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IBBC CAPITAL ACADEMY / 2027

Capital allocation, beta and performance ratios

Independent IBBC Capital draft content for self-study. Not affiliated with or endorsed by CFA Institute. New lessons await subject-matter review. No CFA designation or official PSM credit is awarded.

Learning goals

  • Explain risk-free combinations using mechanisms and limitations.
  • Explain systematic pricing using mechanisms and limitations.
  • Explain performance diagnostics using mechanisms and limitations.

Draft · approximately 25 minutes, excluding further revision.

Risk-free combinations

Combining a risk-free holding with one risky portfolio creates a capital allocation line whose slope is that portfolio’s Sharpe ratio, under a common borrowing/lending rate.

The capital market line uses the market portfolio and total standard deviation for efficient combinations; the security market line uses beta to price individual systematic exposure.

Systematic pricing

Beta equals covariance with the market divided by market variance; diversifiable residual risk does not earn extra expected return in the CAPM equilibrium.

CAPM assumes a stylized market including common expectations and frictionless opportunities; its expected return is risk-free plus beta times market premium, not a promised realized payoff.

Performance diagnostics

Sharpe divides excess return by total volatility, while Treynor divides by beta; zero or negative denominators require careful interpretation rather than mechanical rankings.

Jensen alpha subtracts CAPM required return from portfolio return; M² rescales risk to benchmark volatility, so neither substitutes for checking mandate fit and measurement period.

Formula and assumptions

Sharpe=(Rp−Rf)/σp; Treynor=(Rp−Rf)/βp; α=Rp−[Rf+βp(Rm−Rf)]

Original applied case: Capital allocation, beta and performance ratios

  1. Portfolio return 11%, risk-free 3%, volatility 16%, beta 1.1; market expected return 9%.
  2. Sharpe=(11−3)/16=0.5; CAPM required=3%+1.1×6%=9.6%.
  3. Jensen alpha=1.4 percentage points; estimation and horizon differences still matter.

Errors to catch

  • Do not assume: CAL slope is the coupon rate of its risky assets.
  • Do not assume: The SML uses total volatility on its horizontal axis.
  • Do not assume: Beta equals market variance divided by covariance.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.