Alpha or Leverage? A Mid-Cap Fund's Performance
The investment committee of a pension fund is reviewing the Arka Mid-Cap Fund. Over the past year the fund returned 16.8% with a standard deviation of 22%. The fund's stated benchmark, the Nifty Midcap 150, returned 13.0% with a standard deviation of 16%. The risk-free rate was 7.0%. The fund's beta to the benchmark was 1.25. The manager claims skill because the fund beat the benchmark by 3.8 percentage points and had a positive Jensen's alpha. The mandate permits a maximum 10% in any single issuer and requires at least 80% in mid-cap stocks. The portfolio report shows 18% in one specialty-chemical stock, 40% in large-cap stocks, and a cash balance of 2%; the rest is mid-cap. The trustee asks whether the outperformance reflects skill, whether the fund complied with its mandate, and how to judge the manager against the benchmark.
1. Compute the Sharpe ratio, Treynor ratio and Jensen's alpha. What do they reveal about whether the 3.8% excess return is skill or leverage?
Read the worked answer
Sharpe = (16.8 − 7)/22 = 0.445; market = (13 − 7)/16 = 0.375. Fund is higher by 0.070. Treynor = (16.8 − 7)/1.25 = 7.84%; market = 6.00%. CAPM required return = 7 + 1.25(13 − 7) = 14.5%. Jensen's alpha = 16.8 − 14.5 = 2.3%.
The 3.8-point raw excess return is not all skill: 1.5 points is compensation for beta of 1.25. The remaining 2.3% is alpha. Positive alpha and higher Sharpe/Treynor suggest some skill, but the residual standard deviation is √(22² − (1.25×16)²) = 9.17%, so the result also contains substantial stock-specific risk. A one-year alpha of 2.3% is not statistically strong without a t-statistic or longer sample.
2. Assess the mandate breaches and explain how they complicate the performance comparison. What should the committee do?
Read the worked answer
Breaches: 18% in one specialty-chemical issuer exceeds the 10% single-issuer limit; mid-cap exposure is 18% + 40% = 58% (if the specialty-chemical stock is mid-cap), below the 80% minimum. Large-cap exposure is 40%, and cash is 2%. These are contractual breaches, not mere style differences. They also weaken the benchmark comparison: a mid-cap benchmark does not match a portfolio with 40% large caps, so the 1.25 beta and the alpha estimate may reflect a different style mix. The 18% position creates idiosyncratic risk that can flatter or distort short-run alpha. The committee should require prompt rebalancing to the mandate, document the breach, and ask for performance attribution against a blended benchmark. It should not rely on the reported alpha until the portfolio is mandate-compliant and the alpha is tested over a longer period.
3. A consultant says the fund's Sharpe ratio proves it is superior and the mandate breaches are irrelevant to performance. Critically evaluate.
Read the worked answer
The consultant is half right. Sharpe is a valid total-risk measure and the fund's 0.445 exceeds the market's 0.375. But Sharpe can be raised in a short sample by concentrated idiosyncratic risk, especially in a 22% standard-deviation portfolio with one 18% holding. The mandate breaches are not irrelevant: they change the fund's risk profile and make the stated benchmark inappropriate. A mandate-compliant fund with the same alpha would be more credible. The committee should treat the Sharpe result as evidence to investigate, not as proof of skill, and should require attribution, compliance remediation, and multi-year significance testing.