free Rate (Rf): 6% per annum.

Q1 - Was Rohan's fund manager able to beat the market and what was the extent of that outperformance?

Options:
· Yes, by 3%
· Yes, by 4%
· Yes, by 2.7%
· No, - 6.5%

View Correct Answer & Calculation

Correct Answer: Yes, by 4%

Step 1: Calculate the required return as per CAPM (Capital Asset Pricing Model)
Formula:

Expected Return = Rf + βp * (Rm - Rf)

Calculation:
= 6% + 1.1 * (16% - 6%)
= 6% + 1.1 * 10%
Expected return = 6% + 11% = 17%

Step 2: Jensen's Alpha (Measure of beating the market)
Formula:

Alpha = Actual Portfolio Return - Expected Portfolio Return

Calculation:
= 21% - 17% = 4%

Conclusion: Yes, Rohan's portfolio manager beat the market. Outperformance (Jensen's Alpha) = + 4% per annum.

Q2 - Did Rohan's portfolio perform better than Priya's portfolio when measured against market returns?

Options:
· Yes, by 2.5%
· Yes, by 3.7%
· Yes, by 3%
· No, 0%

View Correct Answer & Calculation

Correct Answer: No, 0%

We already calculated Rohan's Alpha as +4%. Let's calculate Jensen's Alpha for Priya's portfolio:

Priya's Expected Return:
= 6% + 1.4 * (16% - 6%)
= 6% + 14% = 20%

Priya's Alpha:
= 24% (Actual) - 20% (Expected) = 4%

Conclusion: Both portfolios generated the same risk-adjusted outperformance of +4% over the market. Therefore, Rohan's Portfolio did not fare better than Priya's.

Q3 - When evaluating fund performance based on total risk, did Rohan's fund outperform his friend Priya's? If so, what was the margin of outperformance?

Options:
· Yes, by 0.125 points
· Yes, by 1.75 points
· Yes, by 0.338 points
· No, 1.75 points

View Correct Answer & Calculation

Correct Answer: Yes, by 0.125 points

Sharpe Ratio Formula (Total Risk):

Sharpe Ratio = (Portfolio Return - Risk-free Rate) / Portfolio Standard Deviation

Rohan's Sharpe Ratio:
= (21 - 6) / 12 = 15 / 12 = 1.25

Priya's Sharpe Ratio:
= (24 - 6) / 16 = 18 / 16 = 1.125

Margin: 1.25 - 1.125 = 0.125

Conclusion: Rohan's fund outperformed Priya's fund on a total risk basis by 0.125 on the Sharpe ratio scale.

Q4 - Considering the systematic risk of each fund, did Rohan's portfolio outperform his friend Priya's? What is the performance score for Rohan's fund?

Options:
· Yes, 15.62
· Yes, 13.64
· Yes, 8.35
· Yes, 16.18

View Correct Answer & Calculation

Correct Answer: Yes, 13.64

Treynor Ratio Formula (Systematic Risk):

Treynor Ratio = (Portfolio Return - Risk-free Rate) / Beta (β)

Rohan's Treynor Ratio:
= (21% - 6%) / 1.1 = 15% / 1.1 = 13.64%

Priya's Treynor Ratio:
= (24% - 6%) / 1.4 = 18% / 1.4 = 12.86%

Conclusion: Rohan's fund performed better than Priya's fund after accounting for systematic risk. Rohan's score was 13.64%.

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Dhaval Visariya

AMFI Registered Distributor (ARN-327925) | Software Developer & Finance Enthusiast

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