## What is the Capital Allocation Line?

Capital allocation line which also refers to the capital market line is the graph that is used to measure the risk related to securities and defines the relationship(the combination of) between risky assets and risk-free assets and it is represented by the line on the graph and it is also known as a reward to variability ratio.

It helps the investor in choosing the right combination of risky and risk-free assets, considering the investor’s risk appetite and identifies the maximum return for that particular level of risk.

- Every investor wishes to earn maximum returns at minimal risk. While constructing their portfolio, every investor is faced with the issue of how much to allocate to the risky and risk-free assets.
- The aim is to optimize the return while keeping the risk at the lowest level.
- The capital allocation line helps investors in determining this allocation percentage.
- It is used to identify the optimal mix of risky and risk-free returns which results in maximum returns at minimal risk.

### Risky and Risk-Free Assets

Risk-free assets are those which do not contain any element of uncertainty as regards its return. It means that the return is guaranteed on those assets without any possibility of default. These assets generally carry a lower rate of interest, given their risk-free nature. Some example of risk-free assets are-

- Treasury Bills;
- Long Term Government Bonds;
- Deposits backed by Government;
- Treasury Notes.

Alternatively, risky assets are those which contain a certain level of uncertainty as regards their return. When the uncertainty i.e the risk is higher, the return promised on these assets is also higher. Some examples of risky assets are –

- Private Equity
- Private Debt Market Instruments;
- Derivatives
- Options
- Real Estate

### Components of Capital Allocation Line

The calculation of capital allocation takes into account the following components–

**Risk of the Portfolio**– The risk of the portfolio would be that of the risky asset in relation to its weight in the portfolio. Risk-free assets, by definition, do not contain any risk and therefore, the risk element would be zero.**Weights of the Assets in the Portfolio**– These are the different percentage mix in which the portfolio may be constructed using the risky and risk-free assets.**Expected Return of the Portfolio**– The expected return of the portfolio is computed taking into account the expected return of both the risky and risk-free assets while considering the volatility (i.e riskiness) of the portfolio.

### How to Calculate Capital Allocation Line?

Let us understand how the formula for the capital allocation line is determined. The return of a portfolio is calculated using the following formula –

**E**

_{p}= E(r_{s}) * w + (1-w) * E(r_{f})where,

- E
_{p }= Expected return of the portfolio - E(r
_{s}) =Expected return of the risky asset - W=Weight of the risky asset in the portfolio
- E(r
_{f}) =Expected return of the risk-free asset

Similarly, the risk of the portfolio is calculated with the following formula –

**σp =σs * ws**

Since the standard deviation (risk quotient) of a risk-free asset is zero, in order to determine the risk of the portfolio, only the risky asset is considered.

Substituting the second formula in the first, we arrive at the following –

**E**

_{p }= r_{f }+ [ E(r_{s}– r_{f})/ σs**] * σp**

This is referred to as the formula for Capital Allocation Line. It can be denoted graphically as below –

The expected return is plotted along the y-axis and the standard deviation (risk) is plotted along the x-axis. The Capital Allocation Line denotes the expected return of a portfolio at varying levels of risk. The excess return received for taking additional risk is referred to as the risk premium – denoted in the graph.

### Advantages Of Capital Allocation Line

- A portfolio allocated optimally based on every investor’s risk appetite and objectives.
- No reliance placed on whims or instincts. rather, the percentages calculated scientifically.
- It helps achieve maximum returns at minimal risk.

### Limitations

- The calculation may not be easily understandable to the normal public. Requires specialization.
- The calculation relies on various information that may not be accessible to all the investors at large.

### Conclusion

A capital allocation line is an important tool for investors in determining their optimal portfolio mix. although its computation mechanism is quite technical, it ensures that returns are maximum for a given level of risk.

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