Treynor Ratio for Indian Portfolios

What the Treynor Ratio Measures

Treynor Ratio (invented by Jack Treynor, 1965) gauges how much excess return a portfolio delivers per unit of systematic risk (β). It answers the question:

"For each percentage point of market‐related risk I bear, how much am I paid above the risk-free rate?"

Formula

\boxed{\;T = \dfrac{R_p - R_f}{\beta_p}\;}

Symbol	Meaning
$R_p$	Annualised portfolio return
$R_f$	Risk-free rate (T-bill / repo)
$\beta_p$	Portfolio CAPM beta (relative volatility to market)

Numerator → reward: excess return above risk-free.

Denominator → risk: only non-diversifiable (systematic) risk.

Contrast with Sharpe Ratio, which divides by total volatility ( $\sigma$ ). Treynor fits best when portfolio is well-diversified and unsystematic risk ≈ 0.

CAPM Link

From CAPM (Capital Asset Pricing Model):

\mathbb{E}[R_p] - R_f = \beta_p \bigl(\mathbb{E}[R_m] - R_f\bigr)

If the portfolio lies on the Security-Market Line, its Treynor Ratio equals the market risk premium:

T_{\text{CAPM}} = \mathbb{E}[R_m]-R_f

A higher $T$ implies positive Jensen's Alpha; lower implies under-performance.

Computation in Our Backend

1. Annual returns / β are already produced in compute_custom_metrics.

2. Treynor is stored as:

treynor_ratio = annual_excess / portfolio_beta   # beta from OLS; excess = R_p - R_f

Annual excess return uses 252-day factor.
β comes from daily OLS regression against the chosen benchmark.

Interpreting Values

Treynor Ratio	Interpretation (given same benchmark)
> MRP	Out-performed market on a β-adjusted basis
≈ MRP	In-line with CAPM expectations
< MRP	Under-performed for its level of market risk

MRP = market risk premium = $R_m-R_f$ .

Advantages vs Limitations

Advantages

Ignores diversifiable risk — Ideal for well-diversified funds and assessing systematic risk exposure.
Comparable across funds — Directly compare funds with different total volatility but similar beta exposure.
Theoretical foundation — Aligns with CAPM theory and Security Market Line concepts.
Asset class assessment — More appropriate for evaluating portfolios within a specific asset class.
Manager skill insight — Provides clear view of a manager's ability to generate excess returns per unit of systematic risk.

Limitations

Ignores idiosyncratic risk — Misleading if portfolio holds large non-systematic risk components.
Beta estimation sensitivity — Results highly dependent on beta calculation period and benchmark choice.
Risk asymmetry blindness — Ignores downside vs. upside risk differences that Sharpe & Sortino may capture.
Linear relationship assumption — Beta calculation assumes linear market relationship that may break during extreme conditions.
Backward-looking — Historical beta may not be representative of future systematic risk exposure.
Not ideal for standalone evaluation — Ignores total risk which matters to undiversified investors.

When to prefer Treynor Ratio:

1. Evaluating managers within the same market segment

2. Comparing funds that are components of a broader diversified portfolio

3. When systematic risk is the primary concern for the investor

Practical Use-Cases

Mutual-fund league tables — rank diversified equity funds.
Beta-target sleeves — choose the most efficient manager within a β band (e.g., 0.8–1.2).
Risk budgeting — find strategies that maximise reward per unit of systematic risk rather than per unit of total volatility.

Example

Metric	Fund A	Fund B
Return	12 %	14 %
β	0.8	1.3
$R_f$	5 %	5 %

T_A=\frac{0.12-0.05}{0.8}=0.0875\quad T_B=\frac{0.14-0.05}{1.3}=0.0692

Even though Fund B earns higher raw return, Fund A delivers more reward per unit of β-risk.

References

Treynor, J. L. (1965). "How to Rate Management of Investment Funds." Harvard Business Review, 43(1), 63-75.
Sharpe, W. F. (1966). "Mutual Fund Performance." The Journal of Business, 39(1), 119-138.
Jensen, M. C. (1968). "The Performance of Mutual Funds in the Period 1945-1964." Journal of Finance, 23(2), 389-416.
Bodie, Z., Kane, A., & Marcus, A. J. Investments (12 ed.). McGraw-Hill, 2021 – Ch. 24 (Portfolio Performance Evaluation).

Treynor Ratio

Measuring excess return per unit of systematic risk