What is the 'Capital Allocation Line' (CAL) in portfolio theory?

[ A ]A technical moving average line plotting gold prices.

[ B ]A straight line depicting all possible risk-return combinations created by combining a Risk-Free Asset (e.g., T-Bills) with an optimal Risky Portfolio of assets.[ CORRECT ]

[ C ]A line connecting commercial bank branches across a metropolitan city.

[ D ]A chart showing corporate tax depreciation schedules.

Takeaway

The Capital Allocation Line is the straight line showing every possible risk-return combination obtainable by mixing a risk-free asset with a chosen optimal risky portfolio, in varying proportions.

Derivation

Starting at the risk-free rate on the y-axis (0% risk), an investor can move along the CAL by allocating progressively more capital to the risky portfolio and less to the risk-free asset, increasing both expected return and risk in a straight-line (linear) relationship — the slope of that line is precisely the Sharpe Ratio of the chosen risky portfolio. Investors can even move beyond 100% risky-asset allocation by borrowing at the risk-free rate to lever up their risky exposure, extending the CAL further to the right. This linear risk-return trade-off, and its slope equaling the Sharpe Ratio, is the specific mechanic the exam wants candidates to connect between portfolio theory and performance measurement.

Why the others fail

A — A technical moving average line plotting gold prices.

A gold-price moving average is a technical-analysis charting tool tracking a single commodity's trend.

C — A line connecting commercial bank branches across a metropolitan city.

Bank branch networks describe physical retail infrastructure geography, entirely unconnected to the theoretical risk-return line combining risk-free and risky asset allocations.

D — A chart showing corporate tax depreciation schedules.

Corporate tax depreciation schedules are an accounting/tax concept for asset cost allocation over time, with no relationship to the Capital Allocation Line's risk-return framework.