Alpha

A Category III AIF that returned 18% in a year when its benchmark returned 17% has not done anything clever. A fund that returned 12% while carrying half the market's risk may have.

Alpha separates those two cases. It starts from a simple question: given how much market risk this fund actually took, what return was it entitled to? Answer that, subtract it from what the fund really delivered, and what remains is the manager's contribution — positive or negative.

The entitlement is computed with CAPM, and the measure of market risk it uses is beta. This page does not re-derive either; it shows what happens when you put them together and read the residue.

Three inputs go in, and the workbook names all three:

• Risk-free rate (Rf) — the return on a T-bill or government security. In the workbook's own illustration this is the 364-day T-bill rate.
• Beta (β) — the fund's volatility against its benchmark. The workbook is explicit that beta here stands for systematic risk: geo-political shifts, macro-economic conditions, market forces the manager cannot control and cannot diversify away.
• Market risk premium (Rm − Rf) — how much the benchmark earned over the risk-free rate. Rm is the benchmark return, not some abstract "market" return, which is why the Benchmarking Agency regime matters to the arithmetic.

The benchmark return must be measured over the same period as the fund return, and the workbook is equally strict about using Net IRR rather than Gross IRR — investors bear the fund's fees and fixed expenses, so the return that belongs in the numerator is the one that actually reaches them.

E(R) = Rf + β × (Rm − Rf)        ← expected return, from CAPM

Alpha (α) = R − E(R)             ← R = return actually achieved (Net IRR)

Positive alpha means the fund beat the return its risk entitled it to. Negative alpha means it did not, however good the headline number looks.

Take Fund XYZ, a Category III AIF with Rs 100 crore of net assets. The workbook runs it through two scenarios:

Best case — what the risk entitled the fund to:

E(R) = 5.60% + 1.30 × (9.25% − 5.60%)
     = 5.60% + 1.30 × 3.65%
     = 5.60% + 4.745%  =  10.35%

Alpha = 12.77% − 10.35% = +2.42%

On Rs 100 crore that is Rs 2.42 crore of return the manager produced — on top of the Rs 10.35 crore the market and the leverage in beta would have produced anyway.

Worst case:

E(R) = 5.60% + 1.50 × 3.65% = 5.60% + 5.475% = 11.08%

Alpha = 3.38% − 11.08% = −7.70%

Minus Rs 7.70 crore. Note what did the damage. The fund still made money — 3.38%, or Rs 3.38 crore. But beta rose from 1.30 to 1.50, so the return it owed the investor rose to 11.08%. It took more systematic risk and delivered less.

The workbook draws the sting itself: expected return went up in the worse year, when intuition says a bad market should lower it. That is a limitation of CAPM, not a feature of the fund.

Alpha runs through four chapters, which is why it is the most examinable single word in the paper. Chapter 3 (Introduction to the Category III AIF Ecosystem) covers alpha management and beta management as the two reasons an institution allocates to a Category III AIF at all. Chapter 6 (Fees Structure, Fund Performance and Benchmarking) carries the CAPM computation above and the worked Fund XYZ example — expect to be handed Net IRR, beta, a T-bill rate and a benchmark return and asked for alpha, or for expected return as an intermediate step. Chapter 7 lists sources of alpha among the factors behind outperformance, and Chapter 2 asks whether Category III AIFs generate alpha in constrained markets. The definitional question — alpha is the excess return over the benchmark / over expected return — is close to guaranteed.

• Alpha is measured against expected return, not against the benchmark return. "Fund returned 12.77%, benchmark returned 9.25%, so alpha is 3.52%" is the wrong answer and it is the distractor the paper offers. Beta has to be paid for first.
• Use Net IRR, not Gross IRR. The workbook makes the assumption explicit: investors ultimately bear the fund's fixed expenses and fees.
• Higher beta lowers alpha, holding return constant. A manager who doubles leverage and doubles returns has generated no alpha at all — see leverage.
• Beta here means systematic risk, the undiversifiable kind. Do not confuse it with standard deviation, which measures total volatility, or with the Sharpe ratio, which divides excess return by total volatility instead of subtracting a risk-adjusted hurdle.
• Periods must match. Annual Net IRR against a 364-day T-bill and a 1-year index. A quarterly fund return against an annual benchmark is a wrong answer dressed as arithmetic.
• Negative alpha is compatible with a profit, and positive alpha with a loss. The sign of alpha and the sign of the return are different questions.