Mr. A, an investor is contemplating to invest a large lump sum investment and shortlisted two equity managers X and Y, of which the most recent…

CA Final · Advanced Financial Management · MTP · November 2026
Mr. A, an investor is contemplating to invest a large lump sum investment and shortlisted two equity managers X and Y, of which the most recent available performance information is as follows: Manager Year 1 Year 2 Year 3 Covariance with the equity market in Year 3 X 10.90% 5.90% 8.00% 0.82% Y 7.50% 2.50% 10.00% 0.61% The equity market delivered a compounded return of 21.74% over the last 3 years and 7.00% over the last year. For Year 3, the standard deviation of the equity market was 8.50% and the risk-free rate was 2.75%. Required: (i) Evaluate the performance of each manager relative to the benchmark i.e. the equity market over the 3-year period. (ii) Calculate the risk-adjusted performance (both in absolute terms and proportionate terms) of each manager based on the Beta of the portfolio. (iii) Comment on the results of parts (i) and (ii) and suggest additional considerations in selecting an equity manager. Note: Round off calculations upto 2 decimal points.

Suggested Answer and Working Notes:

(i) Performance = (1 + y 1 ) * (1 + y 2 ) * (1 + y 3 ) - 1 Performance of Equity Manager X = (1 + 0.109) * (1 + 0.059) * (1 + 0.08) - 1 = 0.2584 i.e. 25.84% Performance of Equity Manager Y = (1 + 0.075) * (1 + 0.025) * (1 + 0.10) - 1 = 0.2121 i.e. 21.21% Evaluation of performance of Equity Managers Manager Return delivered in last 3 years Benchmark Return Excess Return Performance X 25.84% 21.74% 4.10% Outperformed Y 21.21% 21.74% -0.53% Underperformed (ii) The following are two risk-adjusted performance measures based on the portfolio's beta: Treynor measure (proportional outperformance): T = (Rp - r f ) / βp Jensen measure (absolute outperformance): J = Rp - Rb Rp is the return on the portfolio Rb is the return as per CAPM To calculate both above measures first we shall calculate the beta (β) of the portfolios of both managers as follows: Calculate β where βi = Covariance (Ri, Rm) / Variance (Rm) β X = 0.0082 / (0.085) 2 = 1.13 β Y = 0.0061 / (0.085) 2 = 0.84 Now we shall calculate both measures as follows: Manager Treynor measure Jensen measure X (8.00% - 2.75%) / 1.13 = 4.65 8.00% - [2.75% + 1.13 (7.00% - 2.75%)] = 0.45% Y (10% - 2.75%) / 0.84 = 8.63 10.00% - [2.75% + 0.84 (7.00% - 2.75%)] = 3.68% (iii) Over the last 3 years, X outperformed the market and Y underperformed the market. However, based on the both the Treynor and Jensen measures, Y outperformed X on a risk-adjusted basis, meaning that considering the risk appetite of the two managers, Y took less risk and achieved a better return compared to X.

Topics: Portfolio Management

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