The Capital Allocation Line (CAL) and the Risk-Free Asset
The common question 'how should I split between stocks and deposits' is elegantly explained by theory as a single straight line. That line is the Capital Allocation Line (CAL).
What Is the CAL?
The Capital Allocation Line (CAL) is the straight line connecting the risk-return combinations created when you mix a risk-free asset (e.g., short-term government bonds) with a risky portfolio in various proportions.
The horizontal axis is risk (standard deviation σ), and the vertical axis is expected return. If you take on no risk at all, you start at the risk-free rate, and as you increase the weight of the risky portfolio, you move up and to the right along the line.
The Slope of the CAL = the Sharpe Ratio
The slope of the CAL is (expected return of the risky portfolio − risk-free rate) ÷ standard deviation of the risky portfolio.
This value is precisely the Sharpe ratio (excess return per unit of risk). In other words, the steeper the CAL, the better the combination, because it delivers 'higher excess return for the same risk.'
So the goal becomes finding, among many risky portfolios, the combination that makes the slope of the CAL (the Sharpe ratio) as large as possible. That point is the tangency portfolio.
The Two-Fund Separation Theorem
Tobin's two-fund separation theorem splits the investment decision into two steps.
Step 1: Among the risky assets, find the 'tangency portfolio' with the highest Sharpe ratio. (This is the same regardless of individual preferences.)
Step 2: How you split between that tangency portfolio and the risk-free asset is decided by your personal risk preference.
The key point is that you can think about 'what to hold' and 'how much risk to take' separately.
If you want to take on more risk, instead of holding the risk-free asset you could even borrow money (leverage) to hold more than 100% of the tangency portfolio. But in that case losses are also amplified, so it is not recommended for beginners.
Preguntas frecuentes
Q. How is the CAL connected to the efficient frontier?
The efficient frontier is a curve made up of risky assets only, while the CAL is a straight line drawn by adding the risk-free asset. The CAL drawn from the risk-free asset so that it is tangent to the efficient frontier is the best combination, and that point of tangency is the tangency portfolio.
Q. Is increasing my cash weight always safe?
Increasing the weight of cash (the risk-free asset) reduces volatility, but if prices rise your real purchasing power can be eroded. 'Safety' should be measured against your goal, not just against nominal losses.
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