Net selectivity

A fund manager can beat the market by two very different routes. He can pick better shares. Or he can simply take more risk and let a rising market do the work.

Net selectivity is built to separate the two. It is described as an absolute measure, so the answer comes out as a return, not a ratio.

It starts with the fund's return for the year and takes away what a risk-free investment would have paid. That leaves the excess return.

Then it takes away something else: the reward the market itself would have given for carrying that much risk. The bigger the risk the fund took, the bigger this deduction.

What is left is the part of the return that the market could not have handed over. In the workbook's words, it shows the excess return earned by the fund manager that cannot have been earned by investing in the market portfolio. That residue is the manager's stock selection, with the luck of a rising market stripped out.

Section 16.6.4 gives the definition in words, not symbols. The Net selectivity measure of Fama is an absolute measure of performance. It is calculated as:

1. The annualised return of the fund, less
2. the yield of a risk free investment; this figure is then
3. reduced by the standardised expected market premium times the total risk of the portfolio under review.

It shows the excess return earned by the fund manager that cannot have been earned by investing in the market portfolio.

Unpack the third step, because that is where the measure does its work. The standardised expected market premium is the market's excess return per unit of risk — the market return minus the risk-free rate, divided by the market's standard deviation. Multiplying it by the total risk of the portfolio gives the return the portfolio should have earned purely for the risk it carried. Anything above that is selection.

Total risk, not systematic risk. The workbook says total risk of the portfolio under review, which section 16.3.1 defines as measured by standard deviation. That is what separates this from beta-based measures.

Where it sits in the chapter. Section 16.6.3 sets up the question net selectivity answers. Market timing is the manager's ability to anticipate market developments; selectivity is the ability to select securities that will generate extra returns. The workbook reports the evidence: most studies have shown that market timing is not the factor resulting in better performance, while the results are mixed on the selectivity front, with some having this ability.

The workbook gives no worked example and no figures for net selectivity. Section 16.6.4 is three sentences of definition with no numbers at all — unlike the Sharpe, Treynor and M2 sections, each of which carries the workbook's own arithmetic. Any figures below are therefore illustrative, built on the workbook's stated definition.

Net selectivity = (Fund return − Risk-free rate)
                  − [ Standardised expected market premium x Total risk of the portfolio ]

where
  Standardised expected market premium = (Market return − Risk-free rate)
                                         ÷ Market standard deviation
  Total risk of the portfolio          = its standard deviation

Illustrative figures, built on the workbook's definition — section 16.6.4 gives none of its own.

Assume for a financial year: risk-free rate 6%, Nifty 50 return 14%, Nifty standard deviation 20%.

Standardised expected market premium = (14 − 6) ÷ 20 = 0.40 per unit of risk.

Two funds, both of which beat the index:

Both funds returned 18% against the index's 14%. On a Rs 20,00,000 investment both handed the client Rs 3,60,000.

But Yamuna took 34% volatility to do it. At the market's own price for risk, that much risk should have produced 13.6% above the risk-free rate, and the fund delivered 12%. Its selection added nothing; it fell 1.6% short of what the risk alone was worth. Ganga carried 22% volatility, needed 8.8%, and delivered 12% — 3.2% of genuine selection, about Rs 64,000 on the same Rs 20,00,000.

The raw returns were identical. Only one of the two managers picked stocks well.

Chapter 16 (Portfolio Performance Measurement and Evaluation), section 16.6.4, immediately after market timing versus selectivity at 16.6.3. Because the workbook gives no arithmetic here, questions are conceptual: what net selectivity measures, that it is an absolute measure, that it deducts the market premium for the portfolio's total risk, and what the residue represents.

• It is an absolute measure, not a ratio. The answer is a return, like the M-squared measure, not a number like Sharpe.
• It uses total risk, not beta. Total risk is the portfolio's standard deviation. The beta-based comparison is the Treynor ratio.
• Two deductions, in order. First the risk-free yield, then the market premium for the risk carried. Stopping after the first gives the plain excess return.
• Beating the index is not net selectivity. A fund can beat the index and still be negative here, if it did so by taking more risk than the market.
• Selectivity is not market timing. Section 16.6.3 keeps them apart, and reports that studies find market timing does not drive better performance while selectivity results are mixed.
• The workbook gives no figures in this section. Do not carry the 35%, 28%, 6%, 42% and 30% of section 16.4.6 into a net selectivity answer; those belong to M2.